Mare means sea. Early telescopic observers, including Galileo (1564--1642)???, speculated that the dark, smoother areas were bodies of water and gave them water-body names. It was only in the early 19th century that it was finally established to everyone's satisfaction that the Moon had no bodies of water (see Wikipedia: Exploration of the Moon: Early history).
Can you see the Leaping Moon Rabbit? Yes / No / Maybe?
It's a lunar pareidolia.
Various cultures in pre-telescopic times identified several different lunar pareidolia on the near side of the Moon.
The most common were the Man in the Moon (i.e., a man's face in profile) probably mostly in Europe and the Moon Rabbit in parts of Asia. Actually, the Man in the Moon looks to me more like the Wolf in the Moon.
One lunar pareidolia that Wikipedia fails to discuss (see Wikipedia: Lunar pareidolia), but the cutest of all to yours truly is the Leaping Moon Rabbit:
Actually, there are two Moon rabbits: the Leaping Moon Rabbit and just aforementioned just plain Moon Rabbit---I call them Bugs and Peter.
Some cultures see one or other of the Moon rabbits.
Yours truly has noticed that the lunar features are most easily seen by the naked eye when the nearly full moon is up in the daytime. At nighttime, the high contrast between dark night sky and the glaring full moon makes seeing the features difficult. The lower contrast between blue sky and Moon in the daytime makes the lunar features clearer. Yours truly can almost make out the Leaping Moon Rabbit in the daytime. A person with sharper vision might see the Leaping Moon Rabbit quite well.
File: Moon afar file: lunar_pareidolia.html.
Caption: "Description: Southward looking oblique view of Mare Imbrium and Crater Copernicus on the Moon. Copernicus is seen almost edge-on near the horizon at the center. The crater is 107 km in diameter and is centered at 9.7 N, 20.1 W. In the foreground is Mare Imbrium, peppered with secondary craters chains and elongated secondary craters due to the Copernicus impact. The large crater near the center of the image is the 20 km diameter Crater Pytheas, at 20.5 N, 20.6 W. At the upper edge of the Mare Imbrium are the Montes Carpatus. The distance from the lower edge of the frame to the center of Copernicus is about 400 km. This picture was taken by the metric camera on Apollo 17, 1972 (Apollo 17, AS-2444)." (Slightly edited.)
Copernicus has a rim diameter of about 90 km and is one of the largest craters on the Moon.
The Copernicus impactor must have been a few kilometers in diameter (HI-141).
Copernicus is a peaked crater and a terraced crater.
Credit/Permission: NASA,
1972
(uploaded to Wikipedia
by User:Srbauer,
2004) /
Public domain.
Image link: Wikipedia:
File:Mare Imbrium-AS17-M-2444.jpg.
Local file: local link: mare_imbrium.html.
File: Moon: Moonscape file:
mare_imbrium.html.
For the modern version see the video KAGUYA taking "Full Earth-rise" by HDTV, 2008apr05 | 1:15.
It's a long road home.
So Selenites would always see the Earth at an approximately fixed point in the sky relative to the surface: i.e., at approximately fixed horizontal coordinates. There would be a little motion due to lunar libration.
Thus, earthrise could only be seen from an orbiting spacecraft.
Kepler's 3rd law applied to the Moon is
where the gravitational constant G=6.67384*10**(-11) in MKS units, r = 1737.10 km is the mean lunar radius, and M = 7.3477*10**22 kg is the lunar mass (see Wikipedia: Moon).
So one can see that relatively low lunar orbits should be ∼ 2 hours.
Caption: The full moon over "Westensee by night. Taken in Felde, Schleswig-Holstein, Germany."
It's a Caspar David Friedrich (1774--1840) brought to life:
Credit/Permission: ©
Andreas Eichler (AKA User:Hockei),
2016 /
Creative Commons
CC BY-SA 4.0.
Image link: Wikimedia Commons:
File:2016.07.18.-65-Westensee bei Nacht Felde.jpg.
Local file: local link: moon_full_westensee.html.
File: Moon afar file:
moon_full_westensee.html.
Moonlight at or near full moon is a significant source of light.
The painter was an ancestor---the great great grandfather of Sherlock Holmes (see Wikipedia: Claude Joseph Vernet: Literary references).
Credit/Permission: Claude Joseph Vernet (1714--1789),
1771
(uploaded to Wikimedia Commons
by User:JarektUploadBot,
2011) /
Public domain.
Image link: Wikimedia Commons:
File:Joseph Vernet - Night - Seaport by Moonlight - WGA24731.jpg.
Local file: local link: moonlight_vernet.html.
File: Art_m file:
moonlight_vernet.html.
So old astronomy mostly, but with a few new astronomy touches.
The new astronomy, which is mostly lunar geology and lunar geological history, we mostly leave to IAL 12: The Moon and Mercury.
And what of the old Moon?
As the Sun is KING of the day, the Moon has always been QUEEN of the night---or vice versa depending on whose culture is counting. Of course, the Moon is often seen in the day.
Anyhow, they have always been with us and for long ages there seemed to be great a symmetry of the universe that their angular diameter were almost the equal: i.e., Sun angular diameter: mean 0.5332°, range 0.5242°--0.5422°; Moon angular diameter: mean 0.5286°, range 0.4889°--0.5683°. But this near equality is just the great coincidence: see Moon file: sun_moon_angular.html.
The figure below (local link / general link: wolf_norse.html) illustrates the Sun and Moon in Norse mythology.
Caption: "The Wolves Pursuing Sol and Mani (the title given to the work in the list of illustrations on page vii of the source)." (Slightly edited.)
In Norse mythology, Sun goddess Sol is pursued by the wolf Skoell and Moon god Mani is pursued by the wolf Hati Hrothvitnisson.
Skoell and Hati Hrothvitnisson are evidently invisible.
Credit/Permission: John Charles Dollman (1851--1934) in
H. A. Guerber's (1859--1929)
Myths of
the Norsemen from the Eddas and Sagas (1909),
1909,
London George G. Harrap and Co.
(uploaded to Wikipedia by
Haukur Thorgeirsson (AKA User:Haukurth),
2008) /
Public domain.
Image link: Wikipedia:
File:The Wolves Pursuing Sol and Mani.jpg.
Local file: local link: wolf_norse.html.
File: Art_w file:
wolf_norse.html.
Caption: "Artemis with a hind, better known as 'Diana of Versailles'. Marble, Roman sculpture, Imperial Era (1st--2nd century CE). Found in Italy." Possibly a copy of a Greek statue by Leochares (4th century BCE).
Artemis (equated to the Roman goddess Diana) was the mythical Greek Moon goddess, the twin sister of Apollo, the mythical Greek Sun god.
Artemis is the eponym of the Artemis program (2017--), NASA's 2nd big program of exploration of the Moon---the follow-up to the Apollo program (1961--1972).
To return to the statue, as yours truly knows from his days in Tennessee, deer are still hunted by the light of the Moon.
Credit/Permission: Marie-Lan Nguyen (AKA User:Jastrow),
2005 /
Public domain.
Image link: Wikipedia:
File:Diane de Versailles Leochares.jpg.
Local file: local link: artemis.html.
File: Art_a file:
artemis.html.
Of course, other traditional problems come with a full moon (see figure below: local link / general link: alien_werewolf.html).
Credit/Permission: ©
David Jeffery,
2003 / Own work.
Image link: Itself.
Local file: local link: alien_werewolf.html.
File: Alien images file:
alien_werewolf.html.
Caption: "Geraldine Ulmar (1862--1932) in The Mikado, 1885". An object of "modified rapture".
The Mikado is an operetta by W.S. Gilbert (1836--1911) and Arthur Sullivan (1842--1900).
The image is proof that some folks have always found a happy Moon---and then they sing of the Moon (see videos below: (local link / general link: moon_song_videos.html).
Caption: "A screenshot from Le Voyage dans la lune (A Trip to the Moon) (1902)." (Slightly edited.)
An early moonshot: literally a shot at the Moon.
See the video: Le voyage dans la Lune, Georges Melies (1861--1938), 1902 | 8:24: Where scifi films began---from here to 2001: A Space Odyssey (1968) and Blade Runner (1982).
The film seems to be a loose combination of Jules Verne's (1828--1905) From the Earth to the Moon (1865), H. G. Wells' (1866--1946) The First Men in the Moon (1901), and the Folies Bergere (1869--).
Credit/Permission:
Georges Melies (1861--1938),
an early French
filmmaker,
1902
(uploaded to Wikipedia
by Magnus Manske,
2008) /
Public domain.
Image link: Wikipedia:
File:Le Voyage dans la lune.jpg.
Local file: local link: georges_melies_moon.html.
File: Art_g file:
georges_melies_moon.html.
Caption: "A moonbase concept drawing from NASA." (Slightly edited.)
The ideas of moonbases and lunar colonization have been with us for a long time, but might realized sometime in the 21st century---maybe "Moonbase 2100"---but they will probably be robotic since low gravity is NOT a healthy environment for humans (see Wikipedia: Weightlessness: Human health effects)---and who'd want to live on the Moon for more than a lunar month = 29.530588861 days (J2000).
Features:
In fact, the Moon setting the lunar months and even more fundamentally the Sun setting the daytime and the nighttime and the seaonal solar year, are natural clocks for the children of the Earth.
In fact, the use of the lunar month (about 29.5 days) both for secular TIME-KEEPING and RELIGIOUS OBSERVANCES goes back to prehistory in many ancient societies---probably in all societies in prehistory.
The lunar month is NOT, of course, the modern calendar month of the modern civil calendar: the calendar month is divorced from the lunar month only retaining the family name month---this divorce began with the Julian calendar (see subsection Julius Caesar Reforms the Calendar below).
The lunar month is illustrated in the two figures below (local link / general link: moon_lunar_phases.html; local link / general link: moon_lunar_phases_animation_2.html).
Caption: A diagram illustrating the lunar phases (i.e., the phases of the Moon) over the course of a lunar month = 29.530588861 days (mean J2000) ≅ 29.53059 days (mean J2000 to 7 digits) ≅ 29.5 days.
Features:
And one also has the abbreviated expressions:
The mean lunar month---the cruellest month---is, in fact, 29.53059 days (7-digit J2000.0 value). We usually round this value off 29.5 days when NOT being precise.
The value 29.53059 days is the 7-digit J2000.0 epoch value and is a good fiducial value for years 1900--2100.
A lunisolar calendars is one that uses lunar month and solar year directly as natural timekeeping devices.
At least in western Eurasian cultures, lunisolar calendars were common before the Julian calendar reform (46--45 BCE).
But there is a calendrical problem using the natural timekeeping devices.
First, (mean) lunar month is NOT an integer number of days (nor weeks), nor is the solar year an integer number of lunar months.
More specifically, the lunar year = 354.36706633 days (J2000) (which is 12 lunar months each = 29.530588861 days (J2000)) and the solar year = 365.2421897 days (J2000).
So the discrepancy between the day count for lunar years consisting of 12 lunar months and the day count for solar years increases by ∼ 11 days per solar year.
How did they do this?
Well, after 3 solar years, the discrepancy is ∼ 33 days or a bit more than a lunar month.
So to keep the count of years about the same for both lunar years and solar years on average, a 13th lunar month (an intercalary month) had to be inserted into a calendar year a bit more frequently than every 3 years.
The intercalary month insertion was usually pretty haphazard and done at different times in different jurisdictions (i.e., cities or states).
Often when the "year was NOT good" (i.e., season and lunar month disagreed: it was winter, but the month was Maius), some local official decided on an intercalary month insertion.
The result of the haphazard procedures for intercalary month insertion was calendrical chaos and it is often hard for modern historians to determine exact dates for events in ancient history or to correlate such events.
For a facetious example, see the figure below (local link / general link: druids.html).
Caption: Two Druids in an 1719 engraving that was copied from a bas-relief found at Autun, France.
This an imaginative portrait of Druids---nevertheless maybe it's NOT so far from the truth, mutatis mutandis.
Perhaps they are debating whether or NOT to insert an intercalary month in their lunisolar calendar---if the Celts had that---the one on the left is holding a crescent moon---or is it a banana:
Credit/Permission: Anonymous artist,
before 1719
(uploaded to Wikimedia Commons
by User:Nyo,
2007) /
Public domain.
Image link: Wikimedia Commons:
File:Two Druids.PNG.
Local file: local link: druids.html.
File: Art file:
druids.html.
Can something be done rather than rely haphazard intercalary month insertion?
Yes. One rather accurate/precise of inserting intercalary month is the 19-year Metonic cycle: see the figure below (local link / general link: metonic_cycle_girl_with_doves.html).
Image 1 Caption: Girl with Doves (c. 440--450 BCE). An artwork of ancient Greek sculpure from the lifetime of Meton of Athens (late 5th century BCE). For a better image, see girl_with_doves.html.
If you ever doubted that the ancient Greeks had ordinary family feeling, their grave steles set your mind at rest.
But from sculpture to astronomy to disgress:
Features:
Explication of the 19-years Metonic cycle:
The Metonic cycle was known in China by an independent discovery and perhaps earlier than in western Eurasia (Britannica: Chinese calendar; but Wikipedia: Metonic cycle: Application in traditional calendars NO longer reports this).
Then came Caesar and his calendar reform of 46--45 BCE. It did away with the lunisolar calendar and banished lunar months and replaced them with the 12 semi-arbitrary modern calendar months.
Of course, only people in western Eurasia knew about the Julian calendar (instituded 46--45 BCE) and its upgrade to the Gregorian calendar (instituded 1582) until in modern times. The Gregorian calendar is, of course, the modern de facto international civil calendar.
For further explication of the Julian calendar and Gregorian calendar, see the figures below (local link / general link: julius_caesar_tusculum_like.html; local link / general link: alien_julius_caesar.html).
Caption: Bust/statue of Julius Caesar (100--44 BCE)---Old Gaius.
Features:
Yours truly always liked Old Gaius' hairstyle---with it, he wandered the world---and with it, he wooed Cleopatra VII (69--30 BCE).
The resulting average year is Julian year = 365.25 days exactly by definition which, indeed, approximates to good accuracy/precision the solar year = 365.2421897 days (J2000).
By the 16th century, the discrepancy amounted to ∼ 11 days from the time of year 1 CE or 10 days from the Council of Nicaea (325 CE) (see Wikipedia: Gregorian calendar: Adoption). This meant, for example, that the vernal equinox was occuring circa Mar10 rather than ∼ Mar21 where it occurred circa year 1 CE. If this disacrepancy had been allowed to continue for millennia, eventually the vernal equinox would happen on Dec25.
Something had to be done.
Caption: Les Tres Riches Heures du Duc de Berry, Juillet (i.e., July), Musee Conde, Chateau de Chantilly. The Palace of Poitiers is in the background.
The month is July as lunette shows.
July was named for Julius Caesar (100--44 BCE)---fair enough since he instituted the Julian calendar in 46--45 BCE.
Credit/Permission: Brothers Limbourg (fl. 1385--1416)
for their patron
Jean, Duc de Berry (1340--1416),
1412--1416,
source/photographer: R.M.N./R.-G. Ojeda
(uploaded to Wikipedia
by User:Petrusbarbygere,
2005) /
Public domain.
Image link: Wikipedia: File:Les Tres Riches Heures du duc de Berry juillet.jpg.
Local file: local link: tres_riche_heures_07_july.html.
File: Art_t file:
tres_riche_heures_07_july.html.
Credit/Permission:
Anonymous
Roman sculptor?,
circa 1st century BCE?,
Anonymous photographer/Alfred von Domaszewski (1856--1927),
1914
(uploaded to
Wikimedia Commons
by User:Pablo000,
2008) /
CC BY-SA 3.0.
Image link: Wikimedia Commons:
File:Caesar.jpg.
Local file: local link: julius_caesar_tusculum_like.html.
File: Art_j file:
julius_caesar_tusculum_like.html.
The Assassination of Julius Caesar on 44 BC Mar15 (AKA the Ides of March) was NOT a consequence of the imposition of the Julian calendar.
But it is true that people do tend to be become irate when longstanding conventions are eliminated no matter how inefficient or klutzy they may be---this is why we still use the Fahrenheit scale.
Credit/Permission: ©
David Jeffery,
2003 / Own work.
Image link: Itself.
Local file: local link: alien_julius_caesar.html.
File: Alien images file:
alien_julius_caesar.html.
Where does the seven-day week come from?
How how does the mighty Thor come in to it?
For Thor, see the figure below (local link / general link: thor.html).
Caption: The Norse god Thor's Battle Against the Jotuns.
He wields mightily his thunder hammer Mjolnir and is riding in his chariot drawn by his goats Tanngrisnir and Tanngnjoestr.
We havn't forgotten old Thor---he has his Mighty Thor comic book series and then there's a whole day named after him: Thursday.
And as we say at University of Nevada, Las Vegas, TGIR.
Credit/Permission: Marten Eskil Winge (1825--1896),
1872
(uploaded to Wikipedia
by User:DcoetzeeBot,
2012) /
Public domain.
Image link: Wikipedia:
File:Marten Eskil Winge - Tor's Fight with the Giants - Google Art Project.jpg.
Local file: local link: thor.html.
File: Art_t file:
thor.html.
The first 3 weeks had 7 days and the last week had to be adjusted to make up the lunar month which observationally varies and has mean length 29.53059 days (7-digit J2000.0 value).
It seems likely that they chose 7 days as their fiducial week length because 7 days is approximately a quarter of the lunar month. Note
This idea for the seven-day week is NOT absolutely proven, but it seems the best hypothesis to yours truly.
The seven-day week then spread to other cultures in the ancient Near East.
The ancient Romans seem to have independently arrived at the seven-day week (see Wikipedia: Seven-day week: Classical Antiquity) about the time of the adoption of the Julian calendar. Earlier they used an 8-day week. Their reasons for either week are NOT explained in the sources.
Perhaps, the work-market-day-rest cycle of 7 or 8 days is just natural for humans and societies (see figure below). The fact that the quarters of the lunar month roughly correspond to 7 or 8 days may have just been a useful coincidence for the ancient Babylonians, the ancient Romans, and other ancient societies.
The merger of the cultures of the ancient Near East and Classical Antiquity with the spread of early Christianity clearly acted to stabilize the seven-day week as the norm in Europe and from there is spread worldwide eventually.
Caption: "In the San Juan de Dios Market in Guadalajara, Mexico." (Slightly edited.)
In traditional societies, market day was a significant part of a cycle of work-market-day-rest.
Perhaps by nature, humans and societies just find this cycle should be about about 7 days, and this is the ultimate determinant of the seven-day week.
The fact that the lunar month is roughly equal to 4 seven-day weeks may just be a useful coincidence that gives an approximate natural clock for the natural-to-humans seven-day week.
Credit/Permission: ©
Christian Frausto Bernal,
2006
(uploaded to Wikipedia
by User:Humberto,
2008) /
Creative Commons
CC BY-SA 2.0.
Image link: Wikipedia.
In this section, we look at important Moon facts, especially those pertaining to the Moon's orbit.
The Moon facts are summarized and partially illustrated in the figure below (local link / general link: moon_facts.html).
Image 1 Caption: An image moon map of the near side of the Moon with the major maria (singular mare, vocalized mar-ray) and lunar craters identified.
List: Earth-Moon-System Facts:
Keywords: apogee, apsis (apogee, perigee), barycenter, celestial mechanics, center of mass, Earth, eccentricity, fixed stars, inertial frame, J2000, mass, mean orbital radius (AKA semi-major axis), Moon, orbit, (circular orbits, elliptical orbit), orbital inclination, orbital period, planet symbols, perigee, radius, semi-major axis, etc.
Image 2 Caption: Earth and Moon numbers (Cox-16,240,303,305).
See also Moon keywords below (local link / general link: moon_keywords.html):
It is striking that the Moon is much less massive than the Earth: only about 1/80 of the Earth mass M_⊕ = 5.9722(6)*10**24 kg = 3.0033*10**(-6) M_☉. To be precise, recall Moon mass M_Mo = 7.342*10**22 kg = 0.0123000371 M_⊕ = 1/81.3005678 M_⊕ ≅ 1/80 M_⊕.
The much lower mass causes the center of mass of the Wikipedia: Orbit of the Moon) to be actually inside the Earth at ∼ 4700 km from the center Earth (see Wikipedia: Moon: Earth-Moon system: Orbit) and this is the center of the center-of-mass free-fall inertial frame (COMFFI frame) that both Earth and Moon orbit in elliptical orbits.
Recall that center-of-mass free-fall inertial frames (COMFFI frames) are unrotating with respect to the observable universe which in modern cosmology defines the zero-point of absolute rotation.
The Earth's orbit about the center of mass is relatively small, and so for most purposes we can just say the Moon orbits the Earth. However, not all purposes. For example, Earth's tides depend on the Earth being in free fall in the gravitational field of the Moon and Sun. Counterfactually, if the Earth were held at fixed point relative to the center-of-mass free-fall inertial frame (COMFFI frame) of the Solar System, the tidal bulges would tend to be only on the sides of the Earth facing the Moon and Sun instead of being on both facing and anti-facing sides. We consider the Earth's tides in IAL 5: Newtonian Physics, Gravity, Orbits, Energy, Tides.
Why is the Moon mass so much smaller than the Earth mass given that its diameter is a ∼1/4 of the Earth diameter?
It's the "linear-cube law" (which is analogous to the square-cube law) in action. If an object's lengths are all scaled by factor f, then its volume and all quantities that scale with volume (e.g., mass) would scale as f**3. So scaling down the Earth's diameter (mean value 12,756.2 km) by 1/4 causes a scaling down of the Earth mass M_⊕ = 5.9722(6)*10**24 kg = 3.0033*10**(-6) M_☉ by (1/4)**3=1/64. So if the Moon had the same density as the Earth, the Moon's mass would be 1/64 of the Earth mass. In the fact, that the Moon's mass is ∼1/81 of the Earth mass shows the Moon's density is less than that of the Earth, and therefore its composition is different on average from that of the Earth. In fact, the Moon's density is 3.344 g/cm which is about the same as typical terrestrial surface rock. This is an important clue to the origin of the Moon which we consider in IAL 12: The Moon and Mercury: The Formation of the Moon.
You note that the diameters of both the Earth and the Moon are pretty small compared to the distance separating them.
This is why even though the Moon has about a quarter of the Earth's diameter its angular diameter on the sky is only about 0.5°.
Actually, both Earth and Moon are large both in diameter and mass among the rocky-icy bodies in Solar System.
Caption: The largest rocky bodies (including the rocky planets) naturally) and rocky-icy bodies in Solar System ranked in order of decreasing diameter.
The rocky-icy bodies do NOT include the Sun and the gas giant planets (i.e., Jupiter ♃, Saturn ♄, Uranus ⛢ or ♅, and Neptune ♆).
Features:
Circa 2022, there are ∼ 3900 known TNOs (see Wikipedia: List of trans-Neptunian objects). The count is growing rapidly with automated searches.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
Local file: local link: rocky_icy_body.html.
File: Solar System file:
rocky_icy_body.html.
Yet another striking feature of the Moon facts is that the sidereal month (i.e., the physical lunar orbital period relative to the observable universe (which is almost the same as relative to the fixed stars as we traditionally put it) is less than the lunar month.
The figure below (local link / general link: lunar_month_sidereal_period.html) illustrates how the difference between the two time periods arises.
Caption: A diagram illustrating how the difference between lunar month (mean value 29.53059 days, (J2000.0 to 7 digits) the sidereal month (mean value 27.32166 days, epoch J2000 to 7 digits) arises.
Features:
It could also be called the synodic period: i.e., orbital period relative to the Sun.
By the time one sidereal month has passed, the Earth has moved eastward along its orbit and the Moon has NOT returned to the new moon position.
It takes the Moon a bit more than two days to get to the new moon position and complete a lunar month.
The eccentricity of the Moon's orbit implies that the Moon's angular diameter varies.
The explication is given in the figure below (local link / general link: moon_angular_diameter_variation.html).
Caption: "Lunar perigee and apogee apparent size comparison (from 2007 April and October 2007, when events occurred near full-phases)." (Slightly edited.)
Features:
The 11 % variation in DISTANCE causes Moon's angular diameter to vary by 11 % too.
But difference in angular diameter of the Moon is striking if you directly compare the angular diameters at perigee and apogee with the correct relative apparent size as in the image.
Astronomical perturbations account for the fact that the mean anomalistic month = 27.554549878 days (J2000) and the mean lunar sidereal month 27.321661547 days (J2000) ≅ 27.32166 days (to 7 digits) ≅ 27.3 days (the true orbital period relative to the observable universe) are NOT the same.
Answers 1 and 2 are sort of right.
In a total solar eclipse, you know by direct observation that Moon's angular diameter is larger than the Sun's.
In annular solar eclipses, the Moon's angular diameter is just smaller than the Sun's, and one sees a bright annulus (or ring) of the Sun (or to be more precise the solar photosphere: see section Solar Eclipses below) around the Moon.
So the Sun is a natural STANDARD OF COMPARISON---but NOT a great one since it can only be used during total solar eclipses annular solar eclipses---and it's NOT that convenient even then.
By the by, You should NEVER look at an annular eclipse with the naked eye.
I suppose the Sun in partial solar eclipses also provide a STANDARD OF COMPARISON, but you should never look at partial solar eclipses either with the naked eye, and, in any case, it would be hard to tell whether Sun or Moon had the larger angular diameter.
We consider solar eclipses below in the section Solar Eclipses.
The Moon's orbital inclination to the ecliptic is 5.145°: i.e., the tilt of the Moon's orbit from the ecliptic plane defined by the Earth's orbit around the Sun. The orbital inclination is illustrated in the figure below (local link / general link: moon_orbit_001.html).
Caption: Tilt of the Moon's orbit from the ecliptic.
To further explicate: The Moon's orbital inclination to the ecliptic is 5.145°: i.e., the tilt of the Moon's orbit from the ecliptic plane defined by the Earth's orbit around the Sun. The orbital inclination is illustrated in the image.
Answer 1 is right.
The inclination to ecliptic of the Moon's orbit badly complicates eclipse phenomena. Without it, eclipse phenomena would be really easy to understand and they would happen all the time instead of being confined to eclipse seasons (see below subsection The Lunar Node Line and Eclipse Seasons).
Of course, if one had zero inclination to ecliptic for the Moon's orbit, then total/annular solar eclipses would only occur in the tropical region which is region on Earth through which passes the Earth-Sun center-to-center line.
The lunar node line and eclipse season are explicated in the figure below (local link / general link: moon_node_line.html).
Caption: A perspective not-to-scale diagram of the Moon's orbit, lunar nodes, and the lunar node line which sets the eclipse seasons.
Features:
The line that connects the lunar nodes (and which passes necessarily through the Earth) is called---very imaginatively---the lunar node line (or lunar line of nodes).
Note that due to the rotation of the lunar node line, the time for the Moon to return to a lunar node is shorter than the sidereal month (27.321661554 days: J2000). This period is called draconic month (27.212220815 days: J2000 (see Wikipedia: Lunar month: Cycle lengths). Actually, there are 5 lunar month types and a full understanding of them is rather difficult (see Wikipedia: Lunar month: Types of lunar month).
Why, why must the lunar node line ROTATE?
An exact gravitational two-body system, would NOT exhibit rotation of the node line relative to the observable universe.
But the Earth-Moon system is a gravitational two-body system only to 1st order. So the orbits of Earth and Moon about their mutual center of mass (which is the origin for their center-of-mass inertial frame: i.e., their inertial frame which is free-fall frame unrotating with respect to the observable universe) are simple only to 1st order.
The Sun and to a much lesser degree the planets add complicated astronomical perturbations to the Earth-Moon system. This results in subtler, complex motions.
We will, of course, NOT go into the celestial mechanics of those subtle motions. But there seems to be an endless regression of them. Once you've detected and analyzed one, there is another smaller, more subtle one to deal with. Yours truly's patience quickly runs out.
This time frame is called the eclipse season or, as yours truly often says, a nodal alginment---it trips off the tongue.
Usually, there are only 2 eclipse seasons in a calendar year, but 3 will happen if the first one occurs early enough in the calendar year.
Answer 1 is right.
Eclipses can happen because the Moon can be very close to the ecliptic plane and be on the Earth-Sun line line (as in seen in projection on the ecliptic plane) at the SAME TIME.
If the lunar node line is NOT closely aligned with the Earth-Sun line, the Moon will be well above or below the ecliptic plane when it is on the Earth-Sun line.
Actually, because of the finite size of Earth, Moon, Sun some kind of eclipses will always happen at times of nodal alignment---but you don't know that a priori. We will discuss this issue below.
We discuss eclipses, nodal alignment, and eclipse seasons further below in sections Eclipses, Lunar Eclipses, and Solar Eclipses.
Caption: A diagram illustrating nodal alginments which determine the eclipse seasons: i.e., the periods when eclipses of any kind can occur.
Features:
So eclipse seasons have a finite time length.
Whether an eclipse of any kind happens in an eclipse season depends on whether the Moon is in the right place at any time in the eclipse season.
Also, yours truly believes eclipses that happen just at the start or end of an eclipse season can NEVER be "total" eclipses But again yours truly CANNOT at this moment find a reference that says this explicitly.
In fact, most people probably consider an eclipse season a dud for lunar eclipses if there is NO total lunar eclipse. Since total lunar eclipses actually happen in only about 28.7 % of eclipse seasons (see Table: Frequency of Lunar Eclipse Types for 3000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) ), most eclipse seasons are probably duds for lunar eclipses for most people.
Note also if two solar eclipses happen in an eclipse season, the lunar eclipse between them is always a total lunar eclipse (Mo-128).
See also Wikipedia: Eclipse season: Details.
Now I know what you are thinking: why oh why must the lunar node line rotate?
For an exact gravitational two-body system of just Earth and Moon isolated in space, it would NOT rotate. But the Earth-Moon system is surrounded by other Solar System objects which exert gravitational perturbations on the Earth-Moon system.
It's enough here to say that gravitational perturbations cause the rotation of the lunar node line.
Usually there are just 2 eclipse seasons. But since 173.31 days is less than half a year (of any kind), there occasionally can be 3 eclipse seasons in a year: one near the beginning, one near the middle, and one near the end.
So much for this section's Moon facts.
There are more Moon facts below, of course.
Form groups of 2 or 3---NOT more---and tackle Homework 3 problems 2--10 on Moon facts---and Moon factoids.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 3.
Ah Brussels---Belgian chocolate, waffles, Belgian beer---the Germans know nothing about making beer---cafes, Brussels lace, le Sablon, le Musee royau de Beaux-Arts, (avec the Fall of Icarus), Pieter Bruegel the Elder (c. 1525--1569), comics, and Belgian comics---you've heard of Tintin---and my old pal Guy.
Credit/Permission: ©
Chmouel Boudjnah (AKA User:Chmouel),
before or circa 2005
(uploaded to Wikipedia
by User:Neutrality,
2005) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Chocolate fountain.jpg.
Local file: local link: chocolate_fountain.html.
File: Art_c file:
chocolate_fountain.html.
Caption: "A waning crescent moon above Earth's horizon in an image by an Expedition 24 crew member on the International Space Station (ISS)."
The phases of the Moon have a haunting beauty.
Note the sky is blue as seen from above as well as below---and for the same reason.
The diffuse sky radiation is atmosphere-scattered light. Earth's atmosphere scatters blue light more than it scatters red light.
Thus, red light is more strongly transmitted as we know from sunrises and sunsets. At those times, we see sunlight transmitted through a thicker air mass than at other times of the day. This means relatively more blue light scattered, relatively more red light transmitted than at other times of the day.
Credit/Permission: NASA,
2010
(uploaded to
by User:Originalwana,
2010) /
Public domain.
Image link: Wikipedia:
File:Expedition 24 Crescent Moon.jpg.
The lunar phases are explicated in the figure below (local link / general link: moon_lunar_phases.html).
Caption: A diagram illustrating the lunar phases (i.e., the phases of the Moon) over the course of a lunar month = 29.530588861 days (mean J2000) ≅ 29.53059 days (mean J2000 to 7 digits) ≅ 29.5 days.
Features:
And one also has the abbreviated expressions:
The total length of the time is thus 29.5 days which is approximately the lunar month (mean length 29.53059 days).
Apogee is the farthest distance of the Moon to the Earth, and so is a stationary point where the angular diameter of the Moon is changing slowly. Choosing to start and end the film near a stationary point prevents obvious sharp jumps in the angular diameter when the film restarts.
The actual period from apogee to apogee (and also perigee to perigee) is the anomalistic month.
The anomalistic month = 27.55450 days (J2000) to 7 digits.
The anomalistic month is not same in period as the lunar month (mean value 29.53059 days (J2000) to 7 digits) nor the sidereal month (mean value 27.32166 days (J2000) to 7 digits).
This side is the near side of the Moon.
The apparent rocking motion is the lunar libration.
The lunar libration is due to the observer seeing slightly different hemispheres as the Moon and Earth move in space. There are actually three effects that add up to the overall lunar libration (see Wikipedia: Lunar libration). Remember "apparent" in astro jargon means as seen from Earth. There's no rocking relative to the inertial frame of the fixed stars---which for most purposes is the same as the Earth-Moon system free-fall frame: i.e., local approximate inertial frame.
In this IAL lecture, lunar phase questions are a big deal.
Answer 2 is right.
The Moon is always approximately along the ecliptic as we discussed in IAL 2: The Sky.
But once you get the hang of them, they are easy.
The diagram in the figure below (local link / general link: moon_phases_calculator.html) illustrates how to answer simple lunar phase questions.
Caption: The ONE DIAGRAM---which you can reproduce for yourself whenever you need it---that allows you to answer all simple lunar phase questions.
Therefore on the diagram, east is counterclockwise and west is clockwise.
Recall, as usual in astronomy, that east and west are actually angular directions.
But once you get the hang of them, they are easy.
You can solve for any ONE variable if you know the other TWO.
The three "variables" are:
Remember the Moon is always near the ecliptic: i.e., in a day, it will be carried around with the celestial sphere on almost the same arc on the sky as the Sun.
Just identify the two variables you know on the diagram and the third variable is then identifiable.
"Your head" points toward the local meridian.
In particular, the Earth and Earth-Moon are actually small compared to the Earth-Moon distance, but "you" are actually a pinprink on the Earth which looks like an infinite plane to "you".
And this is actually true for exact lunar opposition. You CANNOT see the center of the Moon rise at exact sunset when the center of the Sun sets.
But the Earth is relatively small, and Moon and Sun have finite sizes, and so "you" see the Moon rise as the Sun sets or "you" see that so nearly as to make no difference to casual description.
Thus to 1st order and as a vast SIMPLIFICATION in using the diagram, "you" can take the Moon as fixed on the rotating celestial sphere and fixed in phase for any single day.
Some lunar phase videos:
Let's do 3 examples of lunar phase problems.
Phase and time are the knowns. Location on the sky is the unknown.
To find the answer, glance again at the lunar phases diagram shown again in the figure below (local link / general link: moon_phases_calculator.html).
Caption: The ONE DIAGRAM---which you can reproduce for yourself whenever you need it---that allows you to answer all simple lunar phase questions.
If the time were midnight, then the Moon would be transiting the meridian.
Time and location on the sky are knowns. Phase is the unknown.
Glance back lunar phases diagram and find the time location on Earth and identify the eastern direction.
The Moon must be a waning crescent.
Location in sky and phase are knowns. Time of day is the unknown.
Glance back at the lunar phases diagram.
It must be sunset.
If the Moon was on the eastern horizon, it would be noon.
---Mother Goose.
Is the image astronomically possible at ANY time of day?
Since the Moon
is at full moon and is on the
horizon,
the cow
must be jumping
at sunset
or sunrise.
Cows
can only jump
the Moon when it
is on the horizon
since they can only jump so high.
Note the full moon in the image means the Moon is in opposition to the Sun. So for a full moon at moonrise/moonset, the Sun must be at sunset/sunrise.
See the video: Hey Diddle Diddle - Nursery Rhyme - With Text | 1:32.
Credit/Permission:
William Wallace Denslow (1856--1915),
1902
(uploaded to
by User:Tagishsimon,
2006) /
Public domain.
Image link: Wikipedia: File:Hey Diddle Diddle 2 - WW Denslow - Project Gutenberg etext 18546.jpg.
Local file: local link: moon_cow_spoon.html.
File: Moon afar file:
moon_cow_spoon.html.
Say you are at the sunset location:
For an example of a lunar phase question, where there is NOT enough information to solve for the time of day NOR the location in the sky, see the figure below (local link / general link: moon_crescent_forest.html).
Caption: Moon Over Forest, West Dolores River, Colorado, 1972:
The image poses a lunar phase question where there is NOT enough information to solve for the unknowns. You know the lunar phase, but NEITHER time of day NOR the location in the sky. With 2 unknown variables, you CANNOT solve for either of them.
Credit/Permission: Boyd Norton (1936--),
1972
(uploaded to Wikimedia Commons
by User:US National Archives bot,
2011) /
Public domain.
Image link: Wikimedia Commons:
File:MOON OVER FOREST - NARA - 544870.jpg.
Local file: local link: moon_crescent_forest.html.
File: Moon afar file:
moon_crescent_forest.html.
Actually the Moon does move a noticeable distance on the celestial sphere during a day. A simple Moon calculation shows this:
Relative to the Sun, the Moon moves 360 degrees / 29.53059 days = 12.19 degrees/day . This is the angular velocity for phase change. Relative to the (observable universe i.e., the celestial sphere or almost exactly for this purpose the observable universe), the Moon moves 360 degrees / 27.321661 days = 13.17 degrees/day . This is the angular velocity for motion relative to stars near the Moon.
Either way, the Moon moves about 0.5 degrees per hour.
Since the Moon itself subtends about 0.5°, it moves about its own angular diameter every hour.
If one checks the Moon against the fixed stars during a night, the Moon's motion can be easily seen.
Not that yours truly has ever done such a thing.
Form groups of 2 or 3---NOT more---and tackle Homework 3 problems 12--17 on lunar phases.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 3.
Credit/Permission: ©
User:4028mdk09,
2009 /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Becher Kakao mit Sahnehäubchen.JPG.
Local file: local link: chocolate_hot.html.
File: Art_c file:
chocolate_hot.html.
This behavior is because of tidal locking.
We discuss the Moon's tidal locking and tidal locking in general in the subsections below.
Since the Moon's axial rotation rate is on average equal to its orbital rotation rate (whether with respect to the Sun or to the observable universe), it always turns the same side to us.
We call this side the near side of the Moon and, until recent history, it was the only side we ever saw.
The figure below (local link / general link: moon_map_side_near.html) shows the familiar near side of the Moon.
Caption: An image moon map of the near side of the Moon with the major maria (singular mare, vocalized mar-ray) and lunar craters identified.
Features:
The lunar phase is full moon or, maybe, waxing gibbous moon just before full moon.
Maria means "seas" in Latin. The early telescopic observers of the 17th century thought the maria might be seas. They soon realized this was wrong. However, the name is still appropriate since the maria are lava plains: i.e., the frozen seas of lava from lava flows welling up from the interior of the young maria formed 3.5--3 Gyr ago though some might be have formed as recently as 1.2 Gyr ago (see Wikipedia: Lunar mare: Ages).
The far side of the Moon has only small maria and looks rather bland and uninteresting compared to the near side.
The maria actually cover only ∼ 16 % of the lunar surface, but they look more extensive to Earthlings just because they cover ∼ 30 % of the near side (see Wikipedia: Lunar Mare).
This is the conventional orientation for modern images and maps of the Moon.
The first crewed landing on the Moon occured there with Apollo 11 in 1969. The landing crew consisted of Neil Armstrong (1930--2012) and Buzz Aldrin (1930--). The third crew person Michael Collins (1930--) stayed in lunar orbit.
Tycho is the most obvious rayed crater---it has large radial rays emanating from it that are fallback from giant plumes that were ejected when the Tycho impactor impacted.
The rays indicate that Tycho is relatively young impact crater. The rays of impact craters are erased by space weathering over gigayear time scales. Tycho is estimated to be 108 Myr old (see Wikipedia: Tycho: Age and Description).
For more Moon features, see Wikipedia: List of lunar craters, Wikipedia: List of lunar features, Wikipedia: List of lunar maria, Wikipedia: List of lunar mountains and mountain ranges.
The figure below (local link / general link: moon_map_side_far.html) shows the unfamiliar far side of the Moon.
Caption: A Moon image of the far side of the Moon.
Features:
So two slivers of the far side are obliquely seen from the Earth.
Before that and throughout human history, the far side of the Moon was a mystery.
For example, the largest of the small far side maria is Mare Moscoviense. It's in the upper left quadrant of the image.
Mare Moscoviense is at 147.9° E longitude in selenographic coordinates which have their zero at the center of the near side. This verifies---when you think about it---that the lunar west is the at the left in the image.
Answer 3 is right.
Caption: An animation illustrating the tidal locking of the Moon to the Earth.
Features:
Hereafter, by rotation, we mean rotation relative to the observable universe.
In the counterfactual case, all faces of the Moon would be directed toward the Earth every lunar orbital period (i.e., mean lunar sidereal month 27.321661547 days (J2000) ≅ 27.32166 days (to 7 digits) ≅ 27.3 days). Of course, an observer on the Earth would only see the parts of the faces revealed by the lunar phases.
Tidal locking is a gravitational effect.
A mutually orbiting pair of astro-bodies tend to become tidal locked to each other (i.e., always turn the same face to each other) because of the tidal force they exert on each other.
The tidal force is explicated in the figure below (local link / general link: tidal_force.html).
The astro-body could be free falling radially to (i.e., directly toward) the gravitational field source, but in many actual cases the astro-body is orbiting the center of mass of a center-of-mass (CM) inertial frame consisting of a system astro-bodies (to which the first astro-body belongs too) and that system (excluding the first astro-body) is collectively the gravitational field source. The simplest case is a gravitationally-bound two-body system.
In brief, the tidal force is a stretching force due to variation in the gravitational field.
The residual gravitational force is called the tidal force.
The lower panel of the image illustrates the tidal force and its stretching effect.
If the tidal force gets too strong relative to the INTERNAL forces, the astro-body can be disrupted. This happens to moons that get too close to their host planet.
Also the tidal force can prevent a planetary ring from coalecsing into a moon under its self-gravity.
Whether tidal locking goes to completion for either of the astro-bodies depends on the strength of the tidal force, the resistance of the astro-bodies to being tidal locked, and the complicating gravitational effects of other astro-bodies. Note:
Caption: A diagram illustrating the tidal force and how tidal locking is effected.
Features:
In the Earth-Moon system, this means that we are viewing the system from the south celestial pole (SCP) side of the celestial sphere.
The situation is similar to that of the Moon and the Earth.
So the near side of the small astro-body is pulled on more strongly than the far side.
Both near and far side are in orbit around the large astro-body. The near side does need more gravitational force than the far side since it has smaller orbit.
When tidally locked, the small astro-body has Ω = ω, and so always turns the same side facing the large astro-body.
From another perspective, the tidal locking is EXACT ON AVERAGE.
For example, tall buildings sway with wind perturbations, but keep returning to being nearly exactly upright.
But the larger astro-bodies in mutually orbiting pairs because of their larger mass almost always initially have more axial rotation angular momentum (resistance to change of axial rotation angular velocity) than smaller astro-bodies. Also the smaller astro-bodies have smaller tidal forces than larger astro-bodies. The result of these two conditions is that it takes longer, often much longer, for the larger astro-bodies to become tidally locked to the smaller astro-bodies, than vice versa.
This is due to libration---which we won't describe here---see Wikipedia: Libration if you must.
Actually, the axial rotation angular velocity of many minor moons are NOT perfectly known, and so it is NOT known if they are tidally locked or NOT.
For some information concerning Solar System moons that are NOT tidally locked, see Wikipedia: Tidal locking: Occurrence: Moons.
Among the planets, only ex-planet Pluto is tidally locked (see Wikipedia: Tidal locking: List of known tidally locked bodies). Pluto and its largest moon Charon are mutually tidally locked.
If you were on the Charon/Pluto-facing side of Pluto/Charon, you would always see Charon/Pluto in the sky at the same location relative to the ground and with its Pluto/Charon-facing side turned toward you.
The other planets have NOT become tidally locked to their moon of strongest tidal force for the reasons given above. Also the effect of the multiple tidal forces (due multiple moons and the Sun) acts against tidal locking to the moon of strongest tidal force.
Why are NO planets tidally locked to the Sun?
Although the Sun has the strongest gravity, its tidal force is too weak as it turns out even for Mercury where it is strongest. Actually, Mercury is an unusual case because it has a 3:2 spin-orbit resonance (see Wikipedia: Mercury: 3:2 spin-orbit resonance). We will NOT go into this complex case.
The Moon's tidal force on the Earth is slowing down the Earth's rotation, and thus increasing the length of the day.
However, the slowing rate is so slow that the Earth will probably NOT become tidally locked to the Moon before the Sun's red giant phase in ∼ 5 Gyr (see Wikipedia: Sun: After core hydrogen exhaustion) when the Sun may well vaporize Earth and Moon (see Wikipedia: Tidal acceleration: Effects of the Moon's gravity)---lucky us.
If the orbit of an astro-body about another astro-body is NOT circular (i.e., has non-zero eccentricity), the tidal force varies with the orbital radius: stronger when orbital radius is smaller, weaker when orbital radius is larger.
The varying tidal force perpetually flexes the astro-body in the noncircular orbit which results in resistive forces inside the astro-body to turn macroscopic mechanical energy from the two astro-bodies's motions into heat energy.
The heat energy can cause some degree of geologically activity.
As explained with the figure above (local link / general link: tidal_locking_origin.html), moons tend to get tidally locked to their parent planets during the course of solar system evolution, but the reverse process has generally NOT happened.
The planets have more angular momentum (which is a measure of rotational stability among other things) than the moons, and so it takes much longer to slow their rotation to the tidally locked situation. More time than the Solar System age = 4.5682 Gyr in all but one case (see just below). Also in planet-moon systems with multiple large moons, the distinct tidal locking effects of the moons will somewhat each other when the planet's rotation gets sufficiently slow. Some moons will be trying to slow planet rotation while others are trying to speed it up. So a tidal locking to any one moon might NOT happen.
Among planets and dwarf planets, mutual tidal locking between planet or dwarf planet and its moon is only found for ex-planet Pluto (now a lowly degraded dwarf planet) and its biggest moon Charon and dwarf planet Eris and its only known moon Dysnomia (see Wikipedia: Tidal locking: List of known tidally locked bodies).
In the Pluto system case, Charon's tidal locking effect is overwhelmingly dominant since the other moons of Pluto are very small and have relatively little gravitational force.
See the Pluto system in the figure below (local link / general link: pluto_system.html).
Image 1 Caption: The Pluto system with ex-planet Pluto (now a dwarf planet) near the center of mass (AKA the barycenter) and 3 of the 5 currently known moons of Pluto.
Features:
The New Horizons spacecraft (2006--) did a flyby of the Pluto system with closest approach on 2015 Jul14. It discovered NO new Plutonian moons, and so it is likely that the 5 currently known ones are all there are.
_______________________________________________________________________________________ The Pluto System _______________________________________________________________________________________ Astro-Body Discovery Year Radius Mass Orbital Radius Orbital Period (km) (10**18 kg) (km) (days) _______________________________________________________________________________________ Pluto 1930 1153 13050 2040 6.3872 70 % Moon 18 % Moon Charon 1978 602 1520 17530 6.3872 35 % Moon 2 % Moon 15.20 Pluto radii Nix 2005 44 1 48708 24.9 Hydra 2005 36 .391 64749 38 Kerberos 2011 20 approx ? 59000 32.1 Styx 2012 10--25 ? 42000±2000 20.2±0.1 _______________________________________________________________________________________
The same orientation relative to the ground means having the same horizontal coordinates: i.e., same altitude and azimuth.
Tidal locking must be common througout the observable universe.
We know now for sure that planetary systems are common and the tidal locking must operate in them all to some degree.
So moons are probably usually tidally locked their parent planets.
Planets very close to their parent stars are probably usually tidally locked to those parent stars unless they become tidally locked to a large moon.
But tidal locking to the parent star did NOT happen in the Solar System for the two closest-to-the-Sun and moonless planets Mercury and Venus. See the discussion of these planets in subsection Tidal Locking to the Sun below.
So tidal locking can be avoided even for moonless planets close to their parent stars in some unusual cases.
The Earth has tidally locked the Moon.
The reverse has NOT happened, but the Moon's working on it.
The great angular momentum (which is a measure of rotational stability among other things) of the Earth greatly slows the process and the competing effect of the Sun's tidal locking effect complicates things---actually, I'd guess the Sun helps slow the Earth's rotation, and so at present is helping toward tidal locking of the Earth to the Moon.
Geological evidence suggests that 620 megayears ago (0.62 gigayears), the solar day was 21.9(4) hours (i.e., 21.9(4) modern standard hours) (Wikipedia: Tidal accelration: Historical evidence).
Historical records for the past 2700 years suggests that currently the solar day is increasing by 1.70(5)*10**(-3) seconds per century (Wikipedia: Earth-Moon case).
At present, the mean solar day - standard metric day ≅ 0.002 s. Circa 1900 (when standard time was being settled) mean solar day was about equal to the standard day.
In order to account for the current 0.002 s difference every 600 days or so a leap second is added to Universal Time (UT) without much fanfare in order to keep solar time synchronized with Universal Time (UT). I suspect that eventually, people will let discrepancies between mean solar time and Universal Time (UT) just accummulate to a full minute and then add an extra leap minute. Computers---our lords and masters---already complain about leap seconds which upset all their algorithms.
If the rate of increase of the solar day were constant, how long until the day is 1 second longer than it is now?
This is an amount-rate-time problem: t = A/R = 1 second / [ 1.70*10**(-3) seconds per century ] ≅ 600 centuries = 60 millennia .
So we'd have to wait 60 millennia for even ONE more second in the mean solar day. One wonders who will care.
In any case, it was so hard getting the 2nd millennium over with.
I spent most of my life waiting for it to end---and now I'm nostalgic for the good old days.
All things considered from the Dark Ages (see figure below: local link / general link: bayeux_tapestry.html) to the World Wide Web, the 2nd millennium wasn't so bad.
The rate of increase of the day is likely NOT constant.
There are all kinds of complicating small effects---like the shifting of material in the Earth's interior.
But without even without an exact prediction, it seems that the slowing rate of the Earth's rotation is so slow that the Earth will probably NOT become tidally locked to the Moon before the Sun becomes a red giant in about 5 Gyr when the Sun may well vaporize Earth and Moon (see Wikipedia: Tidal acceleration: Effects of the Moon's gravity)---lucky us.
Caption: A detail of the Bayeux Tapestry, now exhibited at the Bayeux Museum, Bayeux, Normandy, France.
The detail shows Halley's comet. The Latin text reads ISTI MIRANT STELLA: These ones are looking in wonder at the star (see Wikipedia: Omen: Good or bad). Of course, comets are NOT stars in modern astro jargon.
The Bayeux Tapestry is sort of a Medieval graphic novel.
It's all about the Norman conquest of England---1066 and All That.
In fact, comets, the long-haired stars, have always been considered portentous, ominous.
They are strange looking---hairy.
They seemed irregular unlike other astronomical phenonema. It was NOT until Edmond Halley (1656--1742) in 1705 recognized the periodicity his eponymous comet (Halley's comet) that comets were tamed to regularity in some cases.
Comets were thought to herald calamities or disasters (i.e., a bad star events):
Credit/Permission: Medieval artists,
circa 1070
(uploaded to Wikipedia by
User:Urban,
2005) /
Public domain.
Image link: Wikipedia:
File:Tapestry of bayeux10.jpg.
Local file: local link: bayeux_tapestry.html.
File: Art file:
bayeux_tapestry.html.
In principle, planets can be tidally locked to the Sun.
None are.
Mercury and Venus are the likest cases one would think a priori since they are closest to the Sun (and therefore are subject to the strongest solar tidal forces) and have no moons that can out-compete the Sun.
It can't serve two masters.
Well maybe there is some tricky way with planet year, moon revolution period, and planet day all equal in length and the moon always on the planet-Sun line.
A very weird system.
In the figure below (local link / general link: mercury_3_2_spin_orbit_resonance.html), we do a digression on Mercury's orbit before returning to the Moon in subsequent sections.
Caption: Mercury's orbit exhibits a 3:2 spin-orbit resonance which is illustrated in the diagram.
Features:
Say you land on Mercury on the equator just at noon on top of a giant mountain.
Now 3/2 axial rotation periods later, 1 Mercurian year has passed (i.e., Mercurian orbital rotation period P_O = 87.9691 days = 0.240846 yr = (3/2)*P_A = (1/2)*P_D has passed).
But since it is 3/2 axial rotation periods, it is now midnight for you.
It takes another 3/2 axial rotation periods to bring you back to noon.
Thus the Mercurian synodic day P_D = 175.942 days = 2*P_O = 3*P_A (i.e., noon to noon) is 3 axial rotation periods = 2 orbital periods (i.e., 2 Mercurian years).
Subtle stabilizing effects damp out any changes in the ratios set by the 3:2 spin-orbit resonance caused by astronomical perturbations.
In the case of Mercury's orbit, the oscillations are axial rotations and orbit rotations.
From the specialized formulae for the synodic period (see Orbit file: synodic_period.html), we have, in fact, Mercurian day equal to 2 orbital periods = 175.9382 days. The diagram also shows why this must be so (as aforesaid).
The accurate Mercurian day = 175.942 days (NASA: Mercury fact sheet, 2021). The discrepancy between our calculated value and NASA's may be due to the specialized formulae being based on assumption that Mercury having a circular orbit which is NOT the case. There might be other reasons for the slight discrepancy: e.g., astronomical perturbations and/or observational error.
Form groups of 2 or 3---NOT more---and tackle Homework 3 problems 12--17 on lunar phases.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 3.
How now can we eat a chocolate Easter Bunny?
Credit/Permission:
Mary Cynthia Dickerson
(1866--1923,
The American Museum Journal, Vol. XVII, 1917
(Natural History (magazine)
(known then as The American Museum Journal until 2002?))
(uploaded to
Wikimedia Commons
by User:Fae,
2015) /
Public domain.
CC BY-SA 2.0.
Image link: Wikimedia Commons: File:The American Museum journal (c1900-(1918)).
Local file: local link: chocolate_easter_bunny.html.
File: Art_c file:
chocolate_easter_bunny.html.
Generally speaking, an eclipse is when one astro-body moves into the shadow of another.
But there is also the transitive verb eclipse which in astronomy means when one astro-body (the subject) blocks your view of another astro-body (the object).
Eclipses happen all over the observable universe: e.g., Mars as illustrated in the film in figure below (local link / general link: mars_phobos_transit.html).
In fact, there is nothing fundamentally important about eclipses. It just happens that those we see on Earth are spectacular for us.
Caption: A film of a Phobos Transit of the Sun---as seen on Mars, of course.
Phobos (mean radius 11.2667 km) is the larger of the 2 Martian moons. The smaller one is Deimos (mean radius 6.2(2) km).
Phobos is NOT round as you can see in the film.
Phobos' mean orbital radius (AKA semi-major axis) is 9377.2 km, but it is still is a finite, if tiny, disk on the sky as seen from the Martian surface. Note Mars' equatorial radius is 3396.2(1) km.
Here little Phobos makes a valiant effort to make a total eclipse of the Sun, but it fails. It's too small. All it can do is an annular eclipse: i.e., it leaves a annulus or ring of the Sun uncovered.
The transit lasts only ∼ 30 s. The film lasts only ∼ 5 s, and so is time-lapsed.
This transit was observed by Opportunity rover (2004jan25--2018jun10) on 2004 Mar10.
By the by, a transit is when one astro-body passes in front of another one from the point of view of an observer---or crosses meridian---which is like passing in front of an imaginary astro-body.
A transiting body always partially eclipses the transited body, but if the eclipsed part is really tiny, one usually would NOT call the event an eclipse.
Credit/Permission: NASA,
2004
(uploaded to Wikipedia
by User:Yaohua2000,
2005) /
Public domain.
Image link: Wikipedia:
File:PIA05553.gif.
Local file: local link: mars_phobos_transit.html.
File: Mars file:
mars_phobos_transit.html.
There's a bit of inconsistency in our terminology for eclipses seen from Earth.
A solar eclipse is when the Moon eclipses the Sun from the point of view of the Earth.
But the Moon is NOT eclipsed from the point of view of the Earth in a lunar eclipse. NOTHING is blocking our view of the Moon.
In fact, a lunar eclipse is a SOLAR ECLIPSE as seen on the Moon
In both cases, the ECLIPSED object is the Sun.
If we wanted consistency---which we don't---we could call a lunar eclipse a solar eclipse as seen from the Moon.
In any case, there's nothing to be done about the inconsistency now.
We could be very clear if we always specified the three astro-bodies: the eclipsed, the eclipser, and the observer.
Usually when discuss eclipses without qualification, we mean eclipses as seen from the Earth: i.e., lunar eclipses and solar eclipses.
These eclipses during eclipse seasons which happens every 173.31 days as discussed above in the section Moon Facts and as recapitulated in the figure below (local link / general link: eclipse_season.html).
Caption: A diagram illustrating nodal alginments which determine the eclipse seasons: i.e., the periods when eclipses of any kind can occur.
Features:
So eclipse seasons have a finite time length.
Whether an eclipse of any kind happens in an eclipse season depends on whether the Moon is in the right place at any time in the eclipse season.
Also, yours truly believes eclipses that happen just at the start or end of an eclipse season can NEVER be "total" eclipses But again yours truly CANNOT at this moment find a reference that says this explicitly.
In fact, most people probably consider an eclipse season a dud for lunar eclipses if there is NO total lunar eclipse. Since total lunar eclipses actually happen in only about 28.7 % of eclipse seasons (see Table: Frequency of Lunar Eclipse Types for 3000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) ), most eclipse seasons are probably duds for lunar eclipses for most people.
Note also if two solar eclipses happen in an eclipse season, the lunar eclipse between them is always a total lunar eclipse (Mo-128).
See also Wikipedia: Eclipse season: Details.
Now I know what you are thinking: why oh why must the lunar node line rotate?
For an exact gravitational two-body system of just Earth and Moon isolated in space, it would NOT rotate. But the Earth-Moon system is surrounded by other Solar System objects which exert gravitational perturbations on the Earth-Moon system.
It's enough here to say that gravitational perturbations cause the rotation of the lunar node line.
Usually there are just 2 eclipse seasons. But since 173.31 days is less than half a year (of any kind), there occasionally can be 3 eclipse seasons in a year: one near the beginning, one near the middle, and one near the end.
The explications of the complications with eclipse phenomena are given above in subsections The Orbital Inclination to the Ecliptic of the Moon's Orbit and The Lunar Node Line and Eclipse Seasons, this section (i.e., section Eclipses), and below in sections Lunar Eclipses and Solar Eclipses or are "obvious". So without comment:
The complications mean that modern-standard high accuracy/precision predictions of eclipses CANNOT be done by explicit formulae, but have to be calculated numerically by the computer.
Examples of computer predictions of eclipses are given below in subsections Frequency of Lunar Eclipses, Frequency of Solar Eclipses, and Predicting Solar Eclipses.
An ancient way of predicting eclipses of very low accuracy/precision going back to Babylonian astronomy (centuries earlier than 1200 BCE--c.60 BCE) (Wikipedia: History of astronomy: Mesopotamia; Wikipedia: Babylonian astronomy; Wikipedia: Babylonian star catalogues) is described below in subsection The Saros Cycle.
Any body illuminiated by a finite source of light has two kinds of shadow: umbra where the source is totally covered (or occulted or eclipsed) and penumbra where the source is only partially covered (or occulted or eclipsed).
Penumbra is Latin for almost shadow.
A point source can only cause umbras.
Of course, when other sources of light are around (including reflecting sources), an umbra won't be totally dark and a penumbra NOT as dark as otherwise.
Caption: Earth's umbra and penumbra as caused by the Sun.
Features:
To be a bit more precise, NO part of the solar photosphere (which is the layer from which most light escapes from the Sun) can be seen by straight line light ray transmission.
We discuss the solar photosphere in IAL 8: The Sun.
As we discuss IAL 3: The Moon: Orbit, Phases, Eclipses, and More: The Coppery Colored Moon, there is some curved-line light ray transmission due to atmospheric refraction, and so the umbra will NOT be totally dark.
There are three main lunar eclipse types: total lunar eclipse, partial lunar eclipse, and penumbral lunar eclipse. The types are illustrated in the figure below (local link / general link: lunar_eclipse_types.html).
Features:
But when we say partial lunar eclipse without further qualification, we usually mean one that does NOT include a total lunar eclipse.
But when we say penumbral lunar eclipse without further qualification, we usually mean one that does NOT include a partial lunar eclipse.
A penumbral lunar eclipse that is total and does NOT include a partial lunar eclipse is a total penumbral eclipse.
Most often the two lunar eclipses in one eclipse season wiil both be penumbral lunar eclipses. However, it is barely possible that one will a partial lunar eclipse. The eclipse season for a partial lunar eclipse is 24 days around exact nodal alignment (Mo-128): i.e., for about 12 days before and 12 days after exact nodal alignment. So if a partial lunar eclipse happens on day -12, then -12 + 29.5 = 17.5 days which is sometimes within the total range of an eclipse season (duration 31--37 days) which stretches at maximum from -18.5 days before to 18.5 days after exact nodal alignment.
A total lunar eclipse including penumbral stage (see below) can last up to 6 hours; totality (when the Moon is entirely within the Earth's umbra) lasts at most 1 hour 40 minutes (Se-41).
The eclipse season for a total lunar eclipse is only 9 days??? around exact nodal alignment (with the Earth-Sun line) (Mo-128, not here): i.e., it extends from about 4.5 days before and 4.5 days after the exact nodal alignment.
Eclipse seasons are explicated in the figure below (local link / general link: eclipse/eclipse_season.html).
Caption: A diagram illustrating nodal alginments which determine the eclipse seasons: i.e., the periods when eclipses of any kind can occur.
Features:
So eclipse seasons have a finite time length.
Whether an eclipse of any kind happens in an eclipse season depends on whether the Moon is in the right place at any time in the eclipse season.
Also, yours truly believes eclipses that happen just at the start or end of an eclipse season can NEVER be "total" eclipses But again yours truly CANNOT at this moment find a reference that says this explicitly.
In fact, most people probably consider an eclipse season a dud for lunar eclipses if there is NO total lunar eclipse. Since total lunar eclipses actually happen in only about 28.7 % of eclipse seasons (see Table: Frequency of Lunar Eclipse Types for 3000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) ), most eclipse seasons are probably duds for lunar eclipses for most people.
Note also if two solar eclipses happen in an eclipse season, the lunar eclipse between them is always a total lunar eclipse (Mo-128).
See also Wikipedia: Eclipse season: Details.
Now I know what you are thinking: why oh why must the lunar node line rotate?
For an exact gravitational two-body system of just Earth and Moon isolated in space, it would NOT rotate. But the Earth-Moon system is surrounded by other Solar System objects which exert gravitational perturbations on the Earth-Moon system.
It's enough here to say that gravitational perturbations cause the rotation of the lunar node line.
Usually there are just 2 eclipse seasons. But since 173.31 days is less than half a year (of any kind), there occasionally can be 3 eclipse seasons in a year: one near the beginning, one near the middle, and one near the end.
The eclipse season for a partial lunar eclipse is 24 days around exact nodal alignment (Mo-128): i.e., for about 12 days before and 12 days after exact nodal alignment.
Because the eclipse season is shorter than the lunar month, a partial lunar eclipse is NOT always possible.
At only about 30 % of nodal alignments is there a partial lunar eclipse without a total lunar eclipse (Fred Espenak: MrEclipse.com: yours truly assumes this is a good source since he works for NASA).
No one gets too excited about partial lunar eclipses without total lunar eclipse, but they are noticeable.
Could he be a Selenite?
Credit/Permission: ©
David Jeffery,
2003 / Own work.
Image link: Itself.
Local file: local link: alien_prototype_selenite.html.
File: Alien images file:
alien_prototype_selenite.html.
Answers 1 and 2 are right.
The eclipse season for penumbral lunar eclipses is 32 days??? around exact nodal alignment (Mo-128, not here): i.e., for 16 days before and 16 days after.
Now 32 days is longer than a lunar month, and so at every nodal alignment, there is at least a penumbral lunar eclipse.
At about 35 % of nodal alignment is there a penumbral lunar eclipse (but usually NOT total penumbral eclipse) without a partial lunar eclipse or a total lunar eclipse (see Lunar Eclipses for Beginners).
No one gets excited about penumbral lunar eclipses.
The Moon just looks a little diminished in brightness in an uneven way. A layer of cloud could have almost the same effect. So penumbral lunar eclipses usually go unnoticed and unannounced.
A special case of the penumbral lunar eclipse, is the total penumbral eclipse which occurs when the Moon goes entirely into the penumbra and never touches the umbra.
These are rare and boring events. They happen only a few times per century.
There was the 2006 Mar14 total penumbral eclipse---you probably read all about it. The next one is 2053 Aug29---you can hardly wait.
A total penumbral eclipse is illustrated in the figure below.
Caption: An illustration of the 1988 Mar03 total penumbral eclipse.
You are looking in the antisolar direction and seeing the Earth's umbra and penumbra and the Moon's path projected onto the celestial sphere.
A total penumbral eclipse is when the Moon goes completely into the penumbra without going into the umbra at all.
These rather rare---and boring---events occur between 0 and 9 times per century.
Credit/Permission:
Tom Ruen
(AKA User:SockPuppetForTomruen and User:Tomruen),
2009
(uploaded to Wikipedia
by Magnus Manske,
2008) /
Public domain.
Image link: Wikipedia:
File:Lunar eclipse chart close-1988Mar03.png.
The occurrences of all kinds of eclipses is sufficiently complex that there is NO simple or even complex formula for predicting them and there is NO exact repeating cycle of them (though there is an approximate cycle: see subsection The Saros Cycle below). The cycles of eclipse seasons, solar day, and of all the types of lunar month (which characterize the Moon's orbit) and the slow evolution of these cycles with time make exact prediction by formula or cycle impossible.
Someone has to do a calculation on the computer. Fortunately, someone has.
See Table: Frequency of Lunar Eclipse Types for 3000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) below for the frequency of lunar eclipse types for the 3000 BCE--3000 CE time period---there are 14442 lunar eclipses.
_____________________________________________________________________________________________________________ Table: Frequency of Lunar Eclipse Types for 3000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) _____________________________________________________________________________________________________________ Type Number Percentage _____________________________________________________________________________________________________________ total 4203 29.1 partial 5012 34.7 penumbral 5227 36.2 all types 14442 100.0 _____________________________________________________________________________________________________________
The 3 lunar eclipse types occur with approximately equal frequency---exact equal frequency for 3 items is 33.3... % frequency, of course.
The penumbral lunar eclipses are those without total lunar eclipse phases or partial lunar eclipse phases partial lunar eclipses are those without total lunar eclipse phases.
Note that two lunar eclipses (but only two penumbral lunar eclipse) can happen in a eclipse season (see Wikipedia: Eclipse season: Details), and so the number of eclipse seasons in the 6000 year period of the table is somewhat less than 14442.
For period 2000 BCE--3000 CE from another source (Ian Cameron Smith: Hermit.org: but NO longer easily found there), there were 191 total penumbral eclipses out of 4479 penumbral lunar eclipses. So roughly 4 % of penumbral lunar eclipses are total penumbral eclipses.
Of course, total lunar eclipses arn't as awe-inspiring as total solar eclipses.
The two kinds of total eclipses occur with the same order of frequency, but there is a major distinction in how many people can see them.
Total lunar eclipses can be seen from the entire night side of the Earth---except where there is cloud cover, of course.
Total solar eclipses can be seen only from a restricted geographic area: see the section Solar Eclipses below.
Thus, everyone will likely see a few total lunar eclipses in their lives---or at least sleep through a few---but to see a total solar eclipse, you must travel to an eclipse path (the region of total eclipse) or be lucky enough to live on one near in time to the occurrence of the total solar eclipse---and be lucky enough NOT to be clouded out.
Now for total lunar eclipse images (see figure below: (local link / general link: lunar_eclipse_2007_mar03.html) and videos (see below: local link / general link: lunar_eclipse_videos.html).
Caption: A series of images of the Moon taken aboard the Wasp-class amphibious assault ship USS Boxer (LHD 4) shows the Moon during the 2007 Mar03 total lunar eclipse.
Click on image and on the next image for the high-resolution image.
In the first and last image of the sequence, the Moon is probably in a penumbral lunar eclipse or partial partial penumbral lunar eclipse.
So we see the sequence penumbral lunar eclipse, partial lunar eclipse, total lunar eclipse, and then the reverse sequence.
The photographer increased the sensitivity of his camera for the totality and near totality images. If he had kept the camera on high sensitivity, the penumbral lunar eclipse would be glaring and if he had kept the camera on low sensitivity, the total lunar eclipse would be very dark.
This is a coppery total lunar eclipse. The coppery color is due to refraction of sunlight by the Earth's atmosphere.
The prominent impact crater with rays (it is a rayed crater) in the south is Crater Tycho.
Credit/Permission: U.S. Navy photos by Mass Communication Specialist Seaman Joshua Valcarcel,
2007 /
Public domain.
Image link: Wikipedia:
File:Lunar eclipse March 2007.jpg.
Local file: local link: lunar_eclipse_2007_mar03.html.
File: Eclipse file:
lunar_eclipse_2007_mar03.html.
At totality of a total lunar eclipse the Moon can take on a coppery color as we see in the US Navy lunar eclipse in the figure above (local link / general link: lunar_eclipse_2007_mar03.html). This is due to refraction of sunlight by the Earth's atmosphere (Se-41).
To explicate: refraction is the bending of light rays as they pass through an interface between different media or a gradually bending of light rays as they propagate through a medium that is gradually changing.
The figure below (local link / general link: refraction_water.html) illustrates refraction.
Caption: Because of refraction, light rays from the drinking straw are bend at the interface between water and air.
This makes the straw look bent at the interface too.
But everyone knows it's NOT bent since this is a common everyday-life phenomenon.
That "water" looks like blue guck.
Credit/Permission: ©
User:Bcrowell,
2005
(uploaded to Wikipedia
by User:Liftarn,
2006) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Refraction-with-soda-straw.jpg.
Local file: local link: refraction_water.html.
File: Optics file:
refraction_water.html.
The bluish light of the Sun is more strongly scattered out of the travel path in the refraction through the Earth's atmosphere, and so it is the reddish light that reaches the Moon and then is reflected back to observers on Earth.
The effect is illustrated in the figure below (local link / general link: lunar_eclipse_redden.html).
Caption: The explication of the reddening of the Moon in a total lunar eclipse.
Features:
Obviously, light rays that beam most directly on the Earth are least reddened and those that traverse the Earth's terminator are most reddened: hence the redness of sunrise and sunset.
Recall, NO straight line light rays from the Sun can reach the Moon when it is inside the Earth's umbra.
The location of the Moon in the Earth's umbra is another factor: the closer the Moon is the center the dimmer it will be all other things being equal and off the center there is a greater tendency for uneven illumination by the refracted light rays.
The scattering is also why sunrise and sunset are red. We are seeing unscattered sunlight from which blue light has been strongly out-scattered. At sunrise and sunset, sunlight takes a long tangential path through the Earth's atmosphere to the observer and this increases the outscattering relative to when the Sun is high in the sky. The redness of of sunrise is illustrated in the figure below (local link: File:Sun rise at CuaLo.jpg).
Caption: Sunrise at Cua Lo, Vietnam.
But forth one wavelet, then another, curled,
Till the whole sunrise, not to be supprest,
Rose, reddened, and its seething breast
Flickered in bounds, grew gold,
then overflowed the world.
Hey, some people are taking a morning swim.
Credit/Permission: ©
User:Handyhuy,
2007 /
CC BY-SA 3.0.
Image link: Wikimedia Commons:
File:Sun rise at CuaLo.jpg.
Local file: local link: File:Sun rise at CuaLo.jpg.
Reddened color of the Moon in a total lunar eclipse depends on the Earth atmospheric conditions at the Earth's terminator: the Earth's day-night line. These conditions will affect the overall brightness and will cause uneven reddening. If the terminator is very cloudy, there may be no obvious reddening and the Moon can look quite dim.
The location of the Moon in the umbra is another factor: the closer the Moon is the center the dimmer it will be all other things being equal and off the center there is a greater tendency for uneven illumination by the refracted light rays.
Caption: "No sudden, sharp boundary marks the passage of day into night in this gorgeous view of ocean and clouds over our fair planet Earth. Instead, the shadow line or terminator is diffuse and shows the gradual transition to darkness we experience as twilight. With the Sun illuminating the scene from the right, the cloud tops reflect gently reddened sunlight filtered through the dusty troposphere, the lowest layer of the planet's nurturing atmosphere. A clear high altitude layer, visible along the dayside's upper edge, scatters blue sunlight and fades into the blackness of space. This picture actually is a single digital photograph taken 2001 June from the International Space Station (ISS) orbiting at an altitude of 211 nautical miles."
The Other Side of the Sky as Arthur C. Clarke (1917--2008) would say.
Credit/Permission: ISS Crew,
Earth Sciences and Image Analysis Lab,
Johnson Space Center,
NASA,
2001
(uploaded to Wikipedia
by Andrew Dunn (AKA User:Solipsist),
2006) /
Public domain.
Image link: Wikipedia:
File:Earthterminator iss002 full.jpg.
No one has been on the Moon for a lunar eclipse which, of course, from the Selenite perspective is a solar eclipse.
However, some approximations to having seen a lunar eclipse from the Moon have occurred. See the figure below for one of these.
Caption: Image from Apollo 12, 1969 Nov24, passing into or out of the Earth's umbra on its homeward journey.
No one has been on the Moon for a lunar eclipse which, of course, from the Selenite perspective is a solar eclipse.
But this Apollo 12 is sort of like a solar eclipse from Selenite perspective.
The image shows the Sun just vanishing or emerging.
You can see the bright edge of the Sun peeping over the disk of the Earth and a partial ring illumination of refracted light around the Earth's terminator.
Note the Earth's angular diameter is 4 times that of the Sun's as seen from the Moon.
Night on Earth in a sense is an eclipse of the Sun by the Earth from a on-the-ground human perspective.
Credit/Permission: NASA,
1969 /
Public domain.
Download site: Johnson Space
Center, Digital Image Collection.
Alas, a dead link.
Image link: Itself.
Lunar eclipses nowadays are of no special scientific value. They are just spectacles---even in Las Vegas---see the two figures below (local link / general link: lunar_eclipse_2014_04_14_hunter_hopewell.html; local link / general link: lunar_eclipse_2014_04_14_robert_machado.html).
Total lunar eclipse: the 2014 Apr15 total lunar eclipse.
The image was taken in the environs of Las Vegas, Nevada where totality started Apr15 12:07 am local time. The partial lunar eclipse started Apr14, 10:58 pm local time.
It was a blood moon.
The Moon is NOT nearly totally dark during a total lunar eclipse because light rays of sunlight are refracted around the Earth by the Earth's atmosphere.
The transmission through the atmosphere preferentially scatters out blue light and makes the transmitted light reddish just as at sunrise and sunset.
How red the Moon becomes depends on atmospheric conditions at the terminator (i.e., the day-night line on the Earth) and the local brightness of the night sky (I think). Near the Las Vegas Strip, the Moon looked only slightly reddish during the 2014 Apr15 total lunar eclipse.
Credit/Permission: ©
Hunter Hopewell, 2014 /
Personal permission.
Image link: Itself.
Local file: local link: lunar_eclipse_2014_04_14_hunter_hopewell.html.
File: Eclipse file:
lunar_eclipse_2014_04_14_hunter_hopewell.html.
Caption: Tales from the Eclipse.
Total lunar eclipse: the 2014 Apr15 total lunar eclipse.
The image was taken in the environs of Las Vegas, Nevada where totality started Apr15 12:07 am local time. The partial lunar eclipse started Apr14, 10:58 pm local time.
It was a blood moon.
The Moon is NOT nearly totally dark during a total lunar eclipse because light rays of sunlight are refracted around the Earth by the Earth's atmosphere.
The transmission through the atmosphere preferentially scatters out blue light and makes the transmitted light reddish just as at sunrise and sunset.
How red the Moon becomes depends on atmospheric conditions at the terminator (i.e., the day-night line on the Earth) and the local brightness of the night sky (I think). Near the Las Vegas Strip, the Moon looked only slightly reddish during the 2014 Apr15 total lunar eclipse.
Credit/Permission: ©
Robert Machado, 2014 /
Personal permission.
Image link: Itself.
Local file: local link: lunar_eclipse_2014_04_14_robert_machado.html.
File: Eclipse file:
lunar_eclipse_2014_04_14_robert_machado.html.
For example, they were interesting for themselves if you didn't understand how they worked or how to predict them.
Lunar eclipses also provided one the earliest pieces of evidence for a spherical Earth.
The shadow of the umbra of the Earth on the Moon is always round.
This would be hard to arrange without having a spherical Earth.
Of course, you have to believe that the Moon shines by reflected light and also that the Earth's umbra is the cause of partial lunar eclipse.
The round umbra argument was given by Aristotle (384--322 BCE), but may have been known earlier.
Parmenides of Elea (early 5th century BCE), who may have been the first proponent of the spherical Earth, may have known the argument.
Answer 3 is right.
I believe the ancient Greeks were the first to realize that solar time varied with locality and that west is earlier, east is later in the solar day. But I CANNOT find a reference at the moment.
Form groups of 2 or 3---NOT more---and tackle Homework 3 problems 18--24 on lunar phases and lunar eclipses.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 3.
Did you know that cocoa may be the great brain food---see Daisy Yuhas, 2013, Is Cocoa the Brain Drug of the Future?---it makes mice smarter---but maybe only in unprocessed form---just when you thought it was safe to scarf.
More debunking of dark chocolate: The dark truth about chocolate: Nic Fleming, The Guardian, Sun 25 Mar 2018---candy, NOT health food.
Credit/Permission: ©
Simon A. Eugster (AKA User:LivingShadow),
2010 /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Schokolade-schwarz.jpg.
Local file: local link: chocolate_swiss.html.
File: Art_c file:
chocolate_swiss.html.
A partial lunar eclipse is "total solar eclipse" as seen from the part of the Moon in the Earth's umbra.
Thus, a total solar eclipse is a "partial eclipse" using the "lunar" sense of the word "partial" since the whole Earth isn't in the Moon's umbra.
A "total solar eclipse" of the Sun in the "lunar" sense never happens on the Earth because the Moon's umbra can only cover a small part of the Earth at most.
There are three main solar eclipse types: total solar eclipse, annular solar eclipse, and partial solar eclipse.
A fourth non-main type is the hybrid solar eclipse which is one that transitions between being a total solar eclipse and an annular solar eclipse.
Every total solar eclipse/annular solar eclipse includes a partial solar eclipse.
Context usually decides when we say partial solar eclipse whether we mean a solar eclipse without a total solar eclipse/annular solar eclipse or one with a total solar eclipse/annular solar eclipse.
Sometimes we have to be explicit about what we mean by partial solar eclipse.
For a discussion of total solar eclipses and annular solar eclipses, see the figure below (local link / general link: solar_eclipse_geometry.html).
Caption: "Geometry of a total solar eclipse." (Slightly edited.)
Features:
However, its umbra is much smaller than a quarter of the Earth's diameter.
The image shows why this is so diagrammatically.
Analysis of umbra size is given in the IAL subsection Umbra Size.
But we do not need that analysis here. We just take the small Moon's umbra as a given.
Solar eclipses can happen when the Moon is at any of its distances during an almost exact nodal algnment (during an eclipse season): but total solar eclipses only when the Moon is relatively near and its umbra touches down on the Earth.
Note the Sun has no sharp edge. The solar atmosphere just morphs into the solar wind as one moves outward.
However, there is a relatively sharp layer from which most light escapes the Sun. That is the solar photosphere.
One should NEVER look at the solar photosphere even the smallest part thereof without proper protection: i.e., a valid astronomical solar filter. We're always catching little glimpses of the solar photosphere, and so one shouldn't be paranoid about this. But minimizing those glimpses is best.
Only during totality is it safe to look at the Sun with the naked eye.
In this case, if you are located below the tip of the umbra's cone, you see the night side of the Moon centered on the Sun with a bright ring (i.e., an annulus) of the solar photosphere surrounding it.
Since part of the solar photosphere is visible, you should NOT look at the Sun without proper protection: i.e., a valid astronomical solar filter.
Both of these distances vary due to the eccentricities of the Moon's orbit (mean value e = 0.0549006 ∼ 5.49 %) and the Earth's orbit (e = 0.0167086 ∼ 1.67 %: J2000).
So as NOT to go into complexities, we'll just say the Earth-Moon distance has to be a little less than its average value (384,748 km = 60.3229 Earth equatorial radii (R_eq_⊕ = 6378.1370 km)) for total solar eclipses since total solar eclipses are a little less frequent than annular solar eclipses.
The frequency of solar eclipse types during eclipse seasons for calendar years 2000 BCE--3000 CE is total solar eclipses 26.7 %, annular solar eclipses 33.2 %, hybrid solar eclipses 4.8 %, partial solar eclipses 35.3 %, and total solar eclipses plus hybrid solar eclipses 31.5 % (see Fred Espenak: MrEclipse.com: scroll down ∼ 60 %). Hybrid solar eclipses flick between being marginally total solar eclipses and annular solar eclipses.
But if the surface is NOT perpendicular to the umbra axis, the umbra tip could be stretched out as shadows are at sunset.
Presumably, this stretching out effect is accounted for in the 267 km at most value reported above. But I cannot find a discussion of this fine point.
v = 1.022 - 0.46511 = 0.5569 km/s = 33.41 km/m = 2005 km/h .
The actual minimum eclipse path velocity varies a bit depending on various factors and is more typically ∼ 1700 km/h (see Wikipedia: Solar eclipse: Occurrence and cycles).
The maximum fiducial eclipse path velocity occurs at the Earth's poles where the Earth's tangential velocity is zero. This maximum value is, of course 1.022 km/s = 3679 km/h.
To first order, the diameter of the region is just that of the Moon: 3464.2 km ≅ 0.273 Earth mean diameters (see Wikipedia: Moon).
This size is obtained by just assuming the Sun's rays are all parallel, the Earth is a flat disk, and all of the Moon's penumbra lands on the Earth.
Answer 1 is right.
When the Moon is closest (i.e., at perigee), its umbra on the Earth is biggest.
We'll look at some total solar eclipse images in the subsection The Main Event: The Total Solar Eclipse below.
Caption: The total solar eclipse of 2002 Dec04.
This image from the International Space Station (ISS) shows the lunar umbra on the Indian Ocean.
The crew were standing on their heads.
Credit/Permission: ISS,
NASA,
2002 /
Public domain.
Download site: Marshall Space Flight Center,
Marshall Image Exchange (MiX) and search for 0300612 (just number, no leading space)
for image 0300612 information
or just click on
0300612
for the image itself. Alas, now a
dead link.
Image link: Itself.
The uncovered photosphere appears as a bright ring around the black (i.e., nighttime-side) Moon. Annulus is just Latin for ring and gives rise to the name annular solar eclipse.
Another perspective on annular solar eclipses is to say the Moon's umbra doesn't reach the Earth.
Annular solar eclipses are further exlicated in the two figures below (local link / general link: solar_eclipse_annular.html; local link / general link: solar_eclipse_annular_2005_oct03.html).
Caption: A diagram giving an explication of annular solar eclipses.
To further explicate: An annular solar eclipse occurs when the Moon passes completely into the disk of the Sun (i.e., the disk of the Sun's photosphere), but the Moon is at a relatively distant part of its orbit and CANNOT cover the complete photosphere.
The uncovered photosphere appears as a bright ring around the black (i.e., nighttime-side) Moon. Annulus is just Latin for ring and gives rise to the name annular solar eclipse.
Another perspective on annular solar eclipses is to say the Moon's umbra doesn't reach the Earth. This perspective is made clear in the diagram.
Credit/Permission: ©
David Jeffery,
2004 / Own work.
Image link: Itself.
Local file: local link: solar_eclipse_annular.html.
File: Eclipse file:
solar_eclipse_annular.html.
Caption: The annular solar eclipse of 2005 Oct03.
This is a typical annular solar eclipse. The night of the Moon is very dark as is space. The solar photosphere is seen as a bright ring (i.e., an annulus).
Note the Moon is NOT exactly centered on the Sun. This is usual. The Moon can only be nearly exactly centered on the Sun only when it transits nearly exactly through the Sun's center (which does NOT happen on every annular solar eclipse) and only at the moment of transit.
Credit/Permission: ©
User:sancho_panza,
2005
(uploaded to Wikipedia
by User:ComputerHotline,
2007) /
Creative Commons
CC BY-SA 2.0.
Image link: Wikipedia:
File:Ecl-ann.jpg.
Local file: local link: solar_eclipse_annular_2005_oct03.html.
File: Eclipse file:
solar_eclipse_annular_2005_oct03.html.
Thus, when the tip of umbra of the Moon passes in front of the Earth, slightly more than half of the time the umbra doesn't touch down on the Earth's surface.
One can also have hybrid eclipses (also called annular/total solar eclipses), where the eclipse shifts between total and annular as the umbra moves across the Earth.
But since there is a total solar eclipse somewhere during a hybrid eclipse, hybrid eclipses are often just counted as total solar eclipses---except by the pedantic---but with Wikipedia, we're all pedantic now.
Annular solar eclipses arn't nearly as popular as total solar eclipses. They are spectacular, but you CANNOT look at them with the naked eye and everything does NOT get nighttime dark.
From the observer's location, the Sun is a crescent.
But NEVER look at any part of the solar photosphere with the naked eye.
The term partial solar eclipse without qualification usually means a partial solar eclipse NOT part of total or annular solar eclipse.
As usual context must decide what one means by the term partial solar eclipse.
In fact, partial solar eclipses NOT part of total or annular solar eclipses do NOT attract much attention usually. The day gets a little darker, but often no more so than if there was some haze. Bright patches of sunlight filtered through trees can become crescent-shaped due to the pinhole projection effect discussed below.
People often pass through partial solar eclipses (unqualified) without noticing a thing.
Partial solar eclipses (unqualified) happen during 35.3 % of eclipse seasons (see below subsection Frequency of Solar Eclipses). But they usually cause no great popular interest, particularly if the penumbra is mostly just over the ocean.
Just as with lunar eclipses, solar eclipses can happen only near a nodal alignment which happens 173.31 days.
Will there be at least a partial solar eclipse every nodal alignment?
Remember the mean lunar month is 29.53059 days (7-digit J2000.0 value).
Answer 1 is right.
Because the lunar month is shorter than the eclipse season, the Moon will be at new moon at some time during the eclipse season.
Even if the eclipse season started just after new moon, the Moon still has enough time to race around the Earth and reach new moon again before the eclipse season ends.
So some kind of a solar eclipse must occur every eclipse season.
In fact, two partial solar eclipses (but they probably are rather slight partial solar eclipses) can occur a single eclipse season if one happens right at the beginning of the eclipse season. The Moon can race around the Earth and gets back to new moon before the eclipse season is over.
Two partial solar eclipses in a single eclipse season is a rare event. But one such event happened in 2018 with partial solar eclipses on Jul13 and Aug11 (see Joe Rao, SciAm, 2018jul26). Another will happen in 2036: the dates for the partial solar eclipses are Jul23 and Aug21 (see Fred Espenak: MrEclipse.com which yours truly assumes this is a good source since he works for NASA: Solar Eclipses: 2031 - 2040).
Two total/annular solar eclipses or a total/annular solar eclipse and a partial solar eclipse in one eclipse season seems to be impossible---at least there is NO mention of such events that yours truly can find.
Thus, in reality total and annular solar eclipses are NOT all that uncommon.
But annular solar eclipses don't usually cause great interest. Recall also that they are somewhat more common than total solar eclipses.
Also total and annular solar eclipses are geographically limited to tight eclipse paths.
Thus, only a lucky few will ever see one without traveling.
Now recall that the occurrences of all kinds of eclipses is sufficiently complex that there is NO simple or even complex formula for predicting them and there is NO exact repeating cycle of them. (though there is an approximate cycle: see subsection The Saros Cycle below)). The cycles of eclipse seasons, solar day, and of all the types of lunar month (which characterize the Moon's orbit) and the slow evolution of these cycles with time make exact prediction by formula or cycle impossible.
Someone has to do a calculation on the computer. Fortunately, someone has.
Below we have Table: Frequency of Solar Eclipse Types for 2000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments).
One sees that hybrid solar eclipse are rarest by far (only about 5 %) and the other solar eclipse types occur with approximately the same frequency of ∼ 30 % each.
_________________________________________________________________________ Table: Frequency of Solar Eclipse Types for 2000 BCE--3000 CE at Eclipse Seasons (AKA Nodal Alignments) _________________________________________________________________________ Type Number Percentage _________________________________________________________________________ total 3173 26.7 (31.5 counting hybrids too) annular 3956 33.2 (38.0 counting hybrids too) hybrid 569 4.8 partial 4200 35.3 all types 11898 100.0 _________________________________________________________________________
In the context of tables like the above, the partial solar eclipses are NOT included in the amounts for the other solar eclipse types though, of course, those types have phases of partial solar eclipse of course.
Note that the number eclipse seasons is slightly lower than 11898 since two partial solar eclipses can happen somewhat rarely in a single eclipse season.
You MUST NOT look at the Sun directly with the naked eye whenever any of the photosphere is visible.
Of course, we're always catching small glimpses without disaster---but one should minimize those glimpses.
Only during totality of a total solar eclipse is it safe to look at the Sun with the naked eye---because the photosphere is totally covered.
The ONLY way to look at the photosphere of the Sun safely is with a proper astronomical solar filter either just for viewing or on a telescope.
Other kinds of filters and old photograph negatives are NOT guaranteed to be adequate, are almost always NOT adequate, and should always be deemed NOT adequate.
Even at sunrise and sunset or through a thick haze, the Sun is still NOT safe to view with the naked eye. We've all, of course, had glimpses, but again one should minimize those.
For more on safety during solar eclipses, see the NASA: Eye Safety During Solar Eclipses.
If you don't have a proper astronomical solar filter, you can use pinhole projection to look at the Sun at any time.
Pinhole projection during solar eclipses is illustrated in the next four figures (local link / general link: pinhole_projection_2.html; unlinked; local link / general link: pinhole_projection_malta.html; local link / general link: pinhole_projection.html).
Actually, the image is INCORRECT for a partial solar eclipse since the Moon really gives convex bite, NOT a concave bite as in the image.
Caption: The pinhole projection method for observing a solar eclipse. In the insert in the upper left corner of the image, you can see the partially eclipsed Sun that was photographed with a white solar filter. In the main image you can see multiple projections of the partially eclipsed Sun.
The image is a bit of fancy work with multiple pinholes in a ping-pong paddle to get multiple crescent images.
Light filtering through leafy trees can give multiple crescent images during a partial solar eclipse.
The solar eclipse was total solar eclipse of 2006 Mar29.
Credit/Permission: ©
User:Brocken Inaglory,
2006
(uploaded to Wikipedia
by User:Mbz1,
2009) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Solar eclipse in Turkey March 2006.jpg.
Caption: The image shows multiple pinhole projections caused by a canopy of tree leaves during the partial solar eclipse that accompanied the annular solar eclipse of 2005 Oct03. The image was taken at St. Julian's, Malta.
Features:
But during partial solar eclipses, you see multiple images of the crescent Sun which looks weird---even if you can't figure out why.
Certainly, the Sun disk has a convex bite taken out of it, but without specially viewing equipment (e.g., a guaranteed-safe solar filter or pinhole projections setup) you CANNOT see that since you should NEVER look at the Sun whenever any part of the solar photosphere is visible.
The sky during partial solar eclipses will just look a bit dimmer than usual as if there were some extra cloud cover and if there is cloud cover the dimming is really hard to notice. Of course, if the sky is very clear, the dimming is quite striking especially the closer to totality the partial solar eclipse is.
There is also a cooling effect that can be quite striking especially the closer to totality the partial solar eclipse is.
If you were unaware of the partial solar eclipse, you might wonder "what the heck".
The multiple-crescent effect was quite noticeable under the canopy of tree leaves of the UNLV boulevard during the annular solar eclipse that whipped through the western USA on 2023 Oct14. So were the sky dimming and cooling effects.
Actually, the image is INCORRECT for a partial solar eclipse since the Moon really gives convex bite, NOT a concave bite as in the image.
The Image 1 shows exactly how point inversion works better than words using light rays and ray tracing.
Point inversion can also be described as a 180° rotation from source to image.
Can you see sunspots? Probably NOT.
Incidentally, can you see narrow dark and bright fringes just near the edges of shadows of an object (e.g., of a pencil)? You need to look really closely. A magnifying glass might help. The fringes are the diffraction patterns set up the object.
The situation is that every point in the aperture acts as an infinitesimal aperture in its own right.
The (observed) image is the sum of the infinitesimal aperture images.
However, these do NOT exactly overlap, and so the image is somewhat fuzzy (i.e., lacking perfect sharpness).
As the aperture gets bigger, the image approaches just being the shape of the aperture which is why a rectangular window with sunlight streaming in creates a rectangular spot of illumination.
The imperfectly overlapping aperture images are spread out by of order "a". The ratio of spreading to image size is of order
a f = -------- , d*tan(θ)
the fuzziness factor.
If f << 1 sufficiently, the image will look sharp to the human eye.
If f >∼ 1, then the image is totally fuzzed.
Just put the projection screen farther away from the aperture to increase sharpness.
You may be able to observe sunspots with pinhole projection---but yours truly has always failed. It is probably marginal at best (see, e.g., Cloudy Nights Telescope Review).
Pinhole projection does work well for observing solar eclipses---especially when you are too lazy to do anything more elaborate.
In fact, when the Sun images become crescents ☽, there is a partial solar eclipse. The crescents are sufficiently striking that people do notice them when they never notice the round light spots. In fact, since partial solar eclipses dim the sky similarly to thin cloud cover, maybe the only casual way to notice partial solar eclipses is by being spooked by the crescents.
We mentioned earlier in IAL 1: Hand Angle Measurements, the great coincidence is that the Sun and Moon have almost the same angular diameters on the sky: i.e., about 0.5°.
The discussion is recapitulated in the figure below (local link / general link: sun_moon_angular.html).
Caption: The great coincidence is near equality of the angular diameters of Sun and Moon as seen on the sky (see EarthSky: Coincidence that sun and moon seem same size? (2013); Wikipedia: Angular diameter: Use in astronomy).
Features:
To be precise, as seen from the Earth's center center-to-center distances in the precise calculation of angular diameters ?????, we find:
Of course, we do NOT observe Sun and Moon from the Earth's center, but that is the standard reference observational point and, in fact, the Earth's size is sufficiently small that its size can be treated as negligible in all but highly precise measurments. Recall Earth equatorial radius R_eq_⊕ = 6378.1370 km. Also observing Sun and Moon on the horizon puts them at nearly exactly the same distance as from the Earth's center.
If the Sun's angular diameter were constant at its mean value, then total solar eclipses would happen (when the Moon is centered on the Sun) when the Moon was slightly closer than its mean distance (i.e., its mean lunar orbital radius = 384399 km = 60.32 Earth equatorial radii = 2.57*10**(-3) AU = 1.282 light-seconds) and the annular eclipses would happen when it was farther. However, since the distance to the Sun (i.e., fiducial value 1 astronomical unit (AU) = 1.49597870700*10**(11) (exact by definition) ≅ 499.00478384 light-seconds ≅ 8.3167463973 light-minutes ≅ 4.8481368111*10**(-6) pc) varies because of the Earth's orbit is elliptical orbit with small eccentricity 0.0167 = 1.67 %, the exact prediction of whether there will be an total solar eclipse or an annular eclipse (when the Moon is centered on the Sun) is complicated. But astrometrists have done that for us in ephemerides.
For example in Greek mythology, the Sun and Moon were viewed as being or as manifesting the twin gods Apollo and Artemis, or, alternatively, just brother-and-sister gods Helios and Selene.
And the great coincidence may indeed be just a coincidence.
On the other hand, there is now an anthropic principle argument for the great coincidence (see Dynamical, biological, and anthropic consequences of equal lunar and solar angular radii, S. A. Balbus, 2014). Maybe our existence as large terrestrial animals anthropically implies the great coincidence. See Biology file: devonian_speciation.html for further discussion of the anthropic principle argument.
Actually, the argument is only for a near great coincidence. The fact that the Sun and Moon angular diameters are as close as they are still seems to be just a great coincidence.
However, this turns out to be a relatively small effect over hundreds of megayears.
Circa 400 Myr Before Present (BP), the mean mean lunar orbital radius was ∼ 97.7% of its current value and its mean angular diameter was ∼ 0.5410° which is bigger than the current mean Sun angular diameter: (mean 0.5332°, range 0.5242°--0.5422°) and almost as big current maximum Sun angular diameter. (see George E. Williams 2000, Reviews of Geophysics, Volume 38, Issue 1, p. 37-60; Wikipedia: Orbit of the Moon: Tidal evolution of the lunar orbit). Assuming the Sun angular diameter was NOT much different than now total eclipses would have been much more common than now during eclipse seasons and annular eclipses more rare.
And 50 Gyr in the future, the Moon's angular diameter will only be reduced to ∼ 0.36° assuming the Earth-Moon system is still around. The Earth-Moon system might well have been long vaporized by then in the Sun's post-main-sequence phase which will start ∼ 5 Gyr from now when the Sun expands into red giant star and then an asymptotic giant branch (AGB) star (see Wikipedia: Sun: After core hydrogen exhaustion).
The Moon's umbra follows an eclipse path on the Earth.
Two motions are compounded to make the umbra move:
The second motion somewhat compensates for the first.
The animation in the figure below (local link / general link: solar_eclipse_path_animation.html) illustrates the motion of the Moon's umbra following an eclipse path.
Caption: An animation of the eclipse path of the Solar eclipse of August 11, 1999 which was a total solar eclipse.
Features:
However, in a hybrid solar eclipse the umbra does NOT touch the Earth's surface during its annular solar eclipse phase, and so the umbra may NOT start or end on the Earth's terminator in hybrid solar eclipses.
However, during the relatively short time of a solar eclipse, the Moon's path in space is nearly a straight line perpendicular to the Earth-Sun line
In other words, NO place on Earth can keep up with umbra: the umbra must move east.
However, counterfactually if the Moon moved slower than the Earth's equatorial rotational speed = 0.4651 km/s, the umbra would have to move west sometimes. The lower the latitude (i.e., the closer to the equator), the more easily westward could be arranged.
Super counterfactually if the Moon were at rest on the Earth-Sun center-to-center line, then the umbra would sweep west (from an fixed Earth view) over the subsolar point (which is always in the tropics) perpetually as the Earth rotates east relative to the observable universe.
amount diameter 2*6378.1370 km t = -------- = ------------ = -------------- = 12480 s = 3.467 hours = 3.5 hours . rate Moon speed 1.022 km/s
(see Wikipedia: Earth equatorial radius R_eq_⊕ = 6378.1370 km; Wikpedia: The Moon's mean orbital speed = 1.022 km/s).
Most Earth contact times for the umbra will be less than 3.5 hours since the umbra will move along a chord that is NOT a diameter on the disk of the Earth.
The Earth contact time for the Solar eclipse of August 11, 1999 was 3.1 hours which is close to maximal which is consistent with the eclipse path being close to a diameter as the animation shows.
Eclipse paths are always followed east because the Moon moves eastward in space at an average speed of 1.022 km/s.
Over the time of solar eclipse, the Moon is moving nearly in a straight line through space: the Moon is only moving a little along its curved orbital path.
The upper limit on the Earth's speed eastward on a parallel path is the Earth's equatorial rotational speed of 0.4651 km/s.
All other speeds of the Earth's surface in one direction in space are less since the rotation speed decreases with latitude north and south and rotation of the Earth means that the direction of motion is NOT in a straight line, but in circular path that is also NOT in the same plane as the Moon's motion.
So only a componet of the velocity is along a path parallel to the Moon's nearly straight line path in space. Since 0.4651 km/s is the maximum velocity of the Earth's surface parallel to the Moon in space, the minimum eclipse velocity relative to the ground eastward is
v_rel = 1.022 - 0.4651 = 0.557 km/s = 2000 km/h .A more exact calculation shows that the minimum umbra speed is about 1700 km/h (Se-43).
Because the Moon goes well above and below the ecliptic plane, the Moon's umbra and penumbra can be at any latitude.
At higher latitudes, the Earth speed is lower---going to zero at the poles---and so the umbra speed is greater with an upper bound of about 3700 km/h.
Given these high speeds and the fact that width of the lunar umbra on the Earth (i.e., the totality region) is 267 km at most in a track-moving direction (see Wikipedia: Solar eclipse: Path), it's NOT surprising that the umbra remains over any one point on the Earth for just over 7 minutes at most (see Wikipedia: Solar eclipse: Path).
Caption: "The Sun's umbra during a total solar eclipse as seen from the International Space Station while over Turkey and Cyprus". (Slightly edited.)
This is the total solar eclipse of 2006 Mar29.
The north half of Cyprus is at the bottom of the image.
Credit/Permission: NASA,
2006
(uploaded to Wikipedia
by Howard Cheng (AKA User:Howcheng),
2006) /
Public domain.
Image link: Wikipedia:
File:Eclipse fromISS 2006-03-29.jpg.
Recall that the occurrences of all kinds of eclipses is sufficiently complex that there is NO simple or even complex formula for predicting them and there is NO exact repeating cycle of them. The cycles of eclipse seasons, solar day, and of all the types of lunar month (which characterize the Moon's orbit) and the slow evolution of these cycles with time make exact prediction by formula or cycle impossible.
There is, however, an approximate cycle of eclipse phenomena, the Saros cycle. The Saros cycle explicated in the figure below (local link / general link: saros_halley.html).
Caption: Edmond Halley (1656--1742) has several claims to fame: he discovered the periodic nature of the great comet we call Halley's comet, he encouraged Isaac Newton (1643--1727) to write the Principia (1687), and he misnamed the Saros cycle by calling it the Saros cycle, a name never used by the Babylonian astronomers.
To explicate the last claim to fame specified above, Halley in 1691 mistakenly concluded the approximate cycle of eclipse phenomena known to Babylonian astronomy (centuries earlier than 1200 BCE--c.60 BCE) (Wikipedia: History of astronomy: Mesopotamia; Wikipedia: Babylonian astronomy; Wikipedia: Babylonian star catalogues) was called the Saros or something like that. Actually, the word "saru" means 3600 in some version of the Babylonian language (see Wikipedia: Saros: History).
The Saros cycle can be used to predict eclipses of all kinds approximately.
Note right off the Saros cycle = 6,585.321347 days (J2000?) = 18 yr + 10.321347 days (5 leap years) or 11.321347 days (4 leap years) (west shift ∼ 120° longitude) and the triple Saros cycle (AKA exeligmos) = 19755.964041 days (J2000?) = 54 yr + 31.964041 days (14 leap years) 32.964041 days (13 leap years) (west shift ∼ 0° longitude). Note Wikipedia: Saros is NOT clear on whether the standard metric day = 24 h = 86400 s or the solar day = current mean value 86400.002 s is used in their description. Since the solar day evolves with time, it is a bit indefinite to use for high accuracy/precision description, and so yours truly assumes Wikipedia: Saros means standard metric day as an excellent approximation to solar day, but with more accuracy/precision.
Features of the Saros cycle:
Using modern values (J2000?) its length is
6585.321347 days = 13 common years + 5 leap years + 10.321347 days = 14 common years + 4 leap years + 11.321347 days = 18 Julian years + 10.821347 days ,with common year = 365 days, leap years =366 days, and Julian year = 3652.25 days. See Wikipedia: Saros: Description.
Note the period of the Saros cycle is empirical, and so has some uncertainty and it slowly evolves with time due to astronomical perturbations.
For a repetition in approximately the same locality with the same approximate solar time, you need to wait a triple Saros cycle (AKA exeligmos) with period 19755.964041 days ≅ 54 years + 32 or 33 days.
So if a total solar eclipse happened right here at noon today, about 54 years + 33 days from now a total solar eclipse would happen somewhere near here near noon.
The Saros cycle was later known to the ancient Greek astronomers, who probably got it from the Babylonian astronomers by some kind of trans-cultural diffusion.
However, they were flat-Earthers and probably did NOT understand that solar time depends on longitude which they also did NOT know about. So they could only predict possibilities of eclipses. The predictions could be unrealized: e.g., a predicted lunar eclipse was unobserved because it was entirely below the horizon; a predicted total/annular solar eclipse was outside their geographical area, and so was unreported.
The ancient Greek astronomers who did have the spherical Earth theory and eventually understood solar time probably did better.
But high accuracy/precision eclipse predictions (eclipse ephemerides) were probably NOT available before the 17th century when more accurate procedures were available than the Saros cycle and triple Saros cycle.
In fact, one of the first high accuracy/precision total solar eclipse predictions was made by none other than Edmond Halley (1656--1742) himself: the prediction of total solar eclipse of 1715 May03.
Caption: "Depiction of Anzu (a bird beast) pursued by Ninurta (a Sun god, god of scribes), palace relief, Nineveh." (Slightly edited.)
Also: "Ninurta with his thunderbolts pursues Anzu stealing the Tablet of Destinies from Enlil's sanctuary."
The reliefs of Assyrian sculpture are the high points of surviving Assyrian art.
Generally, Assyria was NOT well like by other peoples of ancient Mesopotamia. God did send a prophet to save Assyria---ah, Jonah.
Credit/Permission:
Austen Henry Layard (1817--1894),
Monuments of Nineveh, 2nd Series, 1853
(uploaded to Wikimedia Commons
by User:User:Georgelazenby
2012) /
Public domain.
Image link: Wikimedia Commons:
File:Chaos Monster and Sun God.png.
Local file: local link: assyria_bas_relief_ninurta.html.
File: Babylonian astronomy file:
assyria_bas_relief_ninurta.html.
High accuracy/precision predictions of solar eclipses---well beyond the accuracy of the Saros cycle---is complicated.
Fortunately, some people have done that for us and provided solar eclipse predictions for centuries in advance. Let us just consider solar eclipse paths for the 2001--2040 period illustrated in the two images in the figure below (local link / general link: solar_eclipse_2021_2040.html).
Image 1 Caption:
Eclipse paths for
bi-decade
2001--2020.
Image 2 Caption:
Eclipse paths for
bi-decade
2021--2040.
The eclipse paths are for both total solar eclipses and annular solar eclipses.
The width of the path is set by region of totality for total solar eclipses and by the region where the annulus of the Sun can be seen for annular solar eclipses.
If counterfactually the Moon's orbit was in the ecliptic plane, we would have total/annular solar eclipses every new moon, the eclipse paths would be confined to the tropics: i.e, ∼ 23.4 south latitude to ∼ 23.4 north latitude.
So the umbra on an eclipse path moves mainly eastward on the surface of the Earth.
Yours truly recalls from somewhere that the umbra on/over the Earth for ∼ 3.5 h at most???.
v = 1.022 - 0.46511 = 0.5569 km/s = 33.41 km/m = 2005 km/h .
The actual minimum eclipse path velocity varies a bit depending on various factors and is more typically ∼ 1700 km/h (see Wikipedia: Solar eclipse: Occurrence and cycles).
The maximum fiducial minimum eclipse path velocity occurs at the Earth's poles where the Earty is NOT rotating at all. The value is, of course 1.022 km/s = 3679 km/h.
Because of the rotation of the lunar node line solar eclipses can happen at any time of the year.
But where can they happen?
The above eclipse-path figures suggest that total solar eclipses can occur anywhere on Earth.
This is true.
The orbital inclination of the Moon takes the Moon above and below the ecliptic plane by an amount greater than the Earth's radius.
If it didn't, there would be solar eclipses every lunar month.
But those same swings above the ecliptic plane mean that solar eclipses will happen at any latitude.
The lunar umbra can touch down anywhere from the equator to the poles.
Now eclipse paths collectively sweep through all longitudes.
So the lunar umbra will occur eventually at all longitudes. These occurrences are NOT completely correlated with latitude for different solar eclipses.
The upshot is that eventually total solar eclipses and annular eclipse will occur at all places on Earth
The estimate is partially illustrated in the figure below.
Caption: All total solar eclipse paths for 1001--2000 CE.
The eclipse paths cover most of the Earth and overlap extensively.
There are some missed regions.
But it is estimated that on average every place on Earth gets a totality every 370 years (Wikipedia: Solar eclipse: Occurrence and cycles).
So if you wait long enough, a total solar eclipses will come to you.
Credit/Permission: ©
User:Yaohua2000,
Fred Espenak (1953--)
2005 /
User:Yaohua2000,
Eclipse predictions courtesy of Fred Espenak,
NASA/Goddard Space Flight Center.
Image link: Wikipedia:
File:Total Solar Eclipse Paths- 1001-2000.gif.
A total solar eclipse is what people travel to see---and with any luck they arn't clouded out.
It's what people want to see.
It's dark as night in the day, animals get confused, Sun gets eaten.
Total solar eclipses are so rare in any locality on Earth (only once every 370 years on average it is estimated: Wikipedia: Solar eclipse: Occurrence and cycles), that they must have been unprecedented and terrifying events for most pre-literate or low-literate societies.
The eclipse path map above (see Total Solar Eclipse Path Map 2001--2025) shows the opportunities for year 2001--2025 period.
The U.S. will get total solar eclipses in 2017 Aug21 and 2024 Apr08.
The 2017 Aug21 total solar eclipse will pass near Topeka, Kansas---but why should you care about Topeka, Kansas.
Here are images in the two figures below From Russia with Love (1963 film).
Caption: A collage of the Total solar eclipse of 2008 Aug01 taken in Novosibirsk, Siberia, Russia.
Click on image and then again to see the high resolution version.
The image is based on 38 photos.
In all except the central photo, you are seeing the photosphere with Moon biting it: i.e., partial solar eclipse photos.
In the central photo, one has totality: i.e., the solar photosphere is completely covered.
ONLY during totality is safe to view the Sun with the naked eye: see NASA: Eye Safety During Solar Eclipses.
The exposure time for the central photo may have been much longer than the others---but I don't know for sure.
The long exposure time may be needed to bring out the outer layer of the Sun called the corona---NOT a beer, but a wispy white halo only visible to the naked eye during totality.
The animation shows File:Solar eclipse animate (2008-Aug-01).gif by A.T. Sinclair shows the eclipse.
Credit/Permission: ©
User:Kalan,
2008 /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:2008-08-01 Solar eclipse progression with timestamps.jpg.
Caption: A partial solar eclipse image of the Total solar eclipse of 2008 Aug01 taken in Moscow---the one in Russia---NOT my old home Moscow, Idaho.
There was no totality in Moscow---just a partial solar eclipse there.
If you didn't know there was going to be partial solar eclipse and it was cloudy, you may never notice that there was one.
If it wasn't cloudy, you might think it odd that sunlight seems a little dim without obvious clouds. You might guess there was some haze.
Actually, sunlight filtering through leaf cover might give rise to odd crescent shape patches of light. The holes in the leaf cover giving rise to crude pinhole projections.
Credit/Permission: ©
Pavel Leman,
2008 /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Solar eclipse of 2008 August 1.JPG.
And one more From Russia with Love (1963 film) in the figure below (local link / general link: solar_eclipse_total_2008aug01k.html).
Caption: An image of the Total solar eclipse of 2008 Aug01 taken in Novosibirsk, Siberia, Russia.
Note that the sky is NOT dark and there is quite a bit of horizon light for some reason, perhaps from city lights of Novosibirsk. I think the image is high-sensitivity in order to show a lot of corona around the Sun.
Stretching away from the Sun to the upper left is the ecliptic on which nearly are seen Venus and Mercury which is only about 1/4 of the distance from the Sun as Venus and much fainter.
Venus and Mercury are inferior planets, and so must always be close to the Sun on the sky. Venus' maximum greatest elongation is ∼ 47° (see Wikipedia: Venus: Observability) and its orbital inclination to the ecliptic is 3.39458°. Mercury's maximum greatest elongation is 27.8° (see Wikipedia: Mercury: Observation) and its orbital inclination to the ecliptic is 7.005°. The different orbital inclinations of the two inferior planets are why they are NOT on the same line.
Finally, at the about the distance from Venus as Venus is from Mercury one does NOT (but one person claims one should) see Saturn as a faint red dot. As Saturn is an outer planet, it can have any angle with respect to the Sun on the sky. It probably has to be farther away than the Sun in spatial distance to be as close to the Sun in angle as it is claimed to be in this image.
Credit/Permission: ©
Michael
2008
(uploaded to Wikimedia Commons
by User:High Contrast,
2010) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikimedia Commons:
File:Solar eclipse of 2008 August 1st in Novosibirsk, Russia.jpg.
Local file: local link: solar_eclipse_annular.html.
File: Eclipse file:
solar_eclipse_total_2008aug01.html.
Caption: A three quarters partial solar eclipse.
There seems to be a sunspot in the upper part of the crescent Sun near the Moon's limb. Recall, in astro jargon, a limb is the edge of an astro-body's projection on the sky.
Credit/Permission: ©
Bill Livingston, NSO/AURA/NSF,
NOAO/AURA /
NOAO/AURA Image Library Conditions of Use.
Image link: Itself.
Downloadsite: Bill Livingston, NSO/AURA/NSF.
Local file: local link: noao_solar_eclipse_001c.html.
File: Eclipse file:
noao_solar_eclipse_001c.html.
Caption: A total solar eclipse with the corona.
Credit/Permission: NSO/AURA/NSF,
1970 /
NOAO/AURA Image Library Conditions of Use.
Download site: NSO/AURA/NSF.
Image link: Itself.
Caption: The diamond ring effect.
In the diamond ring effect, the solar photosphere just peeps through a single notch (e.g., valley) at the edge of the lunar disk.
Credit/Permission: ©
National Solar Observatory (NSO),
AURA,
NSF,
Bill Livingston/NSO/AURA/NSF,
1983 /
NOAO/AURA Image Library Conditions of Use.
Download site: Bill Livingston/NSO/AURA/NSF.
Image link: Itself.
Caption: A set of images of the Solar eclipse of August 11, 1999.
I think the images are a sequence. The end ones are partial solar eclipse images.
The middle one shows totality with a clear corona.
The others may be just different exposures times for totality, but I think they might be just on the verge of totality.
The 2nd to last image on the right seems to be showing the diamond ring effect.
The solar prominences (the reddish features) seen.
Credit/Permission: Luc Viatour AKA User:Lviatour /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia;:
File:Film eclipse soleil 1999.jpg.
We will discuss the corona and solar wind later in IAL 8: The Sun.
But we can give brief discussion here.
The obvious surface of the Sun---the thing that the Moon just covers in a total solar eclipse---is the solar photosphere as discussed above.
This is the surface of the Sun from which most of the light travels to us without further scattering by solar matter.
But there are very rarefied layers of the Sun above the photosphere.
The corona is the most obvious outer layer though it is only visible to the naked eye during a total solar eclipse.
The corona is a very tenuous, but very hot, gas of solar composition (hydrogen and helium mainly).
It's temperature is of order 10**6 K which is much hotter than the photosphere which is about 6000 K.
The corona's low density causes it's low emission even though it is extremely hot.
To the eye the corona is a milky white.
The corona varies in time, and so looks a bit different in all images. It's part of solar weather.
Of course, the images themselves are taken with different exposure times, and so all images look different for that reason too.
Because of its high temperature all the gas in the corona is IONIZED: the atoms are split into positively charged particles atoms---which are called ions---lacking some or all of their electrons and free electrons.
The corona really has no sharp outer edge. From high-altitude balloons or aircraft it can be traced out to 30 solar radii (Se-151).
The corona just gradually changes into being the solar wind: a stream of solar gas that is being blown out into interstellar space from the Sun.
Caption: "A coronal mass ejection (CME) hits Comet Encke and rips off the comet's tail." (Slightly edited.)
A coronal mass ejection is a very strong blast of the solar wind.
A comet is a rocky-icy body on a high eccentricity elliptical orbit that causes it to plunge into the inner Solar System where sunlight heats it and causes explosive evaporation of the comet's ices.
Comets CANNOT live forever. After some number of passes near the Sun, all their ices have been evaporated and they become extinct comets which are very similar to asteroids. In fact, they are like near-Earth asteroids which means that astronomical perturbations will on the time scale of 10 Myr cause them to impact an inner Solar System astro-body (Sun, Earth, etc.) or be gravitational assisted out of the inner Solar System and in some cases on an escape orbit from the Solar System.
For information on this film, see NASA Science, "The Sun Rips off a Comet's Tail", 2007 Oct01 and spacecraft STEREO (2006--c.2020s). Comet Encke was just inside the orbit of Mecury when this film was captured by spacecraft STEREO (2006--c.2020s). The film is probably in white light (see Wikipedia: STEREO: Science instrumentation: Sun Earth Connection Coronal and Heliospheric Investigation (SECCHI)).
Credit/Permission: NASA,
2007
(uploaded to Wikipedia
by User:0815jan,
2007) /
Public domain.
Image link: Wikipedia:
File:Encke tail rip of.gif.
Local file: local link: coronal_mass_ejection_comet.html.
File: Sun file:
coronal_mass_ejection_comet.html.
The particles in the corona spiral away from the Sun along magnetic field lines (see below). This is what gives the corona a wispy or haired appearance.
The figure below shows the wispy appearance more clearly.
Recall the structure of the corona is time-varying, and so the image is just a typical appearance for some exposure time.
Caption: total solar eclipse 1999 Aug11 as imaged in France.
This was a total solar eclipse.
Around the dark night side of the Moon, the image shows the corona: the white whispy haze around the Sun that is only visible to the naked eye during total solar eclipses.
The corona looks different in all images because it is always changing---it is part of Sun weather---and because of different exposure times in taking the images.
The whispy appearance is because the ions (i.e., charged atoms) that make up the corona are forced to helix around magnetic field lines of the solar magnetic field by the magnetic force.
The corona is very hot (of order 10**6 K), but is so dilute that it radiates low intensity in comparison with the Solar photosphere.
This is why it is safe to view with the naked eye.
The image also shows solar prominences: the red filaments close to the limb of the Moon.
Solar prominences arise in the solar photosphere and extend out in the corona.
Their composition, temperature, and color are similar to that of the chromosphere??? (i.e., the layer of the Sun between solar photosphere and the corona). They are also strongly dependent on the solar magnetic field.
Credit/Permission: ©
Luc Viatour (AKA User:Lviatour),
1999
(uploaded to Wikipedia
by David Iliff (AKA User:Diliff),
2006) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Solar eclipse 1999 4.jpg .
The Sun is surrounded by a complex and time-varying magnetic field.
The magnetic force on free particles caused by this field partially traps the charged particles in the direction perpendicular to the field lines (which we'll discuss later, but you've probably heard of them before).
The particles tend to helix around the field lines.
As a result charged particles of the solar wind tend to helix outward along field lines.
When the solar wind particles interact with the Earth's magnetic field, they can also go into spiral motion as illustrated in the figure below (local link / general link: earth_magnetic_field.html).
Caption: A cartoon of Earth's magnetic field.
Correct "Charge solar wind particle" to "Charged solar wind particles".
A key fact is that magnetic fields tend to cause charged particles to helix along magnetic field lines. This is because the magnetic force acts perpendicularly to the velocity.
Keywords: charged particles, Earth, Earth's magnetic field, helix, magnetic field, magnetic field lines, magnetic force, magnetic poles (magnetic north pole, magnetic south pole), magnetosphere, perpendicular, Van Allen radiation belts.
Credit/Permission: ©
David Jeffery,
2003 / Own work.
Image link: Itself.
Local file: local link: earth_magnetic_field.html.html.
File: Earth file:
earth_magnetic_field.html.
Another feature of the Sun easily visible from the Earth during total solar eclipses are solar prominences.
We will discuss them in a little more detail later in IAL 8: The Sun.
These are vast eruptions of material that can shoot up from the Sun in a few hours and last weeks or months. They are also controlled by magnetic fields it seems.
The solar prominences are part of solar weather. Solar weather is magnetic phenomenon among other things.
The prominences can be seen as little tongues of fire in solar eclipse images: see the figure below (local link / general link: solar_eclipse_prominence.html).
Caption: A total solar eclipse solar prominences: the pink fuzz on the limb of the eclipsed Sun.
Note the Sun's diameter is just about 109 times that of the Earth.
Consequently, the solar prominences are huge---they can be bigger than the Earth.
Credit/Permission: ©
Richard J Kinch (AKA User:Rkinch),
2017 /
CC BY-SA 4.0.
Image link: Wikimedia Commons:
File:Solar eclipse of 2017-08-21 totality short exposure.jpg.
Local file: local link: solar_eclipse_prominence.html.
File: Eclipse file:
solar_eclipse_prominence.html.
Note 10000 K is hotter than the photosphere's 6000 K, but much colder than the 10**6 K that is characteristic of the corona.
Form groups of 2 or 3---NOT more---and tackle Homework 3 problems 25--28 on solar eclipses.
Discuss each problem and come to a group answer.
Let's work for 5 or so minutes.
The winners get chocolates.
See Solutions 3.
Ah Brussels---Belgian chocolate, waffles, Belgian beer---the Germans know nothing about making beer---cafes, Brussels lace, le Sablon, le Musee royau de Beaux-Arts, (avec the Fall of Icarus), Pieter Bruegel the Elder (c. 1525--1569), comics, and Belgian comics---you've heard of Tintin---and my old pal Guy.
Credit/Permission: ©
Chmouel Boudjnah (AKA User:Chmouel),
before or circa 2005
(uploaded to Wikipedia
by User:Neutrality,
2005) /
Creative Commons
CC BY-SA 3.0.
Image link: Wikipedia:
File:Chocolate fountain.jpg.
Local file: local link: chocolate_fountain.html.
File: Art_c file:
chocolate_fountain.html.
The notes are primarily for the benefit of instructors.
But students who are keeners might like them too.
What is the size of the umbra at a general distance behind an astro-body?
Hm. Tricky.
Let the Sun have radius R, the astro-body radius r, and the umbra radius u.
Let the Sun-astro-body distance be a, the astro-body-umbra-location distance be b, and astro-body-umbra-location-to-umbra-apex distance be c.
You are encouraged to draw the appropriate diagram.
We have three similar triangles with common angle θ that satisfy the following sequence of equations:
tan(θ)=R/(a+b+c) tan(θ)=r/(b+c) tan(θ)=u/c u/c=R/(a+b+c) u/c=r/(b+c) (u/c)(a+b+c)=R (u/c)(b+c)=r (u/c)a+r=R (u/c)(b+c)=r (u/c)a+r=R u(b/c+1)=r (u/c)a+r=R 1/c=(r/u-1)/b ua(r/u-1)/b+r=R (a/b)(r-u)+r=R r-u=(b/a)(R -r) u=r-(b/a)(R -r) u=r[1+(b/a)-(b/a)(R/r)] u=r[1+(b/a)(1-R/r)] .
So the formula for the umbra radius is
u=r[1+(b/a)(1-R/r)] . In the usual case, R/r >> 1, and so u≅r[1-(b/a)(R/r)] .
For a lunar eclipse, b/a ≅ 1/400 and R/r ≅ 100. Thus,
u≅ 6400 km * (1-1/4) = 4800 km .
which is approximately correct (see How big is the Earth.s shadow on the Moon? ).
The umbra diameter at the Moon is about 9600 km.
For a solar eclipse, b/a ≅ 1/400 and R/r ≅ 400.
u ≅ 0
which is approximately correct. The Moon's umbra at the Earth is very tiny by comparison to the other length scales. One must do an accurate precise calculation to get an accurate precise answer. And the answer changes with the location of the Moon in its orbit.
Sometimes u will be negative.
Then c will also be negative and the mathematical solution is valid. However, there is no umbra for c < 0. This is the situation of annular eclipses.