IAL 3: The Moon: Orbit, Phases, Eclipses, and More

Don't Panic

Sections

  1. Visions of the Moon
  2. Introduction
  3. The Moon and Timekeeping
  4. Moon Facts
  5. Phases of the Moon
  6. Lunar Rotation and Tidal Locking
  7. Eclipses
  8. Lunar Eclipses
  9. Solar Eclipses
  10. Background Notes: Not a Required Reading

  1. Visions of the Moon

    2. Some visions of the Moon:

  2. Introduction

    He rode a sliver of moonlight
    to the height of a jerry hill,
    turned and backed into black night,
    whither and whither still.

    In this lecture, we consider the     Moon as an astronomical object in the old sense---a body seen on the sky, its motions on the sky, and its role in eclipses.

    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, it's always been with us.

    The figure below (local link / general link: wolf_norse.html) illustrates the Sun and Moon in Norse mythology.

    And, of course, the     Moon turns up in Greek mythology as illustrated in the figure below (local link / general link: artemis.html).

    Although much fainter than the     Sun, the Moon, particularly at full moon or nearly full moon, is a significant light source, very noticeable in the absence of modern lighting---moonlight, you know. The Moon is the brightest astronomical object in the sky after the Sun.

    In fact, astronomers, when NOT looking at the Moon itself, consider moonlight a source of light pollution and are always desirous of dark time when the Moon's away.

    Of course, other traditional problems come with a full moon (see figure below: local link / general link: alien_werewolf.html).

    But some find a happy     Moon (see figure below: local link / general link: mikado.html).

    On the other hand, some have always wanted to take a shot at the     Moon (see figure below: local link / general link: georges_melies_moon.html; see videos below: local link / general link: moon_videos.html).

    Still for the     Moon, past images of the future continue to tantalize (see figure below: local link / general link: moonbase.html).

  3. The Moon and Timekeeping

    4. The Moon since prehistory---probably as far back as people could count---has been used CALENDRICALLY: e.g., "it was many moons ago" is a perfectly sensible thing to say. MOON in "it was many moons ago" is a synonym for lunar month (AKA lunation) which is the time period for a full cycle of the lunar phases.

    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.

    1. The Lunar Month:

      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_2b.html).

      If you count the       lunar month as starting from the first visible crescent after new moon as was often done, then the lunar month alternates between 29 and 30 days. And if you had to wait out cloudy evenings to see a crescent for the first time in a lunar month, then the old month could be longer than 30 days and the new month shorter than 29 days.

      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.

    2. The Lunisolar Calendar:

      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.

      But despite this discrepancy in day counts, many ancient societies tried to count years in lunar years and solar years at the same time: i.e., they used a lunisolar calendar.

      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).

    3. The Metonic Cycle:

      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).

    4. Julius Caesar Reforms the Calendar:

      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).

    5. The Seven-Day Week: Reading Only:

      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).

      The origin of the       seven-day week seems to be in the practice of the ancient Babylonians who started a 4-week cycle with the first crescent (see Wikipedia: Seven-day week: Origins).

      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

      29.53059 days/4 ≅ 7.4 days .

      Note also, the quarters of the lunar month are clearly marked by the phases: new moon, 1st quarter moon (which is a half moon), full moon, and 3rd quarter moon (which is also a half moon).

      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.

  4. Moon Facts

    5. In this section, we look at a few Moon facts, especially those pertaining to the Moon's orbit.

    Some Moon facts are summarized in the list (local link / general link: moon_facts.html).

    And the figure below (    local link / general link: moon_numbers.html) illustrates some Moon facts graphically.

    Let's expand a bit on some of the facts:

    1. The Mass of the Moon:

      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.

    2. The Diameters of the Earth, Moon, and Other Solar System Rocky-Icy Bodies:

      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.

      The figure below (local link / general link: rocky_icy_body.html) illustrates the ranking of the rocky-icy bodies of the Solar System in order of decreasing diameter: the Earth is number 1 and the Moon ranks pretty high too at number 9.

    3. The Sidereal Month: AKA the Moon's Orbital Period:

      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.

    4. The Eccentricity of the Moon's Orbit:

      The eccentricity of the Moon's orbit is 0.0549 or 5.49 %.

      This means the Earth-Moon distance varies up and down from the mean Earth-Moon distance by about 5.5 %. The total range of variation is 11 %.

      The 11 % variation in DISTANCE causes Moon's apparent angular diameter to vary by 11 % too.

      The variation in angular diameter is probably too small ever to be noticed by casual observation since we usually see the Moon at perigee and apogee without a convenient sufficiently accurate natural STANDARD OF COMPARISON.

      But difference in angular diameter of the Moon is striking if you directly compare the angular diameters at perigee and apogee as in the figure below (local link / general link: moon_angular_diameter_variation.html).

    5. The Orbital Inclination to the Ecliptic of the Moon's Orbit:

      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).

      The       Moon's orbital inclination has a important consequences for eclipse phenomena.

      Now for the lunar node line: see the figure below (local link / general link: moon_node_line.html).

      The figure below (local link / general link: eclipse_season.html) explains when eclipses can occur: i.e., the eclipse seasons.

      We discuss eclipses, nodal alignment, and eclipse seasons further below in sections Eclipses, Lunar Eclipses, and Solar Eclipses.

    6. End of Moon Facts

      So much for these Moon facts.

      There are more Moon facts below, of course.

  5. Phases of the Moon

    6. The Moon has phases (i.e., varying amounts of illumination) because we see varying amounts of the day and night sides of the Moon as it orbits around the Earth.

    A nice waning crescent moon is shown in the figure below.

    1. The Lunar Phases Explicated:

      The lunar phases are explicated in the figure below (local link / general link: moon_lunar_phases.html).

      The       animation in the figure below (local link / general link: moon_lunar_phases_animation.html) shows the lunar phases---and the lunar libration too which we will briefly consider below in section Lunar Rotation and Tidal Locking.

    2. Lunar Phase Questions Are a Big Deal:

      In this IAL lecture, lunar phase questions are a big deal.

      It's true that simple lunar phase questions often seem very difficult to people.

      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.

      The       applet in the figure below (local link / general link: naap_lunar_phase.html) dynamically illustrates the lunar phases.

    3. Lunar Phase Videos:

      Some lunar phase videos:

    4. Example Lunar Phase Questions:

      Let's do 3 examples of lunar phase problems.

      1. The Moon is full and it is sunset. Where is the Moon on the sky?

        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).

        The         Moon must be on the eastern horizon. It is just rising. It is in opposition to the Sun as it must be when it is full.

        If the time were midnight, then the Moon would be transiting the meridian.

      2. The Moon is in the eastern sky at sunrise. What is its phase?

        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.

      3. The Moon is half-full at 1st quarter moon and is transiting the meridian. What time of day is it?

        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.

      Now for another question, see the figure below (local link / general link: moon_cow_spoon.html).

      Here are other examples that the       students can read through and solve at their leisure to see how everything goes.

      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).

    5. The Angular Velocity of the Moon:

      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 fixed stars),
    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.

  6. Lunar Rotation and Tidal Locking

    7. The Moon's axial rotation rate is on average equal to its orbital rotation rate. And, in fact, the rates are very nearly exactly equal all the time whether relative to the observable universe or the Sun.

    This behavior is because of tidal locking.

    We discuss the Moon's tidal locking and tidal locking in general in the subsections below.

    1. Tidal Locking and Our View of the Moon:

      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.

      Throughout       human history until 1959, the far side of the Moon was a mystery.

      The figure below (local link / general link: moon_map_side_far.html) shows the unfamiliar far side of the Moon.

      Another illustration of the tidal locking of the Moon to the Earth is shown by the animation in the figure below (local link / general link: tidal_locking_moon.html).

    2. The Cause of Tidal Locking:

      Tidal locking is a gravitational effect.

      A mutually orbiting pair of astro-bodies tend to become tidal locked to each other (i.e., always face to each other with the same sides) 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).

      Typically, the pair are NOT formed in a       tidally locked configuration.

      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:

        The closer the astro-bodies the stronger the tidal locking effect.

        The more massive the astro-body of any pair resists tidal locking more strongly because it usually has larger rotational inertia (which is a measure of the resitance to changing its axial rotation rate) simply by having more mass. Everyday experience shows that it is harder to change the rotation of a massive body than a less mass of body all other things being equal.

        The complicating effects of other astro-bodies are various. But one thing is clear, an astro-body CANNOT be tidal locked to two other astro-bodies (except maybe in some very unusual cases). For example, the Moon CANNOT become tidal locked to the Sun without stopping being tidal locked to the Earth---it CANNOT serve two masters.

      The figure below (local link / general link: tidal_locking_origin.html) explicates the origin of tidal locking.

    3. Tidally Locking in the Solar System:

      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).

    4. Tidal Locking Throughout the Observable Universe:

      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.

    5. Can the Earth Become Tidally Locked to the Moon?

      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.

    6. Tidal Locking to the Sun:

      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.

        A planet CANNOT be tidally locked to the Sun and a moon simultaneously---or to two moons simultaneously.

        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.

      But Mercury and Venus are both rather strange cases. Let's skip Venus until IAL 13: Venus. Its rather strange spin-orbit (i.e., rotation-orbit) characteristics are NOT fully explained yet---at least according to Wikipedia: Venus: Orbit and rotation, circa 2018.

      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.

  7. Eclipses

    8. In this section, we cover some general topics on eclipses. In sections Lunar Eclipses and Solar Eclipses, we specialize to, respectively, lunar eclipses and solar eclipses.

    1. Eclipses in General:

      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 universe---e.g., Mars as illustrated in the film in figure below (local link / general link: mars_phobos_transit.html).

    2. An Inconsistency in Our Eclipse Terminology:

      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.

    3. Eclipses in as Seen from the Earth:

      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).

  8. Lunar Eclipses

    9. Now for lunar eclipses.

    1. Some Basic Facts Re Lunar Eclipses:

      1. Lunar eclipses can only occur during eclipse seasons: i.e., near the times when the lunar node line aligns with the Earth-Sun line. This happens every 173.31 days as discussed above in the section The Moon's Orbit. Exact alignment is NOT necessary since Earth, Moon, and Sun all have finite sizes.

      2. Also lunar eclipses can only occur at full moon: i.e., when the Moon is in opposition to the Sun.

    2. Lunar Eclipses Require the Earth's Umbra and Penumbra:

      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).

        Umbra is Latin for shadow.

        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.

      The Earth has an umbra and penumbra due to the Sun as explicated in the figure below (local link / general link: earth_umbra.html).

    3. The Three Main Lunar Eclipse Types:

      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).

      Now to expand on the three main       lunar eclipse types:

      1. Total Lunar Eclipse: In a total lunar eclipse, the Moon goes entirely inside the umbra and is quite dim compared to the ordinary full moon phase.

        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).

      2. Partial Lunar Eclipse: In a partial lunar eclipse, the Moon goes partially into the umbra.

        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: I assume 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.

      3. Penumbral Lunar Eclipse: In a penumbral lunar eclipse, the Moon is only in the penumbra of the Earth and is never touched by the umbra.

        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.

    4. Frequency of Lunar Eclipses:

      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
_____________________________________________________________________________________________________________

    5. Total Lunar And Solar Eclipses as Spectacles:

      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.

    6. Total Lunar Eclipses:

      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).

        EOF
    7. The Coppery Colored Moon:

      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.

      The       Earth's atmosphere has a continuous variation in properties, and so give a continuous bending or refraction effect.

      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).

      The scattering of bluish light is, of course, the reason why we have a       blue sky. We are see the scattered sunlight.

      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).

      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.

    8. A Lunar Eclipse as Seen from the Moon:

      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 have have been seen as the figure and caption below show.

    9. Scientific Value:

      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).

      In the past,       lunar eclipse were scientifically interesting.

      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.

        Question: Everyone on the night side of the Earth can see a total lunar eclipse. They see each part of the event at:

        1. the same clock time: i.e., they would all read the same time off their own local clock.
        2. the same time as read from the position of the Sun: i.e., true solar time for wherever they were on Earth.
        3. the same time. Really, really, the same time (i.e., simultaneously) NOT counting light travel-time effects, or special or general relativity effects.











        Answer 3 is right.

      Comparisons observations of lunar eclipses from different locations was one of the first ways that people became aware that solar time (i.e., time told by the Sun) depended on longitude.

      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.

  9. Solar Eclipses

    10. Now for solar eclipses.

    1. Some Basic Facts Re Solar Eclipses:

      1. Solar eclipses can only occur during eclipse seasons: i.e., near the times when the lunar node line aligns with the Earth-Sun line. This happens every 173.31 days as discussed above in the section The Moon's Orbit. Exact alignment is NOT necessary since Earth, Moon, and Sun all have finite sizes.

      2. Solar eclipses can only occur at new moon: i.e., when the Moon is in conjunction with the Sun.

      3. More on the inconsistency in terminology between lunar eclipse and solar eclipses:

        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.

    2. Three Main Types of Solar Eclipses:

      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.

      1. Total Solar Eclipse: In a total solar eclipse: The Sun is totally covered by the Moon.

        For a discussion of total solar eclipses and annular solar eclipses, see the figure below (local link / general link: solar_eclipse_geometry.html).

        See the figure below for a pretty big umbra on the Earth: i.e., totality region

        We'll look at some total solar eclipse images in the subsection The Main Event: The Total Solar Eclipse below.

      2. Annular Solar Eclipse: An annular solar eclipse occurs when the Moon passes directly in front of the Sun, but the Moon is at a relatively distant part of its orbit, and so CANNOT cover the photosphere of the Sun.

        The uncovered photosphere appears as a bright ring around the black Moon. Annulus is just Latin for ring.

        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).

        Annular solar eclipses are somewhat more frequent than total solar eclipses.

        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.

      3. Partial Solar Eclipse: A partial solar eclipse occurs when the observer is in the lunar penumbra.

        From the observer's location, the Sun is a crescent.

        But NEVER look at any part of the solar photosphere with the naked eye.

        Partial solar eclipses don't 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 without noticing a thing.

        Partial solar eclipses without total and/or annular solar eclipses happen about 35.3 % of the time. But they cause no great popular interest.

    3. Frequency of Solar Eclipses:

      Just as with lunar eclipses, solar eclipses can happen only near a nodal alignment which happens 173.31 days.

      Total and annular solar eclipses combined are more frequent than just partial solar eclipses.

      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
_________________________________________________________________________
    4. Eye Safety:

      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).

    5. The Great Coincidence:

      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).

    6. The Moving Umbra:

      The Moon's umbra follows an eclipse path on the Earth.

      Two motions are compounded to make the umbra move:

      1. The Moon is moving east on the sky causing it's umbra to move east.
      2. The Earth is spinning east as well.

      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.

      We can do a nifty approximate calculation of the speed of       umbra on or over the Earth.

      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).

      The figure below shows another nice a nice umbra.

    7. The Saros Cycle:

      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).

      See figure below (      local link / general link: assyria_bas_relief_ninurta.html) apropos of ancient Mesopotamia and remotely Babylonian astrology.

    8. Predicting Solar Eclipses:

      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).

    9. Where Can Total Solar Eclipses Occur?

      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 above argument is NOT completely rigorous. I still looking for one of those.

      It is estimated that on average every place on Earth gets a totality every 370 years (Wikipedia: Solar eclipse: Occurrence and cycles).

      The estimate is partially illustrated in the figure below.

    10. The Main Event: The Total Solar Eclipse:

      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.

        It will probably be a cloudy day there then---maybe with tornados.

      There are great solar eclipse images on the web---and nowadays at last some can be used---with proper credit.

      Here are images in the two figures below From Russia with Love (1963 film).

      And one more From Russia with Love (1963 film) in the figure below (local link / general link: solar_eclipse_total_2008aug01k.html).

      Here are some other total solar eclipse figures below (      local link / general link: noao_solar_eclipse_001c.html; others unlinked) and below them are Solar eclipse videos (local link / general link: eclipse/solar_eclipse_videos.html)

        EOF
    11. Corona and Solar Wind:

      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.

      The mechanism causing the       solar wind is NOT entirely understood, but it is a small loss and has no great effect on the Sun's overall properties at present.

      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.

    12. Magnetic Fields: Just a Brief Word:

      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).

    13. Solar Prominences:

      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).

      The red color of       prominences comes from the emission of strongest visible line of the hydrogen atom (i.e., the Hα) at temperatures of order 10000 K (Se-150,160).

        We will discuss lines in IAL 7: Spectra but for now they are just narrow wavelength bands in which atoms emit light.

      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.

  10. Background Notes: Not a Required Reading

    11. Background notes are NOT a required reading.

    The notes are primarily for the benefit of instructors.

    But students who are keeners might like them too.

    1. Umbra Size:

      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.