Rubaiyat of of Omar Khayyam, 1st edition, Verse 1 by Omar Khayyam & Edward Fitzgerald
And you know it is REMOTE because the astro-bodies to the unaided eye and even to simple instruments shows NO parallax.
Answer 2 is right.
Ergo, the astro-bodies are very remote compared to the size of the Earth.
No parallax for small displacments: i.e., small baselines.
If you just stay in one region of the Earth, the astro-bodies could be pasted on a big DOME OF THE SKY over the ``flat Earth.''
Perhaps the ancient Sumerians and Babylonians, who never got out of the Tigris-Euphrates valley, perceived the sky this way---I don't think we know---they probably had various ideas.
Perhaps they thought Babylon was the center of the universe. Some days it still seems that way. As Alexander may have said ``How many miles to Babylon?''
Babylonian cosmology?
Then you might guess that the sky was a
There is no right answer.
If you can't tell distances to astro-bodies, you can't say anything about the geometry of the astro-bodies in 3 dimensional space.
But the simplest picture is that the astro-bodies are pasted on a big sphere that surrounds the Earth.
No simple observation contradicts this CELESTIAL SPHERE THEORY.
The CELESTIAL SPHERE THEORY even makes philosophical sense if you know the Earth is ROUND and believe it is at the CENTER OF THE COSMOS.
An early sketch by Parmenides of Elea (early 5th century BCE) of his
round Earth model.
In fact they did measure the distance to the Moon and eventually figured out it was at about 60 Earth radii away (No-102).
But the they never did get any of the other distances which are much larger, of course.
Their geometry was strong, but their instruments were weak.
So in their geocentric, round Earth view of the dominant Aristotelian theory, the fixed stars were pasted on a rotating celestial sphere.
The other astro-bodies were carried on other compounded, invisible spheres. See IAWL Lecture 4: History of Astronomy to Galileo.
The Aristolelian cosmos was passed on to the Middle Eastern, Indian and European societies.
When COLUMBUS met the professors of the Salamanca University, he didn't have to convince them that the world was round: they already knew that.
He had to convince them that a voyage of practical length could reach China. They said he was wrong and they were right.
And COLUMBUS never did get to China.
But it just goes to show you should always listen to your professors, right?]
The planets and stars are NOT pasted on a big sphere, but spread through space.
But for purely positional astronomy---i.e., finding astro-bodies on the sky---the CELESTIAL SPHERE THEORY works.
You can locate astro-bodies on the celestial sphere by angular position and the angular positions are the same for everyone on Earth because there is NO SIGNIFICANT parallax as you move about the Earth or, for extra-solar-system bodies, as the Earth moves about the SUN.
The basic idea of the
celestial sphere.
Very often in science you have a theory or model that you know is wrong, but it works for some special purpose and it's easy to apply.
Therefore you use it for that special purpose.
The CELESTIAL SPHERE THEORY---which is a very, very wrong theory---is in this category.
Special points and circles can be readily located on the celestial sphere.
These help with finding astro-bodies on the celestial sphere and tracing their motion.
celestial sphere
elaborated.
The extension of the Earth's axis forms the celestial axis with a north celestial pole (NCP) and a south celestial pole (SCP).
Polaris is the handle end star of the Little Dipper. The Little Dipper is not a particularly obvious constellation and finding Polaris directly is not quite easy. But the Big Dipper can easily be identified and a line northward from the two end stars of the bowl point nearly to Polaris: these stars are called the pointer stars.
Technically the Little Dipper and Big Dipper are asterisms [groupings of stars on the sky] in modern precise definition. They are, respectively, part of Ursa Minor and Ursa Major constellations.]
Now the Earth rotates eastward daily in the frame of the Sun and the fixed stars, but if you take the Earth's as your frame of reference, the whole celestial sphere rotates west.
This means that most astro-bodies are carried around daily on on the celestial sphere on circles parallel to the celestial equator.
There are TWO COMPLICATIONS in seeing the circling of the astro-bodies:
The Earth is round, but to a little human anywhere on the Earth seems like an infinite flattish plane.
celestial sphere
elaborated again.
A simple example is an observer at the NORTH POLE or the SOUTH POLE. He/she would see one hemisphere of the celestial sphere spin around: no star would ever rise of set.
Stars that never rise or set are called CIRCUMPOLAR: thus all the stars that a North or South Pole observer would see are circumpolar.
The schematic sky map shows sky from the North Pole.
The edge of the sky map is at the observer's horizon: every direction is due south on the Earth.
A few constellations are shown in outline approximately: the Little Dipper, the Big Dipper and the pointer stars, Cassiopeia, and Gemini.
The curve across the sky is the ecliptic which we will discuss below. It is the path of the Sun on the sky.
If you are NOT at the North Pole, the NCP is NOT at zenith and the stars do NOT move in circles around zenith.
They move in circles around the celestial axis.
In the northern hemisphere looking to the north, the NCP is above the horizon and you see the stars circling it. Those stars sufficiently close to the NCP that they don't pass below the horizon are circumpolar as aforesaid.
We can show a diagram of their motion.
Star paths looking north.
A long exposure photograph shows this motion too.
GEMINI NORTH is an 8-meter telescope on Mauna Kea, Hawaii.
Mauna Kea is at 4,145 m (13,600 ft) and is one of the world's best observing sites---located fortunately in one of the world's best tourist sites---still the air is thin up on the mountain.
Here we see a swirl of stars.
The star trails seem to be about 30 degrees, and so the exposure was about 2 hours.
Is the image looking:
Answer 3 is right.
There is METEOR trail just about perpendicular to the star trails.
The red-yellow streaks are the tail lights of cars driving up the mountain during the exposure
Looking at this image it is possible to why some of the ancient Greek philosophers imagined the cosmos as a giant VORTEX (Fu-140).
Credit: Gemini Observatory /NOAO /AURA/NSF.
In the northern hemisphere looking to the south, the SCP is below the horizon and NO stars stay above the horizon all the time.
There are stars that are always below the horizon: those sufficiently close to the SCP.
Stars that are always below the horizon can be called circumpolar too.
Star paths looking south.
In the northern hemisphere, how far in angle above the horizon is the NCP: i.e., what is its altitude?
A great circle is a circle that cuts a sphere in half.]
NCP altitude and latitude. (Internet Explorer won't show this
image!!! Netscape does.)
Thus, the local altitude of the NCP is equal to the local latitude value.
Answer 2 is right.
Las Vegas is at latitude 36 degrees 10 arcminutes 19 arcseconds north and longitude 115 degrees 8 arcminutes 38 arcseconds west.
Answer 2 is right.
A spread hand is about 18 degrees (Se-18).
The system chosen is analogous to terrestrial latitude and longitude. Astro-bodies are located north or south of celestial equator along meridian lines by an angle called DECLINATION.
The NCP is at 90 degrees north declination.
The ``longitude'' angle is called RIGHT ASCENSION or RA and is measured eastward from the vernal equinox (which we will discuss below).
The declination/RA system is fixed to the ``fixed stars,'' and so every day all RAs are visible as where sky spins around us, but NOT all declinations unless we live on the equator since the Earth gets in the way.
Right ascension and declination.
There is also a LOCAL MERIDIAN SYSTEM. The meridian is the meridian that passes from due north on your horizon through your zenith: i.e., the point straight up from the center of the Earth through your location.
When an astro-body crosses the meridian that is called TRANSITING the meridian
Transiting
the meridian
What is the special name for when the Sun transits the meridian?
Noon!
But not clock noon. True solar noon. In the old days,
clocks were set by local solar time and that was good enough.
But once railroads and railroad schedules came along, time
had to be standardized for a fairly large region of the
Earth, and so
A cruder, but more easily remembered way of locating an astro-body is to located it by what constellation it is in.
One can say, for example, that the Sun is in Aquarius about March 1 (Se-21).
We will look at constellations in the section Constellations and following sections.
But those changes arn't easily noticed in a human lifetime.
What is obvious is that the SUN, MOON, PLANETS, ASTEROIDS, COMETS AND HUMAN-MADE PROBES AND SATELLITES do change position on the celestial sphere relative to the fixed stars on human time scales.
We'll start with the Sun in this section and consider the other bodies in the section The Moon, Planets, Asteroids, and Comets on the Celestial Sphere.
Physically the Earth goes round the Sun on a nearly circular orbit.
The plane of this orbit is called the ecliptic plane. The ecliptic plane has a perpendicular which we can call the ecliptic pole.
The axis of the Earth is tilted from the ecliptic pole by 23.5 degrees.
From the EARTH'S PERSPECTIVE then the plane of the Earth-Sun orbit (the ecliptic plane) is also tilted by 23.5 degrees from the celestial equator.
The ecliptic plane cuts the celestial sphere in a great circle.
This great circle is the path of the Sun on the celestial sphere as it travels around the Earth in a year.
Thus the Sun moves about 1 degree per day relative to the fixed stars.]
Remember the daily motion is a circle parallel to the celestial equator and westward.
When considering the yearly motion of the Sun, one can think of the celestial sphere as fixed and the Earth as spinning on its axis if that helps.
The highest declination point of the Sun is the summer solstice; the lowest is the winter solstice.
These occur on or about June 22 and December 22.
Where the Sun crosses the ecliptic one has an equinox: the vernal equinox occurs on about March 21 and the fall equinox on about September 22.
Solstice and equinox can mean either the event with the Sun or the point on the sky where the event occurs: context must decide.
The vernal equinox (the point on the sky) is the zero of the RA scale.
Instead of following the Sun on the celestial sphere, you can follow the Earth in its orbit about the Sun and see things from a Sun-centered perspective.
Seasons from the Sun's perspective.
When the Sun is above the celestial equator, it beams more directly down on the northern hemisphere of the Earth and stays above the horizon longer in the northern hemisphere. In fact to some latitude south from the North Pole, the Sun never sets.
The amount of sunlight energy absorbed per unit area by ground surface depends on the orientation of the surface to the incoming beams. The amount is higher, the more directly the beams strike the surface.
The effect of direction on energy (really power)
absorbed per unit area.
The upshot is that the northern hemisphere tends to be warmer when the Sun is above the celestial equator because the beams strike the northern hemisphere ground more directly then.
The heating effect of the Sun in the northern hemisphere summer.
When the Sun is below the celestial equator, you have the reverse situation: the northern hemisphere receives light less directly, days are shorter, the north polar region is always in darkness, and the northern hemisphere tends to be colder.
The heating effect of the Sun in the southern hemisphere summer.
On the equinoxes, the Earth's axis is perpendicular to the Earth-Sun line
At this time, the day and night are both exactly 12 hours everywhere on Earth.
At the North and South Poles, the Sun is steady just on the horizon.
At the equinoxes.
How does the Sun traverse the sky on a day of an equinox as seen from some northern latitude? The figure below shows how.
The Sun's path on the sky on a day of
an equinox.
On a great circle because the Sun is sitting on the celestial equator on an equinox day.
The equinox days have exactly 12 hours of day and 12 hours of night.
When the Sun is above the celestial equator, it is carried about on a circle that is still perpendicular to the NCP, but higher up. It is above the horizon longer than 12 hours.
When the Sun is below the celestial equator, it is carried about on a circle that is still perpendicular to the NCP, but is lower down. It is above the horizon less than 12 hours.
The illumination by the Sun is the MAIN SOURCE OF TERRESTRIAL HEAT at ground level.
About 700 W/m**2 (day side average ????) comes from the Sun and only 8*10**-2 W/m**2 from geothermal heat flux (Col-46).
Of course, there is no net build up of heat energy---if there were, we'd just get hotter and hotter until we fryed.
All the heat we get from visible light (high temperature light) gets re-radiated back to space eventually as infrared light (low temperature light).
The heat sources at the
Earth's surface.
But because it takes time for air, water, and ground to heat or cool, there is a SEASON LAG of about a month between the Sun's energy input to a hemisphere and the average conditions (Se-23).
Thus the hottest period is about a month after the summer solstice and the coldest is about a month after the winter solstice---in the northern hemisphere, of course.
Thus it does make sense to define summer and winter as beginning at their respective solstices.
Spring and fall are defined as beginning at, respectively, the vernal equinox and fall equinox. Similarly that makes sense because of SEASON LAG.
Actually the Earth's orbit is not perfectly circular. It is elliptical with the Sun at one focus.
The Earth's distance from the Sun varies up and down from the mean distance by 1.67 %: i.e., 0.0167 is the Earth's eccentricity.
The PERIHELION is actually in the first week of January and the APHELION in the early July (Se-23).
This distance variation has some effect on climate, but the dominant effect---from a geocentric point of view---is the location of the Sun on the ecliptic.
Answer 1 is right.
Unless you also invoked some wild compensating effect, I think answer 1 is the only valid answer.
The planets, and asteroids move on the celestial sphere near the ecliptic and their direction is EASTWARD MOST OF THE TIME relative to the fixed stars like the Sun.
The Moon's orbital plane is tilted by 5 degrees, 9 arcminutes from the ecliptic (Se-33).
The Earth-Moon system roughly to scale
(Cox-16,305).
The tilts (i.e., ecliptic angles) of the planets can be in the Table of Planet Distances, Eccentricities, and Ecliptic Angles.
The orbits of MERCURY AND PLUTO have the most extreme deviations from the ecliptic plane.
The largest ecliptic orbit angles.
The near alignment of planet and Moon orbits is due to the formation history of the solar system which is discussed in IAWL Lecture 9: The Life of the Sun.
There is some special terminology for alignments of Earth, Sun, and planets.
When outer planets are near the Sun-Earth line and opposite the Sun, then they are said to be in opposition.
Superior conjunction is when any planet is on the Earth-Sun line but is on the far side of the Sun.
Opposition and
conjunction.
The planets as stated above, move EASTWARD MOST OF THE TIME, but they can move WESTWARD on the celestial sphere for relatively short times near opposition for outer planets or inferior conjunction for inner planets.
This WESTWARD MOTION is called retrograde motion.
For example, consider Mars retrograding between constellations Leo and Virgo.
Mars retrograding.
Retrograde motion is a consequence of observing other Sun-orbiting planets from a Sun-orbiting Earth.
To over-simplify for a moment, retrograde motion is like observing a car move backward relative to the landscape when you are passing it.
When the car is far ahead or far behind it appears moving forward relative to the nearby landscape at least: i.e., curbs and shoulders and bushes by the roadside.
It is most easy to understand retrograde motion from a top view of the solar system (i.e., looking down from the NCP side of the ecliptic plane).
First, let us consider Mars as an example of an outer planet.
I leave it as an exercise to the students to understand why inner planets retrograde near inferior conjunction. HINT: Just consider the Mars retrograde motion diagram from Mars' point of view.
Retrograde motion was a great puzzle to the ANCIENT GREEK ASTRONOMERS and led them (along with other things) to epicycle geocentric models of the solar system.
When the heliocentric solar system of Copernicus was introduced, the puzzle of retrograde motion vanished.
These historical issues are discussed IAWL Lecture 4: The History of Astronomy to Galileo.
Answer 2 is right
Yes, it is because SUN and MOON both orbit the Earth geometrically. Thus the situation for retrograde motion never arises.
The asteroids mostly behave like small planets as objects on the sky: but they are unresolvable in ordinary observations and look star-like: hence the name asteroid which means star-like.
They mostly have orbits near the ecliptic plane and move counterclockwise as seen from above and have retrograde motion when in opposition or inferior conjunction.
But there may be some oddballs among the asteroids.
We will discuss asteroids later in Intro-Astro Lecture 16: Minor Planets, Asteroids, Icy Bodies, Meteoroids, and Target Earth.
COMETS? Comets have rather different orbits from the astro-bodies we've discussed above.
Comets have highly elliptical orbits with huge eccentricities. They come in two broad classes: SHORT-PERIOD COMETS and LONG-PERIOD COMETS (Se-569).
The short-period comets have orbital periods less than about 200 YEARS, have orbits at inclinations to the ecliptic plane that tend to be less than 30 degrees, and mostly orbit counterclockwise about the Sun.
Long-period comets can have orbital periods of hundreds of thousands of years ??? and sometimes infinity ??? (i.e., they escape the solar system). Their orbits have random orientations and can be clockwise or counterclockwise.
Schematic long-period comet orbits.
From the above discussion, it is clear that comets can appear anywhere on the celestial sphere: they are not confined to the region near the ecliptic: for example, they can go near or over the NCP and SCP.
The comet facts will be explained in IAWL Lecture 17: Pluto, Icy Bodies, Kuiper Belt, Oort Cloud, and Comets.
For a longer discussion click on the site Constellations, Clusters of Stars, and Star Names.
Let us just look at a sky map with constellations labeled on.
The northern constellations: a mid-winter night-time
view judging from the position of old man Orion.
The Milky Way is not displayed, but it passes through Cassiopeia and over the Betelgeuse (eastern) shoulder of Orion.
Credit: Mount Wilson Observatory StarMap program by Bob Donahue. StarMap is fortran program, but it's been broke since 2000jan03. Download site: Univ. of Tennesse, Knoxville Astro course; more precisely here.
The number of stars that one can see with the unaided eye is only about 2800??? (Unaided-Eye Stars).
Answers 2 and 3 are right.
Thus, these local stars are rather RANDOMLY located on the 2-dimensional celestial sphere.
The local stars are often called the fixed stars.
The orbits by the way, are not fixed either. The stars are subject to constant small GRAVITATIONAL PERTURBATIONS and so their motions are a bit chaotic.
Note ARBITRARY groupings: there is no special physical connection between the stars in a grouping and the groupings could and have been done in many ways.
These groupings we call constellations.
We can't know for sure how ANCIENT CONSTELLATIONS were settled on or why.
Probably the process was somewhat RANDOM itself and the name assigned to a constellation in many cases may have been just MNEMONIC without implying anything intrinsic about the nature of the constellation.
The Big Dipper was certainly so called because it looks like a set of dots outlining a dipper---but certainly it was NOT so identified by all cultures: e.g., in England it is often THE WAIN (the Wagon).
The Big Dipper
But even with connecting lines (which, of course, arn't on the sky) most constellations look like the object they are named for ONLY in an abstract-in-eye-of-the-beholder way.
Without connecting lines, except for the Big and Little Dippers, the shapes of constellations have almost no relation to the names assigned to them.
The names of constellations names were no doubt often assigned to honor a god or a legend.
For example, Taurus (the Bull) which goes back at least to the Babylonians of the 5th century BCE and, perhaps, much earlier, may honor a bull god or a sacred bull. The Golden Calf of the Bible is not forgotten.
Orion and Taurus.
Credit: John Flamstead (Atlas celeste, Paris, 1776, Ed. J. Fortin); modern credit Linda Hall Library; more information.
Then there is Orion.
Betelgeuse imagined by the HST.
Betelgeuse is an M1 Iab red supergiant star. It is 131 pc from Earth.
It is the eastern shoulder of Orion: i.e., the left shoulder on the image.
Orion is, of course, a giant hunter of Greek mythology: he pursued the Pleiades and was slain by Artemis (Ba-855).
The lines joining the stars are NOT present on the sky, of course.
Orion is one of the three constellations anyone can recognize: the other two are the Big Dipper (officially an asterisms in Ursa Major) and Cassiopeia (the big W): both are in the northern sky and are all-year constellations.
Credit: NASA/HST.
Different human cultures have come up with different sets of constellations.
For example, Chhien Lu-Chih (5th century CE) working in the CHINESE TRADITION of astronomy grouped 1464 stars into 284 CONSTELLATIONS (No-139--140).
The Yin-Yang symbol.
The GREEKS had close contacts with BABYLONIAN ASTRONOMY after Alexander's conquest of the Persian empire (circa 330 BCE) (No-17,35,39,93) and probably acquired the Babylonian constellations sometime after 330 BCE.
Greek astronomer Ptolemy (circa 100--175 CE) in his star catalogue groups 1022 fixed stars in 48 constellations many (most???) following the Babylonian constellations (No-113)
Ptolemy's set of constellations are the basic set of classical constellations from which modern constellations of the northern hemisphere sky are derived.
These classical constellations include the Zodiac constellations.
They arn't all animals: there is Libra (Scales) for example.
The word Zodiac is from the Greek meaning circle of animals.
It is actually a belt on the celestial sphere that is centered on the ecliptic and contains, more or less, the Zodiac Constellations.
When Europeans first visited the southern hemisphere they saw stars they'd never seen before, and they eventually started inventing new constellations---the idea of asking the native southern hemispherians for what constellations were already there probably occurred to no one.
The first new southern constellations seem to have been introduced by Johann Bayer in his Uranometria (Augsburg, 1603): he made up 12 new ones including Tucana (Toucan), Grus (Crane), and Phoenix.
Tucana (Toucan), Grus (Crane), and Phoenix.
Credit: Johann Bayer ( Uranometria, Augsburg, 1603); modern credit Linda Hall Library; more information.
In the 17th and 18th centuries there was a lot of making up of new constellations to fill in gaps between the ancient ones. Many of these didn't survive at all.
For examples of 16--18th century images of constellations see constellations from the Great Celestial Atlases downloaded from Linda Hall Library exhibit Out of This World: The Golden Age of the Celestial Atlas.
The IAU decides on the
constellations.
The constellations as mentioned in the above figure are not just the star groupings, but regions on the sky that surround the star groupings in the modern usage. These regions cover the sky without overlap.
So every right ascension-declination location is in some constellation and only in that constellation.
A cartoon of the region of
ursa major and
surrounding constellation regions.
The modern constellations include many of the traditional constellations of Ptolemy and some of the modern inventions particularly for southern hemisphere sky.
A good list of the modern 88 constellations is at the Munich Astro Archive.
The Archive gives the astronomical details and the mythical background if there is one.
There are more objects in the above enumeration because some constellations include multiple objects.]
Any of these non-IAU angular groupings, is an asterism.
In modern usage the term asterism is NOT used for IAU OFFICIAL CONSTELLATIONS. But in older usage an asterism could be a synonym for constellation. These lectures I will use asterism only in the modern sense.
The most famous asterism is the Big Dipper which is still often called a constellation in it's own right, but it is not in the official IAU constellation list: it is part of Ursa Major (the Great Bear).
The Big Dipper
A good photographic image of Ursa Major is at the Stellar Scenes site of Naoyuki Kurita: Naoyuki Kurita's Ursa Major (the Great Bear).
Similarly the Little Dipper (part of Ursa Minor [the Small Bear]) is an asterism. Polaris (the North Star or the Pole Star) is at the end of the handle of the Little Dipper: in year 2000 epoch coordinates it is only 44 arcminutes, 9 arcseconds from the NCP.
Partially, it is just that astronomers and folks in general are FOND of their constellations---they're traditional and part of the romance of astronomy---so we should keep them in an orderly fashion.
The Alien.
There is also a practical use for both professional and amateur astronomers.
The modern constellations (i.e., regions on the sky) provide a useful rough and easily memorized location system---the constellations act as SKYMARKS.
One can always locate an object precisely using declination and right ascension, but for just a ROUGH LOCATION one can use constellation mnemonics: e.g., for Polaris as described above.
Also for a rough position one can say the object is in such or such a constellation: i.e., in that region on the sky that is labeled by that constellation.
For example, one can say there is a bright supernova in Virgo: this is a relatively frequent occurrence since there is a large nearby cluster of galaxies in Virgo (the Virgo cluster), and so bright supernovae are relatively frequently found in Virgo.
The locution object x is in constellation y, although perfectly natural given the modern definition of constellation, does have astrological suggestiveness as if there was a magic sympathy between object and constellations---Venus is Virgo or Venus is in Taurus--- but this is just a vestige of where we've come from.
