Physics Phenomena

"Physics is Fun"

(Feimer's Physics Page)

Astronomy Facts

A. Since who knows when, people have been watching the sky. It has been a means of tracking time, of navigating, of superstition, and a form of entertainment.

B. Looking at the night sky people started doing an imaginary connect the dots with the stars and other celestial objects that appear to be stationary. These patterns of dots connected with imaginary lines are called constellations.  The names given to constellations date back at least to Greek and Roman times with some names referring to their various gods and their mythology. (Here mythology is used in its most basic definition. Mythology refers to a civilization's creation stories.)

C. Some common constellations are the Big Dipper which is actually part of a larger constellation called Ursa Major (the Great Bear) and the Little Dipper, part of Ursa Minor.  Ursa Major is among the largest of the constellations.  The smallest constellation is the Crux.  The patterns made up of the stars and other objects forming the constellations are supposed to look like objects, but most often they don't.  It required imagination and familiarity with myths and legends to see things in the sky when imaginary lines were used to play connect the dots.

D. Constellations are used to specify certain regions of the sky.  On modern star charts the entire sky is divided into 88 constellations. The constellations appear to have changed position since they were first identified by the Greeks some 2500 years ago. That is, for the time of year, the constellations that we see are not exactly in the same place as they were for ancient people.  This shift raises interesting questions in Astrology, because the signs (certain constellations) are not in the same places in the sky as they used to be.  Therefore, if you place any superstitious faith in the pseudo science of astrology, you would either have to be ignorant of the shift in constellation positions, or you would have to pretend real hard that there was no change in position.

E. People noticed that some of the objects in the heavens appeared to move.  The Greeks called these objects planets, which means wanderer. They noticed that while the background stars appeared to occupy the same positions, these planets appeared to change their position with respect to everything else in the sky.

F. There are nine identified planets in our solar system.  They are in the order as they appear moving towards from the sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto.  You may have heard recently the debate over whether Pluto should be called a planet due to its small size and that it is apparently a captured object in the solar system rather than one that formed as part of the solar system. For now, Pluto remains on our list. (My Very Earnest Mother Just Served Us Nine Pizzas)

G. When you watch the night sky, you notice that all of the objects in the night sky appear to be moving across the sky very slowly from east to west. The apparent speed and motion of everything is due to the rotational speed of the earth.  The earth rotates on its axis at about 1,000 miles/hr.
This causes some objects to rise during the night, while others set during the night. We see this in the daytime also, but except for the moon all other objects except for the moon are "drowned" in the bright light from the sun.
Did you know that if you could temporarily turn off the sun in the daytime you would see the sky full of stars.  In fact you would be seeing the sky as it was at night six months earlier.

H. The earth moves around the sun in a period of time equal to 365.25 earth rotations.  On the average we say that the year (the period of the earth orbiting the sun) is on the average 365 days, acknowledging the need for a leap year every 4th year to take up the slack off throwing away 0.25 days every year.  Once every 400th year we throw in a leap year too, because it isn't exactly 365.25 days per year, but is just a tiny fraction over 365.25 each year. That fraction would be about 1/(365.25 x 400) days.

I. When you look at the night sky you are looking outwards into the heavens away from the center of the solar system (the sun).  If you were looking into the solar system, it would be daytime and you would see the sun.  If you wait six months and look at the night sky you are looking out away from the center of the system in the exact opposite direction from six months ago. The night sky as it will look six months from now or as it did look six months ago is the sky blotted out by the luminous sun in the daytime.  All those stars are there, but you can't see them because of the brilliant light of the sun.  Only the moon is close enough and large enough in the sky for the reflected sunlight off of its surface to make it visible in the daytime when it is on the same side of the earth as the sun.

J. The one exception to seeing the sky "behind the brilliance of the sun" is during a total solar eclipse.  When the moon blocks the sun completely over an area of the earth "the stars come out" and you can see the daytime the rest of the sky, the sky you saw at night six months earlier.

K. A lunar eclipse is the opposite of a solar eclipse.  Instead of the moon moving between the earth and the sun (a solar eclipse) casting its shadow on earth, the earth comes between the sun and the moon casting its shadow over the moon.

L. There are so many stars in the heavens no one has an accurate count. It would be reasonable to say trillions and trillions and still be modest in your description. Many of the brightest stars visible to the unaided eye have been named in "ancient" times. The customs and traditions for naming stars have changed over time.  Many stars have Arabic names assigned in medieval times when, among Islamic nations, astronomy was a strongly developed science. Star diagrams show Arabic names for the seven stars in the Big Dipper.  Later, when Latin was used by European astronomers stars like Polaris (the North Star) were named.

M. Naming an memorizing star names can be a real challenge.

1. Johann Bayer (1603) used the letters of the Greek alphabet.

2. In constructing a star name, a Greek letter is used with the Latin possessive form of the name of the constellation in which the star is located.

The Greek letters are:

a b g d e z h q i k l m

u x o p r s t u f c y w

Their names respectively are:

alpha, beta, gamma, delta, epsilon, zeta, eta, theta, iota, kappa, lambda, mu

nu, xi, omicron, pi, rho, sigma, tau, upsilon, phi, chi, psi, omega

3. The 12 constellations of the zodiac with their Latin possessives are listed here.  The zodiac refers to a band of 12 constellations around the sky centered on the ecliptic, the apparent path of the sun across the heavens during each year of time.  Throughout the year the sun is found in front of one of these constellations.  The constellation is not visible due to the brightness of the sun, but it is there none the less.

Constellation   Possessive

Aries     Arietis
Taurus    Tauri
Gemini    Geminorum
Cancer    Cancri
Leo     Leonis
Virgo     Virginis
Libra     Librae
Scorpius    Scorpii
Sagittarius    Sagittarii
Capricornus    Capricorni
Aquarius    Aquarii
Pisces    Piscium

4. In most cases, the brightest star in the constellation is a, the second brightest is b, the third brightest is g, and so on. For example the brightest star in Libra is called a Librae.

5. The drawback to this type of nomenclature such as Johann Bayer's is that the Greek alphabet has only 24 letters.  Any constellation having more than 24 stars of diminishing brightness can't have all of its stars named.

6. Since Astronomers are interested in a whole host of stars beyond the limits of a system such as Bayer's, they make use of designations from standard star catalogues.

7. One early catalog of importance was the Bonner Durchmuterung produced in Germany around the mid-1800's.  This catalogue was prepared by F. W. Argelander at the Bond Observatory and listed 320,000 stars.

8. A commonly used catalogue is the Henry Draper Catalogue, which was produced in the U. S. around 1920. Stars from this catalog are listed by their HD numbers.  For example, HD 87901 is a Leonis (also called Regulus), the brightest star in Leo.  This catalog was named after a physician and financed by his widow.)

9. As you study the night sky you recognize the fact that there are many faint non-stellar objects such as galaxies, nebulae, and star clusters.  Roughly 100 of the brightest non-stellar objects are listed in a well known catalogue by the 18th century French astronomer Charles Messier.  These objects are often refereed to by astronomers by their M numbers.  For example, the Orion Nebula is the 42 object in the list prepared by Messier, and so it is refereed to as M42.

10. William Herschel (19th century) and his son John Herschel observed and catalogued almost 5000 faint non-stellar objects.  J. L. E. Dreyer came along in 1888 and enlarged as well as published this list. He called it the New General Catalogue.  More information was added in the 20 next years such that its listings reached close to 15,000 objects.  Astronomers refer to galaxies and nebulae by their NGC numbers. For example, the Crab Nebula is called NGC1952.

N. The celestial sphere: An imaginary sphere of very large radius centered on the observer or what we can refer to as the apparent sphere of the sky. It is a tool of the mind based upon the sky appearing to be a huge [round] sphere upon which we perceive all of the Celestial objects and their
respective motions.

1. The unaided eye can see about 6,000 (some sources say 7,000) stars over the entire sky.  This means that in the northern hemisphere about 3,000 stars can be seen (3,500).  This is true at any position on the earth.  The viewer can only see above the horizon at what ever position they occupy and accordingly can only see half of the visible sky at any time.

2. The earth rotates from west to east once every 24 hours.  Whereas objects appear to move overhead from east to west during each 24 hour period.  For example, the sun and the moon appear to rise in the east and set in the west.  The stars also appear to rise in the east and set in the west.

3. This daily, or diurnal, motion of the stars is very apparent in a time exposure photograph, because the stars appear as streaks due to their apparent motion, or, if you prefer, due to the rotation of the earth under the objects seen in the sky.

4. Many ancients peoples believed the earth to be the center of the heavens, the universe. They also believed that the stars, etc., were attached to a huge sphere with earth at the center of this immense sphere. This imaginary sphere is still a useful idea to use to discuss the objects and there apparent change in position across the sky. We call this sphere the Celestial Sphere.

5. Now in reality the sky has depth and distances to the various stars are not at the all at the same distance from earth as the Celestial Sphere model would suggest.  Instead the stars are varying distances from earth. Many of the brightest stars are from 10 to 1000 light years away.  Many objects are much, much further away.

6. The brightness of stars and other celestial objects is a function of their distances as well as their real brightness.

7. The Celestial Sphere idea will be used to describe directions to objects in the sky.  When all we want to discuss is position in the sky and not distance or brightness the Celestial Sphere model is a great tool.

8. Description of the Celestial Sphere:

a. Imagine a large transparent sphere with the earth suspended at the center.

b. Now imagine the earth's equator projected out onto the sphere.  This is called the celestial equator.

c. Imagine the earth's north and south pole projected out onto the sphere. These would be called the north celestial pole and the south celestial pole respectively.

d. To describe objects you need to describe both the declination of an object and the right ascension of the object.

--> declination:  This is an angular distance north or south of the celestial equator, measured along a circle passing through both celestial poles. Declination corresponds to latitude on earth.

--> right ascension:  This is the angular distance from the vernal equinox eastward along the celestial equator to the circle used to measure declination.  Right ascension corresponds to longitude on earth.  Traditional practice requires that this angular distance be described in time units of hours, minutes, and seconds. corresponding to the time for the celestial sphere to rotate through this angle.  For example, 1 hour is equivalent to 15 degrees of rotation.

e. In catalogues of faint stars, galaxies, and nebulae the position of objects are given by their right ascension and declination.  This allows the astronomer to point the telescope at the precise point in the sky where the object is to be found.

O. The seasons are caused by the tilt of the Earth's axis.

1. The Earth's axis is not perpendicular to the plane of the earth's orbit but in fact is tilted 23.5 degrees to the plane of the earth's orbit.

2. The earth constantly maintains this tilt as it orbits the sun.

3. During that part of the year that the northern hemisphere is tilted towards the sun we experience summer and the people in the summer hemisphere experience winter.  Six months later things are reversed and we in the northern hemisphere experience winter and the people in the southern hemisphere experience summer.

4. The seasons of spring and fall occur between the seasons of summer and winter.  The order of the seasons is spring, summer, fall, and winter.

5. This seasonal change can be represented on the celestial sphere by looking at the sun's apparent motion against the background constellations.  Remember that from your position on earth the sun appears from day to day to change position against the background sky, the stars, galaxies, nebulae, etc.  Of course we don't see this as the sun is too bright to see the background in the day time.  Astronomers however understand the phenomenon and study the apparent motion of the sun against the background sky.  As amateurs we can see the background sky when Total Solar Eclipses occur and the "stars come out".

6. If you watch the sun from day to day, you would notice that its rising and setting positions at the east and west horizon change from one day to the next.  You would also notice that its highest point in the sky each day (at noon) changes also.  This phenomenon is due to the tilt of the earth's axis.

7.  Because of the axis tilt, the rotation of the earth, and the orbiting of the sun the sun appears to trace out a very definite sine curve against the background sky.  Twice during the year the sun's path crosses the celestial equator as it changes its apparent position against the background sky.  These two positions are called equinoxes, Latin for equal night.  The most obvious observation of the suns apparent motion at the equinoxes, in addition to equal periods of daylight and darkness, is the rising of the sun exactly in the east and the setting of the sun exactly in the west.  The apparent annual path of the sun on the celestial sphere (the background sky) is called the ecliptic.

8. The equinox in the spring is called the vernal equinox (the moment spring begins).  The equinox in the fall is called the autumnal equinox (the moment fall begins).

9. Between the vernal equinox and the autumnal equinox the sun appears to rise north of East and set north of West.  Its maximum northern position is marked by the summer solstice (the moment summer begins).  Between the autumnal equinox and the vernal equinox the sun appears to rise south of East and set south of West.  Its maximum southern position is marked by the winter solstice (the moment winter begins).

10. The maximum distance north of east that the sun will rise or north of west that the sun will set occurs at the point called the summer solstice.  This is also point where we have the longest daylight period and the shortest period of darkness.

11. The maximum distance south of east that the sun will rise or south of west that the sun will set occurs at the point called the winter solstice.  This is also point where we have the shortest daylight period and the longest period of darkness.

12.  The information about the apparent motion of the sun in the sky can be summarized by the following table.

 Event   Day light / Darkness Approximate time of         the year

 Vernal Equinox 12 hours / 12 hours March 21
 Summer Solstice longest / shortest  June 21
 Autumnal Equinox 12 hours / 12 hours September 21
 Winter Solstice shortest / longest  December 21

13. On the celestial sphere the ecliptic and the equator are tipped at 23.5 degrees to one another. On the ecliptic the points for vernal equinox, summer solstice, autumnal equinox, and winter solstice have exact positions.

14. As you become acquainted with the sky you need reference points.  Two points on the celestial sphere that are always used is the zenith (the point directly over your head) and the nadir (the point 180 degrees from the zenith. It is directly beneath your feet.).

15. At summer solstice the sun is as far north as it is going to get providing the maximum number of daylight hours of any time during the year.  There are certain locations north of the arctic circle where the sun does not set at all during summer nights.  A similar phenomenon occurs at the south pole when we have winter solstice in the north.

16. The region around the north pole where you can see the sun for at least one continuous 24 hr period is bounded by the arctic circle.  In the southern hemisphere the region is bounded by the Antarctic circle.  The arctic circle lies 23.5 degrees south of the north pole and the Antarctic circle lies 23.5 degrees north of the Antarctic circle.  The same regions that experience one or more 24 hour periods of daylight in the summer will experience one or more periods of continuous darkness during winter six months later.

17. On any date during the year the sun appears directly overhead at high noon with in a band of locations encircling the earth.  This band is bounded on the north by the Tropic of Cancer which is 23.5 degrees north of the equator and is bounded on the south by the Tropic of Capricorn which is 23.5 degrees south of the equator.  On the summer solstice the sun is directly overhead along the tropic of cancer latitude line.  On the winter solstice the sun is directly overhead on the tropic of capricorn latitude line.  Between the summer and winter solstices the sun slowly shifts southwards latitude line by latitude line from 23.5 degrees north of the equator to 23.5 degrees south of the equator.  Between winter and summer solstice the sun slowly shifts northward completing the cycle on the summer solstice.

18. To summarize consider the following table.  Measurements are from zero degrees (the equator) to 90 degrees north or south (the poles).

 Region or Zone  Location

 Arctic    66.5 degrees north to 90 degrees north
 Antarctic   66.6 degrees south to 90 degrees south
 North Temperate  23.5 degrees north to 66.5 degrees north
 South Temperate  23.5 degrees south to 66.5 degrees south
 Tropic of Cancer  0 degrees (equator) to 23.5 degrees. north
 Tropic of Capricorn 0 degrees (equator) to 23.5 degrees. south

18.  The earth is tilted on its axis 23.5 degrees with respect to the plane of the ecliptic (the orbital plane of the earth's orbit about the sun).  Because the earth is spinning much like a top that is titled it wobbles very slowly.  This is due to the combination of gravity and rotation.  The result is that over a long period of time the earth's axis is tracing out a circle in the sky that has a diameter of 23.5 degrees. This wobbling of the earth affects the position of the equinoxes such that they very slowly migrate along the ecliptic as seen on the celestial sphere.  This explains why the position of the sun against the zodiac changes very slowly.  For example, the position of the equinox (the position of the sun with respect to the background sky seen at the beginning of spring) is in the constellation Pisces.  However, 2,000 years ago it was located in the constellation Aries.  By the year 2,600 the vernal equinox will have moved into Aquarius.  This process is called the precession of the equinoxes.  (It does make hash out of astrology, which is very rigid about the zodiac.  Astrology is not a science. At best it is a form of entertainment and at its worst a superstition for people afraid to act independently of some outside influence controlling their lives.)

19. Since the precession of the equinoxes messes up position data when using star catalogues, astronomers are always updating the information as the coordinates for celestial objects change.  Astronomers always make a note of the date called the epoch for which a particular set of coordinates are exactly correct.  Most publications out now are set for Jan 1, 2000 and will be usable over the next few decades.  When looking for the less than very obvious objects, such as the big dipper, be sure to check the epoch (the date) for which the information applies.

P. Astronomers have always been the keepers of time.

1. There has always been a need to keep track of time.  For Example, in Egypt the Pharaoh needed to know when the Nile would flood.  The proper timing of seasonal religious events is very important in most societies.  Even today many seasonal traditions are tied to the seasons and we need to have accurate time to schedule events accordingly.

2. For short intervals of time, such as for daily events, we want our time measurement to coincide with the position of the sun in the sky.  For most everyone our biological rhythms are tied to periods of light and darkness.  We have schedules and appointments which most of us want to keep.  The sundial was developed to keep track of apparent solar time.  An apparent solar day is the time to go from one high noon to the next high noon.

3. For more exact measurements of time, astronomers use the meridian, which is a circle on the celestial sphere that passes both through the zenith (the point directly overhead) and both celestial poles.  Local noon occurs when the sun crosses the meridian above the horizon.  Local midnight occurs when it makes the opposite crossing below the horizon. This crossing cannot be observed directly, but would be equivalent to local noon (plus 12 hours) exactly on the opposite side of the earth.

4. The crossing of the meridian by any object in the sky is called a meridian transit.

5. An apparent solar day is formally defined as the interval between two successive upper meridian transits of the sun (local noon crossings) as observed from any fixed spot on the earth.

6. Astronomers realized that the sun is not the best time keeper.  The length of the apparent solar day (as measured by a device such as an hourglass) varies from one season to another.  The speed of the sun's eastward movement against the background stars varies over the course of the year.

7. There are two reasons to explain the variation in time.

a. The first reason is that the earth's orbit is not a circle.  It is actually an ellipse, which looks sort of like a flattened circle or oval shape.  The sun occupies one of the two focus points of the ellipse.  Because this focus point is not at the center of the orbit, the earth travels closer to the sun during one part of its journey and travels farther from the sun during the other part of its journey.  The effect of this change in distance and the force of gravity pulling the earth and sun towards one another causes the earth to speed up and slow down at different points in its path.  The earth speeds up as it approaches the orbital point closest to the sun  (winter in the northern hemisphere) moving an angular distance of more than 1 degree per day in January.  It slows down as it approaches the orbital point furthest from the sun (summer in the northern hemisphere) moving an angular distance of less than 1 degree per day in July.

b. The second reason is that because the ecliptic is inclined by 23.5 degrees to the celestial equator a significant part of the suns motion around the time of the equinoxes is in a north-south direction and less in an east-west direction as compared to apparent movement near the solstices when apparent movement is more in the east-west direction.  The daily eastward progression in the sky is slow around the equinoxes (that is the shift in the length of daylight vs darkness is foreshortened and rise and set times for the sun change very little from one day to the next).  The daily eastward progression around the time of the solstices in the sky is faster than around the equinoxes (that is the shift in the length of daylight and darkness is not for shortened and the rise and set times at a regular, more normal rate).  This faster apparent motion is more like what would be expected if the axis were not tilted.  This can be explained also in terms of the overhead position of the sun between the tropic of cancer and the tropic of capricorn.  The suns position overhead from day to day changes slowly from day to day when it is near the equator (the time of the equinoxes), but changes fairly quickly when it is near the tropic of cancer (the time of the summer solstice position) or near the tropic of capricorn (the time of the winter solstice position).

8. To handle the problem of using the sun to keep time a new term was introduced called the mean sun.  This refers to an imaginary object that moves along the ecliptic at a uniform rate changing position by the same amount each day.  (The term mean comes from statistics and may also be called average.)  The mean sun moves at a constant rate and works well as a tool for keeping time.  Sometimes the mean sun is ahead of the real sun in the sky and sometimes it is behind, but on the whole it averages out because the mean sun time per day is equal to the average of the real sun time per day.

9. A mean solar day is the time interval between successive upper meridian transits of the mean sun.  This time interval is exactly 24 hours long. It is equivalent to the average of the length of the apparent solar day.  Our sense and measure of time on a daily basis is linked to the mean solar day.  We can refer to this in terms of mean solar time.

10. The apparent solar time (based on the actual sun) and the mean solar time (based on the mean sun) can differ by as much as 15 minutes at certain seasons.  The difference between the two is called the equation of time.  There are graphs available that allow you to correct the apparent solar time as seen with a sundial to mean solar time.  These graphs give you the difference and you can add or subtract accordingly to get the mean solar time from the sundial.  The equation of time equals the apparent solar time (AST) minus the mean solar time (MST).   It is the amount by which a sundial is in error because the sun's eastward motion against the background stars is not constant throughout the year.

 AST - MST values    What does it mean?

 difference = 0    Sundial value is correct
 difference > 0    Sundial value is ahead of MST
 difference < 0    Sundial value is behind MST

11. Time zones were invented for convenience in commerce, transportation, and communication.  In a time zone everyone agrees to set their clocks to mean solar time for a meridian that runs approximately through the center of that time zone.  Time zones are centered on meridians equaling whole number multiples of 15 degrees.  For example, 0, 15, 30, 45, and so forth. The earth is divided into 24 time zones each equal to 15 degrees of longitude around the globe.  This results in four time zones across the continental United States. (The distance from New York to California represents 60 degrees of angular distance across the whole earth.)  This results in a 3 hour difference in time between the east and west coasts, a factor affecting travel, TV programming, etc.

12. Everyday life has time measurements tied to the sun.  However, astronomers tend to focus much of their efforts studying the stars and other distant objects.  They prefer to use sidereal time, which is based on the stars rather than the sun.  Sidereal time is used when aiming telescopes.  An astronomer is likely to have access to a sidereal clock.

13. It is best to view distant objects like stars and galaxies where there is the least distortion of the object due to the atmosphere.  This means that when working with ground based telescopes they should be viewed when they are as high in the sky as possible and from as high elevations are as possible.  This "best possible" position is where an object crosses the upper meridian (the one passing directly over head and through the celestial poles.  To know when objects are crossing the meridian, astronomers use sidereal clocks that tells sidereal time.

a. Sidereal time is simply the right ascension of any object on the meridian.

b. Example:  Suppose an astronomer wants to observe the bright star Regulus in the constellation Leo.  From a reference book such as the Astronomical Almanac, they would find the coordinates of Regulus.

The coordinates are:

R. A. (right ascension) is 10^h 07^m 28.0^s  (means superscript unit)

Decl. (Declination) = 12deg. 03' 03"

From this they would conclude that Regulus will be on the meridian at 10:07 according to the 24 hour sidereal clock.

c. The value of a sidereal clock is that it tells the astronomer the right ascension of the objects most easily seen at the moment.  This information emphasizes why astronomers measure right ascension as the time on a 24 hour clock.  The earth rotates once a day on its axis resulting in all of the stars in the sky to cross the meridian once every 24 hour period.

d. While right ascension is measured in time related to the rotational period of the earth declination (how far from the celestial equator an object is found.) is expressed in angular measurements.  It uses the same degrees, minutes, and seconds associated with studying circles in geometry.  Most often a plus (+) sign is associated with measurement north of the celestial equator and a negative (-) sign is associated with measurements south of the celestial equator.

f. It is convenient to be able to convert between angular measurement and sidereal time measurement.  Twenty four (24) hours is equivalent to 360 degrees.  From this we can produce the following conversions.

 Time measurement  Angle measurement

 1 hour (1 h)    15 degrees or 1 deg.
 1 minute (1 m)   15 minutes or 15'
 1 second (1 s)   15 seconds or 15"
 4 m     1 deg.
 4 s     1'
 0.067 s    1"

g. Sidereal time is useful to astronomers and navigators who deal with the stars.  It is not that useful to people in other walks of life.  Sidereal time is different from the time people see on clocks.  It is based upon the position of the vernal equinox which is located in the constellation Pisces. This is the position from which right ascension is measured.  Our "usual" day is based upon the sun's apparent position and the concept of solar mean time.

h. To move from one sidereal day to the next the earth need only turn 360 degrees because the "object" being sited upon is way out in space and during the year appears to be stationary with respect to the rest of the background sky.  The sidereal day begins when the vernal equinox position in the background sky crosses the upper meridian.  The sun's position does not affect the sidereal day.  By definition the sidereal day is the time between two successive vernal equinox crossings of the upper meridian.

i. To move from one solar day to the next the earth has to turn 361 degrees because the object being sited upon is near the center of the earth's orbit and continually appears to move with respect to the background sky because of the earth's movement along its orbital path.  In fact if we used a 360 degree rotation for the earth each day, the sun would appear to be further to the east by about 1 degree each day and soon our clock time would not match the sun's appearance in the sky as we perceive it now.  The apparent solar day is the time between two successive crossing of the upper meridian by the sun.

j. The extra one (1) degree of rotation by the earth each day is equal to 4 minutes of time.  This is the amount of time by which a solar day exceeds a sidereal day.  That means that 1 sidereal day = 23 h  56 m  4.091 s, where the hours (h), the minutes (m), and the seconds (s) are in mean solar time.

k. One day according to the clocks we use everyday is based on solar mean time which is 24 hours of solar time.  The sidereal clock measures sidereal hours, minutes, and seconds.  The sidereal day is also divided into 24 sidereal hours.  Because the side real day is 4 solar minutes shorter than the solar day, sidereal clocks tick at a slightly different rate than solar clocks.

14. Astronomical observations and the calendar:

a. The year as defined by the earth's motion about the sun does not divide equally into 365 days.  Rather, the year is about 365.25 days.  Julius Caesar is credited with the idea of the "leap" year to deal with the extra one-quarter of a day.  This idea was developed to insure that the astronomical events like the beginning of spring would occur on the same date every year.

b. It so happens though, that the earth doesn't orbit the sun exactly in 365.25 days each year.  Precession also complicates matters, because, even if the year were exactly 365.25 days long, the seasonal events as witnessed in the sky change.  (i.e. the vernal equinox position slowly changes with respect to the background sky as time goes by due to the precession of the earth.)

c. The earth's precession is a wobbling type of motion like a spinning top.  Anything affecting the motion of the earth affects what is perceived in the sky (apparent motion).  Thus this wobbling has an affect on what is perceived from earth.  Precession was addressed before in terms of what is perceived in the sky.  Most noticeably, the equinoxes appear to slowly advance along the ecliptic from year to year such that the background constellation of the equinoxes changes slowly over hundreds of years.

d. The sun and moon both exert gravitational pull on the earth.  This pull has a definite affect on the earth's rotation, because the earth is not perfectly spherical.  The earth bulges at the equator.  It has about a 43 km or 27 mile larger diameter when measured along the equator as compared to being measured pole to pole.  As a result of this equatorial bulge the earth is often refereed to as an oblate spheroid rather than a sphere.  The gravitational pull on the bulge has a gradual but definite affect on the earth causing a change in the earth's axis of rotation.

e. The observations of a spinning top help explain the motion of earth as it spins on its axis.  If the top is not spinning it falls over on its side.  A similar phenomenon would occur if the earth were not spinning.  The gravitational tug would attract the bulge and would straighten up the earth.  But the earth is spinning (rotating) so it neither falls over nor straightens up with respect to the plane of its orbit.  Also gravity causes a top whose axis of rotation is not perpendicular to the plane upon which it resides to wobble.  This wobble causes the axis of rotation to trace out a circle.  This phenomenon of a top's axis, or the earth's axis, to trace out a circle is called precession.  Precession is caused by the combined actions of gravity and rotation cause the Earth's axis to trace out a circle in the sky while it remains tilted about 23.5 degrees to the perpendicular.

f.  The earth's rate of precession is not very fast at all.  At the moment the axis points (within 1 degree) towards the star Polaris.  5,000 years ago it pointed at the star Thuban in the constellation Draco.  In 14,000 AD, the "pole" star will be Vega in Lyra.  It requires 26,000 years for the north celestial pole to complete one precessional circle around the sky.

g. Due to the fact that there is not exactly 365.25 days in the year as Caesar suggested by the introduction of a leap year and that the earth does precess affecting what is perceived in terms of the background sky, there is a need to look at more than one time system for describing the earth's motion and what appears to happen in the sky.  The sidereal year is the time for the sun to return to the same position with respect to the background stars in the sky as it started out with.  This period of time is equal to 365.2564 mean solar days (the way we ordinarily measure time).
The sidereal year is the true orbital period of the earth with respect to the stars.

h. Our calendar year, however, is not based on the sidereal year.  Most people prefer to have seasonal events happen on the same date as much as is possible.  As an example, people prefer to have the March 21 as the first day of spring.  Spring begins when the sun reaches the vernal equinox (the point against the background stars where the sun's path, the ecliptic, crosses the celestial equator on its northward journey).  The problem of using the sidereal year as a calendar year arises when the fact that the vernal equinox moves slowly against the background stars is taken into account.  The using of the sidereal year as the calendar year could result in the calendar dates and the seasons getting out of sync because the sun returning to the same background star position (the definition of the sidereal year) is not the same as saying the sun returns to the equinox position in the sky (which slowly moves from year to year).

i. To keep dates synchronized with seasonal changes or events, the calendar year must be based upon the need for the sun to go from one equinox position to the next equinox position.  This time interval is called a tropical year and equals 365.2422 solar mean days.  Because of precession the tropical year is shorter than the sidereal year by 20 minutes and 24 seconds.

j.  At least as far back as the Greeks, this discrepancy was known about.  During the second century BC, a man by the name of Hipparchus calculated the length of the tropical year within six minutes of the currently known value.  He is also known for being the first person to detect the precession of the equinoxes when comparing his own observations to that of Babylonian astronomers' observations three centuries earlier.  It is interesting to note that Caesar's tropical year of 365.25 solar days was actually further off than Hipparchus' measure.  He was off by 11 minutes and 14 seconds.  This error amounts to about 3 days every four centuries.  Interestingly Caesar's advisors were aware of the error, but felt it wasn't that important.  However, by the 16th century the first day of spring was occurring on March 11.

k.  Pope Gregory XIII decided to fix things with a calendar reform.  He dropped 10 days, declaring Oct. 5, 1582, to be Oct. 15, 1582.  This put the first day of spring back on March 21.  He then proceeded to fix Caesars calendar.  Caesar had added leap years to every year evenly divisible by 4.  In recent times 1980, 1984, 1988, 1992, and 1996 are leap years.  Now it is true that 2000 was a leap year, but not just because of Caesar's idea.  Gregory decided that if every 4th year was a leap year the error of 3 calendar days per every 400 years would just occur again.  So he declared that only whole century years divisible by 400 years would have leap years.  Thus, under his new system, 1600 did have a leap year, but 1700, 1800, and 1900 would not.  Then 2000 did and 2400 will, while 2100, 2200, and 2300 will not have leap years.  Under Caesar's leap year calendar rule all whole century values would have a leap year and the 3 days per 400 year error shows up over time.

l. So the world now operates under the Gregorian calendar, though some cultures for non-international commerce purposes use other calendars not related to the western civilization, Christian based calendar.  The Gregorian system we uses a year equal to 365.2425 solar days long.  This is very close to the actual length of the tropical year.  Pope Gregory's efforts have reduced the error to such a small value that it amounts to one day per every 3300 years.  There is no urgency to addressing this error as no problems are anticipated for a very long time.

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