2007Lecture2

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By: andrei (125 month(s) ago)

This is a very useful training aid.

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The Celestial Sphere: 

The Celestial Sphere

Basic Principles: 

Basic Principles ● Everything appears to move around us as though we were at the center of the Universe. ● Celestial Sphere (천구) : an imaginary concept that is a useful tool for understanding some workings of the sky: - Sphere of infinite radius with Earth at center. - Stars on “surface of sphere”.

Slide3: 

● Great Circle (대원) - any circle that shares the same center point as the sphere itself. - a great circle exactly divides the surface area of a sphere in half. - (ex) celestial equator, horizon ● Small Circle (소원) - any circle drawn on the sphere that does not share the same center as the sphere. - (ex) lines of latitude on the Earth, path of circumpolar stars

Slide4: 

It often seems surprising to people used to looking at flat maps that the shortest distance between two points takes them over unexpected places on air flights. The loxodrome is a straight line constant heading on the Mercator Projection and the great circle, although appearing longer than the loxodrome, is actually the shortest route between New York and London.

Slide5: 

● Primary great circle ● Secondary great circle - a great circle that goes through the poles of a primary great circle.

The Horizon System : 

The Horizon System ● Zenith (천정) : point directly above you ● Horizon (지평선) ● Meridian (자오선): arc that contains the zenith, the north celestial pole, and the due north and south points on the horizon. Your meridian divides your sky in half Circle from north celestial pole through zenith to south pole cuts the horizon in south point all objects on it are due south of the observer (남중)

The Horizon System : 

● Altitude (고도): how far above the horizon to look for an object, from zero degrees at the horizon to 90 degrees at the zenith. ● Azimuth (방위각): the direction towards the horizon one must face to look up from the horizon to the object. In this system we start from 0 degrees for the north meridian, then 90 degrees for due east, etc. (북쪽에서 동쪽으로 측정) The Horizon System ● Zenith Distance (천정거리): 90o - altitude

The Horizon System : 

The Horizon System

The Horizon System: 

The Horizon System ● One often finds this system of coordinates used on instruments with mainly terrestrial applications, such as military spotting scopes and (at least in terms of azimuth) airport runway designations. ● Drawbacks to its use in astronomical contexts: - Objects in sky constantly moving - altitude and azimuth changing. (지구 자전에 의해 altitude와 azimuth가 계속 변화) - Since stars change their position with respect to horizon through the night, their altitude-azimuth position change - Each observer has own reference system (note the frequent use of word "your" above!). ● THUS: This type of reference system can never be universal, i.e., specifying the position of an object complicated - altitude and azimuth not constant for an object over all times for all observers.  not useful for the catalogue of position

Terrestrial Latitude and Longitude: 

Terrestrial Latitude and Longitude ● latitude : - 0 ~ +90 deg/-90 deg - lo : line of latitude ● longitude - angle from a zero of longitude (i.e., Royal Observatory, Greenwich, London = Greenwich meridian) - 0 ~ 180 deg west or east - Lo : line of longitude

Terrestrial Latitude and Longitude: 

Terrestrial Latitude and Longitude (cf) Time Zone - alternative longitude angle unit - the Earth has 24 zones, each normally 15o wide (i.e., 1 hour)

The Celestial Equatorial System: 

The Celestial Equatorial System ● The center of the Celestial Sphere is the center of the Earth. ● The rotational axis of the Earth defines the apparent rotational axis of the Celestial Sphere. Consequently, the poles of the Earth define the Celestial Poles of the Celestial Sphere. ● The equatorial plane of the Earth is perpendicular to the rotational axis of the Earth. Therefore the plane of the Celestial Equator, which is perpendicular to the Celestial Poles, must be coincident with the Earth's equatorial plane.

The Celestial Equatorial System: 

The Celestial Equatorial System ● Because much of the apparent motion of objects in the sky can be attributed to the daily rotation of the Earth, it is more useful to use a sky reference system that relates to the entirety of the Earth (not just your specific view of the sky).

The Celestial Equatorial System: 

The Celestial Equatorial System

The Celestial Equatorial System: 

The Celestial Equatorial System

Slide16: 

● Right Ascension (RA = ) : measured angle eastwards from the zero of celestial longitude - zero of celestial longitude : a particular point on the celestial equator that is fixed with respect to the distant stars (i.e. constellation Aries  vernal equinox: 춘분점) - hour: minute: second (ex. 13h 25m 31s) ● Declination (DEC = ) : measured angle from the celestial equator - 0 ~ +90 deg and 0 ~ -90 deg - o   (ex. +53 o 13 45)

Slide17: 

Advantages of celestial equatorial system ● Celestial equatorial system is fixed with respect to the stars ● Coordinates of most celestial objects remain approximately constant over time and for all observers. ● Easy to specify unique and universally understandable positions for objects.  useful for the catalogue of position ● System automatically accounts for the rotation of Earth - it ignores it... (cf) precession (세차) : change of the position of celestial pole & equinox. no effect on the relative positions of stars (cf) epoch (e.g. 1950.0, 2000.0, 2000.6)  (ex) a(2000), d(2000)

How Do the Observer’s Reference System and the Celestial Sphere Relate?: 

How Do the Observer’s Reference System and the Celestial Sphere Relate? For a polar observer (in this case, North Pole) ● The North Pole is at the zenith. ● The Celestial Equator is exactly on and around the horizon.

How Do the Observer’s Reference System and the Celestial Sphere Relate?: 

How Do the Observer’s Reference System and the Celestial Sphere Relate? For an equatorial observer ● The North (and South) Celestial Pole lies on the horizon. ● The Celestial Equator goes through the zenith.

Slide21: 

For an observer at other latitude “LAT” ● The North Celestial Pole (when LAT > 0o) is at an angle LAT above the north horizon on the meridian.  그 지방의 위도 ~ 북극성의 고도 (For an observer with LAT < 0o, the South Celestial Pole is at an angle -LAT above the south horizon on the meridian.)

Slide22: 

For an observer at other latitude “LAT” ● The Celestial Equator crosses the meridian (90o-LAT) above the south horizon and LAT degrees below zenith (to the south). (For an observer with LAT < 0 degrees, the Celestial Equator crosses the meridian (90o-|LAT|) above the north horizon and |LAT| degrees below zenith (to the north).

Slide23: 

When a star is on the meridian (i.e., 남중할 때) ● The altitude of a star above the southern horizon (SALT in the diagram above) : SALT = DEC + (90o - LAT) ● LAT = 36o at Daejeon, so here SALT = DEC + 54o. ● Objects with DEC = LAT have altitudes of 90o, i.e. they cross through your zenith. ● The celestial equator (DEC = 0o) has SALT = (90o - LAT).

Slide24: 

● Two arcs with arrows : stars with different declinations  paths of rising and setting stars across the sky ● The celestial Equator intersects the horizon exactly at the due East and due West ● (Q1) Approximately what latitude does the figure represent? (Q2) What are the approximate declinations of stars A & B?

Consequences of the Earth’s Rotation on its Axis: 

Consequences of the Earth’s Rotation on its Axis

Slide26: 

For a polar observer ● Polar observer can only ever see ½ the entire Celestial Sphere ! The celestial sphere for an observer at the North Pole. The NCP is straight overhead at the zenith and the celestial equator is on the horizon. Stars rotate parallel to the Celestial Equator, so they move parallel to the horizon here – they never set! Stars move parallel to the horizon. The Celestial Equator is on the horizon.

Slide27: 

For a polar observer

Slide28: 

For an equatorial observer The celestial sphere for an observer on the Equator. The Celestial Equator goes through the zenith. Stars rotate parallel to the Celestial Equator, so they move perpendicular to the horizon here. All stars are visible for 12 hours. Both celestial poles are visible o the horizon. Stars rise and set perpendicular to the horizon. The Celestial Equator reaches zenith and goes through due East and West on the horizon.

Slide29: 

For an equatorial observer

Slide30: 

For an observer at latitude ~ 67o ● Celestial equator는 남쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ? ● Celestial north pole은 북쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ?

Slide31: 

For an observer at latitude ~ 45o ● Celestial equator는 남쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ? ● Celestial north pole은 북쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ?

Slide32: 

For an observer at latitude ~ 33o ● Celestial equator는 남쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ? ● Celestial north pole은 북쪽하늘에서 지평선으로부터 얼마만큼 고도를 갖나 ?

Slide33: 

For any other observer

Slide34: 

● The North Celestial Pole (when LAT > 0o) is at an angle LAT above the north horizon on the meridian. - Now consider what happens to a star that is located at an angle less than LAT from the North Celestial Pole...these stars never set below the horizon.

Slide35: 

● But note also that the South Celestial Pole (when LAT > 0o) is at an angle LAT below the south horizon on the meridian. - Now consider what happens to a star that is located at an angle less than LAT from the South Celestial Pole...these stars never rise above the horizon.

Slide36: 

● The Celestial Equator crosses the meridian (90o-LAT) above the south horizon and LAT degrees below zenith (to the south). - All stars between (90o-LAT) and -(90o-LAT) spend some time above the horizon.

Slide37: 

● North circumpolar region : (90o – LAT) < Dec < 90o ● South circumpolar region : -(90o – LAT) > Dec > -90o We can define several groups of stars based on the above rise/set characteristics for stars of different declination.

Slide38: 

● Objects on the Celestial Equator (DEC = 0o) : - rise due East - are above the horizon 12 hours a day - set due West - are below the horizon 12 hours a day

Slide39: 

● Objects with 0o < DEC < (90o - LAT) - rise North of due East - are above the horizon more than 12 hours a day - set North of due West - are below the horizon less than 12 hours a day

Slide40: 

● Objects with 0o > DEC > -(90o - LAT) - rise South of due East - are above the horizon less than 12 hours a day - set South of due West - are below the horizon more than 12 hours a day

Slide41: 

● You know from experience that in the summer the Sun is above the horizon more than 12 hours in a day (i.e., the daytime is longer than the nighttime). What does this imply about the declination of the Sun during summer? ● You know from experience that in the winter the Sun is above the horizon less than 12 hours in a day (i.e., the nighttime is longer than the daytime). What does this imply about the declination of the Sun during winter? ● The word "equinox" comes from the Latin for "equal night" - in the sense that the day is equal to the night in duration. What does this imply for the declination of the Sun on the day of the Vernal Equinox (Mar. 21)? The Autumnal Equinox (Sep. 23)?

More Consequences of Earth’s Rotation : Passage of Time and the Hour Angle: 

More Consequences of Earth’s Rotation : Passage of Time and the Hour Angle ● Transit (남중) : When a celestial object moving from East to West due to the diurnal motion of the Earth crosses your meridian, we say that object transits . ● Solar Day (태양일) : length of time between two successive transit of the sun, from astronomical noon until astronomical noon the following day (= 24 hour). ● Sidereal Day (항성일) : the period for a star to go from one transit to the next transit (= 23 hour 56 min).

Slide43: 

● Sidereal time (항성시) = RA of a star currently on the meridian ● The spin of the Earth is counterclockwise (eastward) as seen from above N pole  apparent rotation of sky is westward ● Because we want units of time to increase : - RA must increase as we look to the East of the meridian (동쪽에 있는 별은 곧 남중함) - RA must decrease to the West of the meridian (서쪽에 있는 별은 이미 남중했음) 동쪽에 있는 별의 RA가 더 큼 !

Slide44: 

● Hour Angle (HA, 시간각) = amount of time before or after transit for any given object = Angle in the sky between meridian and the line of RA corresponding to the object of interest ● Hour Angle (HA) of an object = Sidereal Time (LST) – Right Ascension (RA) of an object  Positive HA (HA > 0) : object가 meridian을 transit 한 후 지나감  Negative HA (HA < 0) : object가 meridian으로 transit하러 감. ● a unit of time (h, m, s) ● Unlike the RA, which is always fixed, the HA of an objects constantly changing (increasing).

Slide45: 

● Examples : - A star with HA = 2 crossed the meridian (i.e. transited) two hours ago. - A star with HA = -1 will be on the meridian in one hour. - An HA of 23 hours is equivalent to HA = -1. ● To avoid confusion over sign, astronomers will often include an “E” or a “W” in the time to indicate east or west of the meridian, respectively. For example, - an hour angle of -1:23 could be written as “1E23”. - an hour angle of +3:07 could be written as “3W07”. ● Through HA you can determine the time of best visibility for any object, which corresponds to transit or HA=0 (cf: airmass).

Consequences of Earth’s Revolution about the Sun: 

Consequences of Earth’s Revolution about the Sun ● Earth is a planet moving in orbit around the Sun ● Orbit is nearly circular (distance to Sun varies only 3%) ● Orbit lies in a plane called the "ecliptic" plane. ● Earth orbits Sun in 365.25 days (one year). Motion is counterclockwise as seen from above N. pole ● The night side of Earth is that opposite the Sun. So the stars visible at night are those "opposite" the Sun.

Slide47: 

● The apparent path that the Sun takes through the sky over the course of a year is known as the ecliptic . ● The constellations that lie along the ecliptic are called the zodiac . ● There are twelve "officially recognized" zodiacal constellations. ● The ecliptic is inclined by 23.5o from the celestial equator.

Slide48: 

● THOUGHT PROBLEM TIME OUT: Recalling the length of time objects below and above the celestial equator spend above the horizon, is it now clear why summer daylight is longer than 12 hours and winter daylight is shorter than 12 hours in duration? ● Objects with 0o < DEC < (90o - LAT) are above the horizon more than 12 hours a day 하지 (DEC of the Sun = +23.5o) ● Objects with 0o > DEC > -(90o - LAT) are above the horizon less than 12 hours a day 동지 (DEC of the Sun = -23.5o)

Slide49: 

When a star is on the meridian (i.e., 남중할 때) ● The altitude of a star above the southern horizon (SALT in the diagram above) : SALT = DEC + (90o - LAT) ● The variation of DEC of Sun for a year : +23.5o (summer solstice) ~ -23.5o (winter solstice) → the variation of SALT!

Slide50: 

● During the passage of the sidereal day, the Earth has advanced in orbit around Sun (the amount is greatly exaggerated in the figure.) The angle the Earth advances in its orbit in one day is approximately equal to (360o/year)/(365.25 days/year) = ~ 1o. ● But in the passage of that one sidereal day, the Sun has not yet transited. In order to do so, Earth must rotate an extra amount, which is, by Euclidean geometry (angle A = angle B in the figure), equal to the ~ 1o . ● Thus, the Earth must turn about 361o every solar day ! The extra 1o rotation takes (360o daily rotation)/(23 hours 56 minutes) = 4 minutes of time. ● Thus, the solar day, corresponding to 361o Earth rotation is 4 minutes longer than a sidereal day, which corresponds to a 360o Earth rotation.

Slide51: 

Now turn things around, to a human time frame. ● In a solar day, since the Earth has turned 361o, the background stars will have actually advanced in position to the West by ~1o with respect to the Sun. ● The Sun will now have moved in RA to the East with respect to the background stars (태양은 고정된 별에 대해 매일 약 1o 씩 동쪽으로 위치  RA 증가). ● The sidereal clock will appear to run 4 minutes fast per day, or 2 hours fast per month. - Thus, every 12 months, the sidereal clock will repeat in its cycle, and so every year on the same day of the year, the same stars transit at the same time. - The one day of the year when the solar and sidereal clocks are synchronized is the day of the Autumnal Equinox (Sep. 22), when the Sun has an RA of 12 hours, and so when the Sun transits the sidereal and the solar time is 12 hours.

Review of Sidereal/Solar Day and the Ecliptic: 

Review of Sidereal/Solar Day and the Ecliptic (1) Variation of RA of the Sun ● A sidereal day is about 4 minutes shorter than a solar day. ● Thus, in one solar day, the Earth has actually rotated with respect to the stars by 361o. ● Thus, at the same solar time each day, the sky advances 4 minutes of hour angle compared to the previous day. Thus, the same stars are progressively moving about 4 minutes westward compared to the Sun per day. ● Thus, the Sun is continually moving eastward with respect to the stars. ● 4 minutes per day is about two hours per month and is 24 hours per year, after which the cycle repeats. ● It thus follows that the Sun's right ascension is continuously changing (i.e., increasing) throughout the year.

Slide53: 

(2) Variation of DEC of the Sun ● Declination changes continuously throughout the year. ● This is a consequence of the Earth's tilt - the difference in its rotational and revolutionary axes.  tilt of ecliptic to the equator ! (QUESTION) - Why the RA & DEC of the Sun change throughout the year ? - What are the RA & DEC of Vernal Equinox, Summer Solstice, Autumnal Equinox, and Winter Solstice ?

Slide54: 

● The Sun moves Eastward (i.e. later) on the celestial sphere by about 4 minutes per day to ascertain the Sun's Right Ascension on any day.

Slide55: 

● As we have learned, the height of an object at transit, where the object rises and sets, and the number of hours that object is above the horizon are all determined by the declination of the object. Thus, the -23.5o to +23.5o range of declination for the Sun affects these various aspects of the Sun's diurnal path through the sky. The Sun's daily path for latitude +40o at monthly intervals.

Slide56: 

Obliquity of the ecliptic : ● The plane of the Earth's orbit is the ecliptic plane. ● The projection of the apparent path of the Sun on the celestial sphere is called the ecliptic. ● The difference between the ecliptic and the celestial equator is determined by the difference in the rotational and revolutionary axes of the Earth, and is called the obliquity of the ecliptic . - The value of the obliquity of the ecliptic is 23.5o.

Slide57: 

● Note that most of the other planets, most of the moons of these planets (including the Earth's moon), and the rings of Saturn are also found to like in the ecliptic plane. ● The zodiac is a band of constellations lying along the ecliptic.

Consequences of the Earth’s Tilt : Seasons and Daylight: 

Consequences of the Earth’s Tilt : Seasons and Daylight The 23.5o tip of the Earth's equator with respect to the plane of the Earth's orbit is the cause of the Earth's seasons.

Slide59: 

It is also the reason why we have different amounts of sunlight on different days of the year. The cartoon attempts to summarize how the daylight and seasons are connected:

Slide60: 

On Vernal Equinox (March 21) and Autumnal Equinox (Sep. 23) ● The Sun is on the celestial equator and (almost) everyone on Earth has about 12 hours with the Sun above and below horizon. ● Note that "equinox" is Latin for "equal night" (to day). ● Note that the rays of the Sun, which is located on the celestial equator, strike the ground exactly vertically for observers on the equator on this day, and the Sun is at the zenith at noon:

Slide61: 

On or around Summer Solstice (June 22) ● The direction to the Sun is 23.5o above the celestial equator. ● Here the days are longer than the nights for the Northern Hemisphere and the nights are longer than the days for the Southern Hemisphere. The longest day in the Northern Hemisphere is when the Sun reaches +23.5o. ● Not only are the days longer for northerners, but the rays of the Sun strike the ground more nearly vertically, meaning they are less spread out (i.e., more concentrated), and thus more energy (e.g., heat) is received per square foot.

Slide62: 

● On or about June 22, the Sun is at the zenith at noon for observers at latitude +23.5o. This latitude is called the Tropic of Cancer (북회귀선). ● For observers above latitude 90o-23.5o=66.5o, there is continuous sunshine. This latitude is called the Arctic Circle (북극권). ● For observers below -66.5o latitude, there is continuous 24 hour darkness. This latitude is called the Antarctic Circle (남극권).

Slide63: 

On or around Winter Solstice (Dec. 22) ● The direction to the Sun is 23.5o below the celestial equator. ● Here the days are longer than the nights for the Southern Hemisphere and the nights are longer than the days for the Northern Hemisphere. ● Now the Southern Hemisphere enjoys longer nights and greater concentrations of energy while the Northern Hemisphere is in winter. ● This is the longest day for the Southern Hemisphere and the longest night for the Northern Hemisphere.

Slide64: 

● On or about Dec 22, the Sun's is at the zenith at noon for observers at latitude -23.5o. This latitude is called the Tropic of Capricorn (남회귀선). ● For northerners, the rays of the Sun reach the ground rather obliquely . With the light spread out more, we actually receive less per square foot, and thus we are less warm. ● For observers above the Arctic Circle (latitude 90o-23.5o=66.5o) there is continuous, 24 hour darkness, and for those below the Antarctic Circle there is 24 hour daylight.

Slide65: 

● Keep in mind the special latitudes of the Earth, which are defined astronomically.

Slide66: 

The number of hours of daylight and the angle at which sunlight strikes Earth's surface determine the "insolation", or the amount of sunlight incident on a unit area of the Earth' s surface during 24 hours. In the end, this differential heating is responsible for the occurrence of seasons in Nature: ● The change in the geographic shadow distribution caused by the Earth's tilt is quite dramatic (even though the shadow always covers exactly one hemisphere of the Earth). Here are two images of the way the shadow is distributed at about 2 PM Eastern time on August 1 (left) and December 1 (right). The Earth's surface moves eastward through the shadow. You can immediately tell from the image which latitudes are receiving more sunlight in a 24 hour period.

Slide67: 

A common misperception is that the Earth's seasons are caused by the distance of the Sun from the Earth. ● If this were true, the Northern and the Southern Hemispheres would have simultaneous seasons. Instead, they are six months apart. ● The Earth is actually closest to the Sun in January!

Twilight: 

When the Sun is below the horizon, the atmosphere of the earth can still catch rays of the sun and scatter them to visibility by an observer. This is called twilight (박명). There are three types of twilight that have been defined: ● Civil Twilight (시민박명): begins and ends when sun is 6o below the horizon. - Used in courts of law, for example. ● Nautical Twilight (항해박명): begins and ends when sun 12o below the horizon. - Brightest stars as well as the sea horizon are visible. ● Astronomical Twilight (천문박명): begins and ends when sun 18o. - 6th magnitude stars visible at the zenith. Twilight

Precession of the Earth: 

This is a 25,800 year periodic wobble of the direction of the Earth's axis of rotation. This has a large effect on coordinates over the period of years. CAUSE: Because the Earth spins, it is in fact a little fatter around the equator. ● The Earth is 43 km larger in diameter across the equator than from pole to pole (a radius of 6378 km toward the equator compared to 6357 km toward the poles). ● Note because the force of gravity goes as 1/r2 and we are 0.33% closer to the Earth's center at the pole, the force of gravity (e.g., your weight!) is about 0.67% greater at the poles. Precession of the Earth

Slide70: 

Because the Moon orbits the Earth in a plane that is more like the ecliptic than the equator, typically the Moon is not aligned with the Earth's equatorial bulge. ● Thus the Moon often is at an angle to the equatorial bulge, and the Moon's gravitational force tends to want to "pull" the equatorial bulge of the Earth toward it - i.e., trying to "erect" the axis of the Earth. ● There are also smaller contributions from the Sun and planets attempting gravitationally to do the same thing.

Slide71: 

These external forces on the spinning Earth creates a "wobble" in the Earth's motion - called precession that is much like the motion seen in a rotating top, wherein the "pole" of the spinning top slowly meanders (어슬렁어슬렁 거리다) in the direction that it points.

Slide72: 

EFFECTS: For the Earth, the precession acts to slowly change the direction that the Earth's rotational pole points. ● The direction of the Earth's North and South Celestial Poles rotate to different points on the Celestial Sphere with a 25,800 year cycle. ● The orbital axis of the Earth stays fixed in space but the rotational axis constantly changes direction. ● This means that the Ecliptic Poles are always in the same place on the celestial sphere (e.g., the North Ecliptic Pole is always at one point in Draco), but the North and South Celestial Poles are circling around the Ecliptic Poles on the sky.

Slide73: 

● The Presently the Earth's North Pole points to Polaris, but 14,000 years ago it pointed towards Vega. ● The star Gamma Cephei is the next "pole star" (it will be 3 degrees from the NCP in 2200 years). ● Note also that if the direction of the poles is changing, so too is the direction of the equator of the Earth as projected on the sky.

Slide74: 

● If the position of the celestial poles and equators are changing on the celestial sphere  the celestial coordinates of objects, which are defined by reference to the celestial equator and celestial poles, must also be constantly changing. - The coordinate systems of RA and DEC that we adopt for one year are actually different for other years! - The effects are quite noticeable, almost an arcminute a year along the ecliptic. - Thus, an astronomer gives the coordinates of an object specifying the year that corresponds to those coordinates. - This specified year for the coordinates is called the EQUINOX of the coordinates. NOTE: A common mistake made by even senior astronomers is to call the year of the coordinates the "epoch" of the coordinates. THIS IS WRONG. An epoch specified with coordinates means something completely different (see proper motions). DO NOT GET IN THE HABIT OF MAKING THIS MISTAKE!

Slide75: 

- Astronomers tend to use "standard" years, like 1950, 2000, 2050 when they cite the Equinox of the coordinates.  Presently we see most people using "J2000.0" coordinates. - Coming to a telescope with coordinates precessed to the wrong year is one of the most common mistakes by observers.  A mistake of 50 years in the coordinate system (most typical) will general move your object of interest off a typical CCD field of view.

Slide76: 

● Since the position of the Celestial Equator is changing, the position of the Vernal and Autumnal Equinoxes (where the Celestial Equator and the ecliptic cross) slowly shifts with time.

Slide77: 

- If the NCP is coming at you, the front side of the Celestial Equator is going down and the back side of the Celestial Equator is going up. - This means that the positions of the Vernal Equinox is sliding to the left (or, to the right from the Earth's point of view). - Thus, the motion of the equinoxes is westward along the ecliptic because of the motion of the equator. - Since in a 25,800 year period the Vernal Equinox will slide 360 degrees, we have that the annual motion of the Vernal Equinox (and Autumnal Equinox) is 360o/(25800 yrs) = 50.3"/yr.

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