,2015

ASTR 3130, Majewski [SPRING 2015]. Lecture Notes

## ASTR 3130 (Majewski) Lecture Notes

### OBSERVABLE CHANGES IN OBJECT COORDINATES

REFERENCE: Roy & Clarke, Chapters 10 and 11. Birney et al.'s Chapters 4 and 7. Kaler's Chapter 5.

For each object in the sky we can assign celestial coordinates.

However, a number of physical effects act to make either the apparent or the actual celestial coordinates of a celestial object change.

We will discuss seven of them pertaining to stars:
1. precession of the earth's equinoxes
2. nutation
3. stellar motions
4. atmospheric refraction
5. stellar parallax
6. aberration of starlight
7. telescope mechanical flexure

1. PRECESSION OF THE EARTH

This is a 25,800 year periodic wobble of the direction of the Earth's axis of rotation.

This is a major effect that can be detected nightly, and which 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 by one part in 298.

• 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.

Because the Moon orbits the Earth in a plane that is more like the ecliptic (within 5 degrees of the ecliptic) than the equator, typically the Moon is not aligned with the Earth's equatorial bulge (unless the Moon is on the Celestial Equator).

• 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.

##### From Abell's Exploration of the Universe, Ed. 3.

• There are also smaller contributions from the Sun and planets attempting gravitationally to do the same thing (e.g., as we have seen the Sun is only on the celestial equator twice a year and at all other times of the year it is pulling the Earth's bulge toward the ecliptic plane).

• 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 in the direction that it points.

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.

• ##### The North Celestial Pole is circling counterclockwise around the North Ecliptic Pole. From Kaler's The Ever-Changing Sky.

• Presently the Earth's North Pole points to Polaris, but 14,000 years ago it pointed towards Vega. Other North "pole stars" in the 25,800 year cycle are shown below.

• The star Gamma Cephei is the next "pole star" (it will be 3 degrees from the NCP in 2200 years).

• Note that it is not the location of the rotational pole on the Earth that is changing, but where that pole points on the Celestial Sphere!

• 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.

• This means that from our earth-bound perspective there are apparent "flows" of stars on the celestial sphere as induced by the precessional wobble.

• Just as stars appear to rotate above us is a reflection of the Earth's rotation, the wobble of the Earth is reflected in the changing positions of stars on our celestial sphere.

• The optical illusion thus makes stars appear to drift past the the North Celestial Pole as if they were on a plate turning about a point at the North Ecliptic Pole.

• The effect is most noticeable at the celestial poles, and the direction and the speed of the "flow" depends on where you are looking on the celestial sphere.

• Obviously, if the position of the celestial poles on the sky is changing, this means which stars/constellations are circumpolar for any observer on the Earth is also changing.

• If the position of the celestial poles and equators are changing on the celestial sphere, this means that the celestial coordinates of objects, which are defined by reference to the celestial equator and celestial poles, must also be constantly changing.

• Because of this change in the direction of the Earth's pole with time, 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, it is proper (and imperative!) that when an astronomer gives the coordinates of an object she specifies the year that corresponds to those coordinates (because they will be significantly different in future years.

• 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 below). DO NOT GET IN THE HABIT OF MAKING THIS MISTAKE!

• 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 (e.g., the book Norton's 2000.0).

• 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 generally move your object of interest off a typical CCD field of view.

• Because the plane of the Earth's orbit is fixed, the position of the ecliptic is fixed -- and so too are the constellations of the signs of the zodiac.
• But since the position of the Celestial Equator is changing, the position of the Vernal and Autumnal Equinoctes (where the Celestial Equator and the ecliptic cross) slowly shifts with time.
• ##### From Kaler's The Ever-Changing Sky.

• In the Figure above, 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 equinoctes 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.

• Notice how in the figure the Celestial Coordinates of the stars Deneb and Achernar are constantly changing, but the Ecliptic Coordinates of these stars remain fixed. Unfortunately, we use the former system to operate our telescopes because it is easier on a day to day basis.

• KEEP THESE IDEAS CLEAR:

• From our point of view at a given latitude on Earth, the direction towards the equator, poles, and ecliptic maintain their same orientation to the horizon every year.

It is the stars that appear to move east along the ecliptic past the equinox and solstice points.

• Stars don't change their ecliptic coordinates from precession, only their celestial coordinates.

• Since the Vernal Equinox is slipping, the dates when the Sun is in a given constellation slowly changes.

• This is why the months associated with certain "signs of the zodiac" do not match with the Sun's true position with respect to them, which is how the dates of the "houses" were originally defined (what day of the year the Sun is in that house does change).

• Another effect of precession is to complicate the definition of a year.

• A sidereal year is the time between the Sun appearing across a given star = 365.2564 days.

• A tropical year is the time between successive Vernal Equinoctes = 365.2422 days.

• The difference is because the Sun is every day moving eastward along the ecliptic while the Vernal Equinox is slipping westward.

• Thus, the Sun has less than 360 degrees to move to go from one Vernal Equinox to the next, because the VE is moving towards the Sun.
• The tropical year is 20 minutes shorter than a sidereal year because it takes 20 minutes for the Sun to move 50.3 arcsecs.

##### From Kaler's The Ever-Changing Sky.

• The 50.3"/yr precession discussed above is actually the total of all precessional affects and is called the general precession.

• The effect of lunar-solar precession is actually a westward motion of the equinoctes by 50.4"/yr on a 25,800 year period.

• The effect of planetary precession (combined gravity of all planets) is actually an eastward motion of the equinoctes by 0.1"/yr.

Planetary precession also acts to change the obliquity of the ecliptic of the Earth (between 21.5 and 24.5 degrees) over a 41,000 year cycle.

Currently the obliquity of the ecliptic is being reduced by 0.5"/yr.

2. NUTATION

• Wobble of the Earth's rotational axis about the mean precessional circle shown above:
• ##### The idea of nutation. Note that the actual number of wobbles is much greater than shown since one precession is 25,800 years but each wobble is only 18.6 years.

• Cause: Variation in the gravitational forces that act on Earth's equatorial bulge.

• Moon predominates precession, and its gravitational effect is to try to make the Earth precess about the pole of the Moon's orbital plane, which is tilted 5.9o to the ecliptic.
• But the Moon's own orbital pole precesses about the ecliptic pole, with a rather short period of 18.6 years!
• Thus, the mean precessional motion will be about the ecliptic pole (as described above) but with a 9 arcsecond oscillation over the course of 18.6 years.
• This 9" oscillation is added or subtracted from the normal obliquity of the ecliptic.
• Because of the nutation oscillations, the actual position of the NCP is up to 17" ahead or behind of the smoothly varying average precessional position.

-->

SMALLER NUTATIONAL EFFECTS

The precession and nutation are just two of over 100 recognized harmonic variations/wobbles in the Earth's position!

Among these effects are things related to:

• The Moon and Sun constantly moving back and forth across the Earth's equatorial bulge.
• Thus, the forces acting to tip the bulge vary from strongest at winter and summer solstice and weakest on an equinox.

This causes wobbles on the period of half and a full year (solar effect) and half and a full month (lunar effect).

• The eccentricities of the the Earth and Moon orbits cause an additional variation in the various gravitational interactions.
• The above mentioned effects show up in the image below which shows: one 18.6 year nutation cycle in panel A, on which is superimposed the half year (panel B) and even smaller half month (panel C) wobbles.

• A true polar motion -- variation in the placement of the Earth's polar axis relative to the surface of the Earth by about 15 meters at the North and South poles on periods of 12 and 14 months.

The 12 month cycle has to do with yearly changes in the distribution of atmospheric and water masses on the Earth.
• The 14 month cycle is known as the Chandler Wobble, discovered by the American astronomer Seth Chandler in 1891.

Can be seen with high resolution studies of the quasar reference frame using radio telescopes.

The origin of the Chandler Wobble has long remained a mystery.

• One theory is that it has to do with the off center distribution of mass on the Earth (e.g., due to landmasses).

• Another holds that it is due to sloshing of the liquid interior of the Earth or interaction with the mantle.

• A recent conjecture has to do with wind patterns pushing water around the Earth.

• A recent claim to have solved the problem is that 2/3 of the effect is caused by changes in the pressure at the bottom of the ocean (due to salinity and circulation changes) and 1/3 by fluctuations in atmospheric pressure.

The Chndler Wobble, unlike the other effects described on this webpage, does change your latitude and longitude (or what declination goes through your zenith) -- by of up to 0.7 arcseconds.

##### (Left) The Geographic South Pole is marked by a small sign and a stake in the ice pack, which is repositioned each year on New Year's Day to account not only for its intrinsic motion (due to things like the Chandler Wobble) as well as the fact (not discussed elsewuere in the notes, and not relevant astronomically) that the polar ice sheet moves across the Antarctic continent at about 10 meters/year, towards the Weddell Sea. The effects are somewhat comparable in size (with the wobble varying as shown above). (Right) The Ceremonial South Pole, which is used for ceremonial purposes and photo opportunities at the South Pole Station, is located near the Geographic South Pole. It features a metallic sphere on a "barber pole" plinth, and is surrounded by flags of countries that are signatories to the Antarctic Treaty.

ASIDE: Major Motions of the Earth

As you can see, the motion of the Earth through space is rather complicated.

But the following are the primary motions:

1. Daily rotation (23 hours, 56 minutes).
2. Chandler wobble -- 15m diameter wide -- 14, 12 month cycles.
3. Earth revolves around Sun, 365.2564 days.
4. Precession of Earth -- 25,800 years.
5. Nutation -- 18.6 year cycle.
6. Reflex Motion about the Earth-Moon barycenter point.

(r1 / r2) = (m2 / m1)

Earth is 80X more massive than Moon, so barycenter is 1/80 the distance from Earth center to Moon center.
7. Earth orbits this point, located 5000 km from Earth center (a point, however, that is still inside the surface of the 6371 km radius Earth).

Period of the motion is one lunar month.

8. Rotation of the Local Standard of Rest (solar neighborhood) about the Milky Way center ~ 220 km/s at 8.5 kpc.
9. Entire solar system shares solar motion in solar neighborhood ~ 20 km/s from the Local Standard of Rest.
10. Milky Way orbiting center of mass of the Local Group of Galaxies (dominated by Milky Way and Andromeda Galaxy -- current motion is towards Andromeda at few hundred km/s).
11. Local Group participating in Virgocentric flow towards Virgo cluster (several hundred km/s).
12. Virgo itself may pulled to even larger mass, the so-called "Great Attractor" (several hundred km/s).
13. Local Group participates in Hubble expansion.

3. STELLAR MOTIONS

Stars in the Galaxy of course have varying relative velocities with respect to the Sun, and these motions can be detected as positional changes in the sky, called proper motions.

The proper motion, μ, has units of angle change per unit time.

• Common units for proper motions (which are typically very small) are:

• milliarcseconds/year (mas/yr)
• arcseconds/century (arcsec/cent)
• THOUGHT PROBLEM: How many mas/yr in 1 arcsec/cent?
• The proper motion reflects one aspect of the space velocity of a star:

where:

VS = space velocity (total velocity of a star)

VT = transverse velocity (velocity perpendicular to line of sight)

VR = radial velocity (velocity parallel to line of sight = Doppler velocity)

##### The true motion (pink) of a star can be decomposed into two components: a radial velocity along the line of sight (red) and a proper motion along the celestial sphere. Credit image and caption: The RAVE Collaboration.

• Note:

• VR can be measured directly by the Doppler effect.

VR is seen as a blueshift (if approaching us) or redshift (if receding).
• VT cannot be measured directly.
• Only the angular change, the proper motion, can be observed.

To convert from the proper motion to the transverse velocity, one needs to know the distance, d, to the star.

When one works out the math one finds that:

• THOUGHT PROBLEM: Derive the above equation.

• By the above equation, we see that a proper motion can be large if:

• the star is close to us (d is small)

• the star has a large transverse velocity with respect to the Sun

• Typical star velocities with respect to the Sun are 10's of km/s.
• Highest speed of stars in the Galaxy with respect to its center (the escape velocity) = 475 km/s.

Sun revolves around Galaxy = 232 km/s

But typical stars are far, so proper motions are small!

• For naked eye stars, typically < 0.1" per year
• But, over time, this amount of motion adds up:

• Only a few hundred stars have proper motions > 1.0" per year
• The largest known proper motion is that of the nearby Barnard's star:

μ = 10.25" per year
• Barnard's Star has a large motion because it is the 4th closest star to us at only 1.8 pc.

This is an animated GIF composed of four images of Barnard's star taken 5, 2 and 1 year apart. First in 1991 on 4th June, 5min exposure on hypered Tech Pan 2415 film, second in 1996 on 24th June, 30s exposure using an SXL8 camera (kindly loaned at the time by Eric Strach) and the last two in 1998 and 1999 using the SX mono camera. Images were exported as JPG files, aligned and made into the animated GIF seen above! A crude pixel to pixel measurement of the motion over 5 years gave just over 10" per annum, very close to the correct proper motion of 10.36" per annum. From www.fornax.pwp.blueyonder.co.uk/images.html.

• Some famous catalogues in astronomy containing high proper motion stars:
• 1976: LHS - Luyten Half-Second Catalogue - all stars μ > 0.5" per annum

• 1955-1961: LTT - Luyten Two-Tenths Catalogue - μ > 0.2" per annum

• 1971: GICLAS Catalogue - LPMS (Lowell Proper Motion Survey)
These catalogues contain lots of interesting stars, because, as mentioned above, there are two ways to get high μ VT / d:

1. large VT = "high velocity stars" - stars with large VT w.r.t. solar motion, stars not moving like the Sun, so typically not a disk star. Halo stars!
2. small d = very nearby stars (e.g. Barnard's), often hard to find in any other way except large proper motion.
• Knowing whether your target has a sizable proper motion is important because outdated coordinates will not point you in the correct place.
• Thus, in addition to giving the equinox of your coordinates -- which tells you what precessional year your coordinate system corresponds to -- for large proper motion stars you have also to give the epoch of the coordinates of the star, which tells you in what year the star was observed relative to other stars (which can be described in any equinox coordinate system).

• PLEASE know the difference between epoch and equinox of coordinates! Both need to be accounted for with stellar positions (though equinox more than epoch).

• If you know the proper motion of the star for one year, you can correct the coordinates to the position the star has in any other year.

• Note that a proper motion is generally a motion in both right ascension and declination.

• Thus, we always have to give information on both the size of the proper motion, and the direction of the motion.

• The direction of motion is called the position angle, θ of the motion, and it is the angle between the direction of the NCP and the direction of motion of the star.

• We define θ = 0o as motion due North and θ = 90o as motion due East.

• Thus, proper motions are given as the pair of values (μ, θ).

• Alternatively, instead of giving total motion and position angle (a "radial coordinate system"), one could break up the motion into components of proper motion in the right ascension and declination directions (similar to a Cartesian coordinate system):

where:

θ = position angle of star = angle between direction to NCP and the direction of motion of the star

Note that the cosδ term is needed to account (again) for the convergence of meridians toward the NCP and SCP. (The cosδ is small when δ is large.)

##### From http://www.astronexus.com/node/36 .

4. ATMOSPHERIC REFRACTION

This effect makes objects appear higher in the sky than they actually are.

The effect is increased at larger zenith distances.

There are a number of atmospheric phenomena that come into play when objects rise and set. Though it happens to all celestial objects, the effects are most commonly recognized/noticed/intuitive with the Sun.

As objects reach the horizon, the airmass grows substantially.

• Recall from previous lecture that the airmass is 1 at the zenith and reaches 38 at the horizon.

There are several important effects that happen as you go to higher airmass. These effects are generally bad from the point of view of observing.

1. The substantially higher amount of Earth atmosphere that you are looking through translates to a higher amount of background contributed (e.g., airglow lines, thermal emission in the infrared) and a higher amount of telluric absorption in spectra.

2. The substantial increase (38 times) in the amount of atmosphere in front of a celestial object means that there is substantially poorer seeing for objects near the horizon.

3. There is substantially more scattering of light at all wavelengths.

• This means objects are always fainter when they are near the horizon and brighter near the zenith.

• You know from experience that the Sun can be viewed directly at sunrise/set but not when the Sun is overhead.

• Blue light is always scattered more than red light, thus, objects become redder in color as they approach the horizon, because less red light is lost than blue light.

• You know from experience that the Sun and Moon often look very red at sunrise/set.

4. Because the atmosphere is a transparent medium of increasing density as you approach the Earth, the atmosphere must also refract light according to Snell's Law, just like a lens.

• Atmospheric refraction has the effect of making every object appear higher in the sky than it really is.

• The effect is more pronounced as you look to lower altitudes (higher airmasses) because of the greater pathlength the light travels through the refracting medium.

• A table of the amount of atmospheric refraction as a function of altitude is given by Norton's 2000.0.

Recall that the angular size of the Moon and Sun are about 30 arcmin. This means that when the Sun and Moon look like they are on the horizon, they are in fact already below the horizon!

Thus, refraction lets you see things when they are already below the horizon (by up to 34.2 arcminutes).

Note that this discussion applies to the true horizon, as seen from sea or towards flat horizon.

• A number of other effects result from differential refraction:

• Because the amount of refraction increases as objects approach the horizon, it has the effect of making objects appear to slow down as they approach the horizon.

• From experience you know that sunsets last longer than the 2 minutes they should take to go from the time the Sun first touches the horizon to fully being below.

• THOUGHT PROBLEM: Where does the value 2 minutes come from in that previous statement?

• Differential refraction make the Sun and Moon appear to flatten as they reach the horizon. The image below explains why.

##### The upper limb of the Sun is refracted less than the lower limb of the Sun. Thus, the lower limb is refracted by amount B which is larger than the amount A. The difference can be as much as one fifth the true angular diameter of the Sun.

• Refraction affects blue light more than red light (note physical difference between scattering and refracting).

• Thus, blue light is always refracted to higher degrees than green light, and we have separation of "images" of the setting source sorted by wavelength. Stars will look like little spectra.

When the Sun is near the horizon, it will look like a series of different Suns, as shown.

##### Setting sun from Torrey Pines, CA by Andrew Young.

• This can result in a phenomenon known as the green flash, as blue/green light is refracted into a blue/green image of the Sun that is higher than the orange/red image of the Sun.

As the Sun sets, the orange/red Sun sets before the blue/green Sun, and, for a brief time, one can often see the upper limb of the green solar image "flash" as the last bit of Sun to sink below the horizon.

Best seen over the ocean, lasts a few seconds, although can last much longer (up to 30 minutes or so) near the poles of the Earth (WHEN??).

##### On May 19, 1999 Pekka Parvianen photographed this green flash from Finland.

• For the above reasons, professional astronomers rarely work when objects are above 2 airmasses.

• RECALL: What zenith distance corresponds to 2 airmasses?

5. STELLAR PARALLAX

• Apparent shift in position of a nearby star because of the orbital motion of the Earth about the Sun.
• ##### From http://www.astronexus.com/node/36 .

• π = difference between the geocentric and heliocentric positions of the star
• Effect is small: π < 1" for all stars
• tan π ~ π (radians) = r / d

To convert to arcsec: π (arcsec) = 206265 π (radians)

then:

If r = 1 Astronomical Unit (A.U.) = 150,000,000 km:

• We define 1 parsec (pc) = 206265 A.U. = 3x1013 km = 3.26 light years (l.y.) Then:

• Nearest star: Proxima Centauri

1.31 pc = 4 l.y.

π = 0.76" = size of dime at d = 6 km!

• Thus, parallaxes are hard to measure (not seen until 1838 -- proof of heliocentric solar system!):

• Best π from ground (e.g. McCormick refractor) π >= 0.01"

d ~ 100 pc - nearest stars (Vyssotsky)
• Best current space π - HIPPARCOS

π >= 0.001"

nearest 1 kpc - some halo stars, some variable star standard candles
• NASA's Space Interferometry Mission (which was going to be launched in 2010, but was cancelled): aimed to obtain π ~ 10-6 "

d ~ 1000 kpc - entire galaxy at least
• ESA's Gaia mission, launched 2014, will be collected π ~ 10-5 "

So will probe the Galaxy well to 10 kpc with 10% accurate distances for 200 million stars and 1% accuracy for about 20 million stars. (Data available starting in 2017.)

• Note: The actual yearly reflex motion of a star on the sky from parallactic motion depends on the position of the star relative to the ecliptic:

• THOUGHT PROBLEM: Why is parallax work from ground best done at ~ twilight (morning, evening)??

6. ABERRATION OF STARLIGHT

This effect has to do with the finite speed of light and the orbital and daily motion of the Earth.

• Imagine walking with a drainpipe (or umbrella!) in the rain.

rain velocity = V

• To have drop go through pipe without hitting edge, need to angle pipe with slope v / V.

(Note: you intuitively angle your umbrella forward when you walk.)
• Same thing happens due to the Earth's motion and the finite speed of light.
• You have to "slope" your telescope forward to "catch" photons.

The telescope must be advanced by:

slope = vEarth / c

= (36 km/s) / (3x105 km/s)

= 20.5 "
• The annual aberration:

Stars appear to move in a small ellipse about their true positions each year.

Shape of ellipse (similar to shapes above for parallax):

• Star perpendicular to ecliptic (at ecliptic poles) show circular aberration over year of radius 20.5".
• Star in ecliptic plane shifts in a line of length 41" per year.
• Everywhere else, shape of ellipse varies between these shapes.
--> Another important proof of the Earth's motion around Sun.
• The diurnal aberration:

Similar effect, but caused by Earth's daily rotational motion.

Obviously a smaller effect:

(0.46 km/s) / (3x105 km/s) = 0.19"

7. TELESCOPE MECHANICAL FLEXURE

Apparent coordinates depend on the stability of the telescope as:

• ... it moves around the sky and experiences differential gravity on the different parts of the scope over the course of a night.

Depends on rigidity of telescope components.

##### Cartoon demonstration of mechanical flexure. From Bely, The Design and Construction of Large Telescopes.
Most telescopes (including Fan Mtn Obs 1-m) have pointing maps that make corrections for this mechanical problem as a function of declination and hour angle.

• ... over long periods of time (e.g., decades).

Generally a small effect, but could be catastrophic (e.g. collapse of the radio telescope at Green Bank!), or sudden (earthquakes or structural fatigue moving telescope polar axis).
##### Before (left) and after (right): Results of catastrophic mechanical flexure (failure) -- the collapse of the 300 ft. radio dish at Green Bank Observatory on Nov. 15, 1988. The collapse was due to the sudden failure of a key structural element. The full story and the figrues above can be found here.

SUMMARY OF CHANGES IN THE APPARENT COORDINATES OF STARS

 Precession     - lunar-solar     - planetary 50.4" / year 0.1" / year Nutation 18" (max) Proper motion 10.25" (max) Atmospheric refraction 34' (max) Stellar parallax < 1" (stars) Aberration     - annual     - diurnal 20.5" (max) 0.19" Telescope mechanical flexure variable

Nutation image from http://www2.globetrotter.net/astroccd/biblio/bellt300.htm. Earth rising image from http://www.lifeinuniverse.org/noflash/ Earthunique-05-02.html All other material copyright © 2002,2006,2008,2012,2015 Steven R. Majewski. All rights reserved. These notes are intended for the private, noncommercial use of students enrolled in Astronomy 313 and Astronomy 3130 at the University of Virginia.