AST 443 / PHY 517 Astronomical Observa<onal Techniques Prof. F.M. Walter
I. The Basics The 3 basic measurements: WHERE something is WHEN something happened HOW BRIGHT something is Since this is science, let s be quan<ta<ve!
Where Posi<ons: 2- dimensional projec<ons on celes<al sphere (theta, phi) Theta, phi are angular measures: radians, or degrees, minutes, arcsec 3- dimensional posi<on in space (x,y,z) or (theta, phi, r). (x,y,z) are linear posi<ons within a right- handed rec<linear coordinate system. R is a distance (spherical coordinates) Galac<c posi<ons are some<mes presented in cylindrical coordinates, of galactocentric radius, height above the galac<c plane, and azimuth.
Coordinate Systems "What good are Mercator's North Poles and Equators Tropics, Zones, and Meridian Lines?" So the Bellman would cry, and the crew would reply "They are merely convendonal signs" L. Carroll - - The Hun<ng of the Snark Celes<al (equatorial): based on terrestrial longitude & la<tude Eclip<c: based on solar system Al<tude- Azimuth (alt- az): local Galac<c: based on Milky Way Supergalac<c: based on supergalac<c plane
Reference points Celes0al coordinates (Right Ascension α, Declina<on δ) δ = 0: projec<on of terrestrial equator (α, δ) = (0,0): where ascending node of the eclip<c intersects the celes<al equator (the first point of Aries = γ)
Reference points Eclip0c coordinates (λ,β) β = 0: plane of the Earth s orbit around the Sun (λ,β) = (0,0) at γ ε: inclina<on of the eclip<c to the celes<al equator, ε=23 o 26'21".448-46".82T - 0".0006T 2 + 0".0018T 3, (T in Julian Centuries from 2000AD) north eclip<c pole: 18 h +66 o 33' (J2000)
Reference points Al0tude- Azimuth (theta, phi) Azimuth Theta measured east of north Al<tude phi measured from horizon to zenith
Reference points Galac0c (l II, b II ) (l II, b II ) = (0,0) is at α=17 h 42 m 24 s, δ=- 28 o 55'. North galac<c pole: (α,δ) =12 h 49 m, +27 o 24' (B1950.0). The galac<c equator is inclined to the celes<al equator by 62.6 o.
When Solar <me Terrestrial <me Sidereal <me
The Second The atomic second is the dura<on of 9,192,631,770 periods of the radia<on corresponding to the transi<on between two hyperfine levels of the ground state of cesium 133. The solar second is 1/86,400 of the length of one solar day, This second is variable in dura<on, a consequence of the irregular and unpredictable rota<on rate of the Earth. The ephemeris second is one/31,556,925.9749 of the length of the tropical year 1900 (vernal equinox to vernal equinox). The atomic second is the same length as the ephemeris second. The mean solar second equalled the atomic second in 1820.
Solar <me Local <me. The Sun transits (crosses the meridian) at noon, local <me. The length of the day varies throughout the year.
Civil Time the mean angular velocity of the Sun is 15 o per hour. Civil <me consists of 24 <me zones, each nominally 15 o wide, centered on lines of longitude which are mul<ples of 15 o (there are local varia<ons). The Eastern <me zone is centered on 75 o west longitude. Noon EST occurs when the fic<<ous mean Sun crosses the 75 th degree of longitude. The fic<<ous mean Sun differs from the true Sun in that it has a constant angular velocity across the sky. The difference (in <me) between the true Sun and the fic<<ous mean Sun, the Equa<on of Time, reaches nearly +/- 15 minutes.
The Equa<on of Time
Universal Time UT is the civil <me at 0 o longitude (the standard meridian), which passes through Greenwich, England. UT is also known as Greenwich mean <me (GMT), and is military <me Zulu (Z). UT is based on the ficddous mean Sun. UT = 12 h + the Greenwhich hour angle (GHA) or Right Ascension of the fic<<ous mean Sun. UT1 is UT corrected for the mo<on of the geographic poles (the Chandler wobble and similar phenomena). UT2 is UT1 with an extrapolated correc<on for the spindown of the Earth. UTC (Coordinated Universal <me) is basically UT1, rounded off. Leap seconds are added to keep UTC within 0.9 sec of UT1. UTC is broadcast by WWV radio. You can see this <me on the seismograph in the ESS lobby.
Atomic Time Kept by atomic clocks since 1958 Stable to 1 part in 10 14 Unaffected by the vagaries of the Solar System
Ephemeris Time ET based on the ficddous mean Sun, with the angular velocity of the Sun on 1900 0.5 January. The RA of the fic<<ous mean Sun = RA=18 h 38 m 45.836 s + 8,640,184.542 s T E + 0.0929 s T E 2 ET- UT = 24.349 s + 72.318 s T E + 29.950 s T E 2 Ephemeris <me was formally abolished in 1984, and replaced with Terrestrial Time (TT; formerly Terrestrial Dynamical Time (TDT) and Terrestrial Barycentric Time (TBT). For all prac<cal purposes, TT = UT1. TT - TAI = 32 s.184 T E = (JD- 2415020.0)/36525, the number of Julian Centuries since 1900 January 0.5
Heliocentric Time Time at the center of the Sun UT corrected for the light travel <me (up to 8.3 minutes)
Terrestrial Barycentric Time TDB = TT + 0.001658 sin(g) + 0.000014 sin(2g) seconds, where g = 357 o.531 + 0 o.9856003 (JD - 2451545.0) g is the mean anomaly of the Earth in its orbit around the Sun. TBD is referred to the barycenter of the Solar System. It is an ideal <me calculated for an ideal Earth in a circular orbit around the Sun. The 1.7 ms periodic devia<on is a general rela<vis<c effect due to the varia<on in the gravita<onal poten<al around the Earth's orbit. TCB: ideal <me corrected for GR effects in a flat space- <me frame far from the Solar System. Due to gravita<onal <me dila<on, TCB is 49 sec/century faster than TDB.
Keeping it all together On 1 January 1958: 0:00:00 TAI = 0:00:00 UT2 = 0:00:32.15 ET
The Year Tropical Year: The interval between two transits of the mean Sun through the mean equinoxes. 365.24219879-6.14x10-6 T days. The length of the Tropical Year decreases by 5.36 seconds per century due to precession of the equinoxes. (now considered obsolete) Sidereal Year: The interval for the Sun to return to the same point on the eclip<c. 365.25636042 + 1.11x10-7 T days Anomalis0c Year: The <me between successive perihelia. 365.25964134 + 3.04x10-6 T days The Anomalis<c Year is 4.5 minutes longer than the sidereal year because the perihelion advances. Julian Year 365.25 days. Gregorian Year 365.2425 days. (accurate to 1 day in 3000 years) T : number of Julian centuries since 1900 January 0.5 (12h UT). A Julian Century is 36525 ephemeris days.
Julian Days the number of ephemeris days elapsed since 12 h UT on 1 January, 4713 BC (- 4712 AD). 1 ephemeris day = 86400 sec Modified Julian Day (MJD) = JD - 2450000.5 1 January 2013, 0:00 UT: JD=2456293.5 The algorithm: JD = fix(365.25*f) + fix(30.6001*(g+1)) + d + A + 1,720,994.5 where y is the year, m is the month, d is the day of the month, f=y for m>2 and f=y- 1 for m<3 g=m for m>2 and g=m+12 for m<3 A=2- fix(f/100) + fix(f/400). Gregorian civil calendar dates only.
Sidereal Time based on the Earth's sidereal rota<on period (rota<on with respect to the stars). sidereal day = 24 sidereal hours, or 23 h 56 m 4 s Solar <me. The difference is due to the angular mo<on of the earth around the Sun. The sidereal <me is a measured locally. The local sideral <me (LST) is RA of the zenith. The hour angle HA of an object with right ascension RA is given by HA=LST- RA GMST (Greenwich Mean Sidereal Time) at 0 h UT = 24110.54841 + 8640184.812866 T U + 0.093104T U 2-6.2x10-6 T U 3 seconds GAST (Greenwich Apparent Sidereal Time) = GMST + the equadon of the equinoxes. The EquaDon of the Equinoxes is the total nuta<on in longitude <me the cosine of the true obliquity of the eclip<c. It ranges from +0.8 to +1.2 seconds. LAST (Local Apparent Sidereal Time): hour angle of the ascending node of the eclip<c. LMST (Local Mean Sidereal Time) = GMST - geode<c longitude. Note 1: both the sideral and solar days are 86,400 seconds long. The sidereal second is shorter than the solar second by 0.997269566414-0.586x10-10 T E Note 2: T U = (JD- 2451545.0)/36525 is the number of Julian Centuries since J2000.0
The Inconstancy of Time Ephemeris 0me, which is referred to the ficddous mean Sun and the mean Equinox is uniform. True local 0me varies from ephemeris <me because of: Periodic varia<ons in the Sun- Earth distance. Secular changes, including: Tidal fric<on, which causes the length of the day to increase by 0.0016 sec/ century. dt/t = 4.5x10-8 sec/day, with an accelera<on term propor<onal to t 2. Irregular varia<ons in the Earth's rota<on due to small changes in the moment of iner<a. The effect is cumula<ve but unpredictable. Rela<ve to 1972, the effect was -.005 seconds in 1871, and +0.002 seconds in 1907. Seasonal varia<ons in I due to weather. man- made changes from reservoirs (increasing I) sea- level changes
How Time Affects Posi<on Because of mo0ons of the measurement frame (the precession of the equinoxes) and intrinsic mo0ons (proper mo<ons), coordinates specified in the Equatorial coordinate system are strictly valid at only one instant of <me. Therefore, it is necessary to supplement the coordinates with two more pieces of informa<on: the epoch of the measurement. This is the <me at which the posi<on was measured. If one knows the intrinsic mo<ons of a moving object, one can then extrapolate to predict the posi<on at other epochs. the equinox of the coordinates, which makes the RA and DEC of a sta<onary object change with <me. One reduces the measured posi<on to a standard equinox (e.g., B1950 or J2000), essen<ally by adding or subtrac<ng the expected precessional shizs. Equinox B1950 was standard prior to about 1980; now J2000 is the standard epoch. Note that the terms "equinox" and "epoch" are ozen confused; the correct term can ozen be discerned from its context. An observa<on made in 1984 and precessed to J2000 coordinates should be referred to as Epoch 1984, Equinox J2000, but is ozen simply referred to as "Epoch 2000". If proper mo<ons are negligable, the difference is inconsequen<al.
Later How Bright