AST 443 / PHY 517
Astronomical Observational 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 quantitative!
• Positions:
Where
– 2-dimensional projections on celestial sphere (theta,
phi)
• Theta, phi are angular measures: radians, or degrees,
minutes, arcsec
– 3-dimensional position in space (x,y,z) or (theta, phi,
r).
• (x,y,z) are linear positions within a right-handed rectilinear
coordinate system.
• R is a distance (spherical coordinates)
• Galactic positions are sometimes presented in cylindrical
coordinates, of galactocentric radius, height above the
galactic 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 conventional signs"
L. Carroll -- The Hunting of the Snark
• Celestial (equatorial): based on terrestrial longitude &
latitude
• Ecliptic: based on solar system
• Altitude-Azimuth (alt-az): local
• Galactic: based on Milky Way
• Supergalactic: based on supergalactic plane
Reference points
Celestial coordinates (Right Ascension α,
Declination δ)
• δ = 0: projection of terrestrial equator
• (α, δ) = (0,0): where ascending node of the
ecliptic intersects the celestial equator (the
first point of Aries = γ)
Reference points
Ecliptic coordinates (λ,β)
• β = 0: plane of the Earth’s orbit around the
Sun
• (λ,β) = (0,0) at γ
• ε: inclination of the ecliptic to the celestial
equator, ε=23o26'21".448 - 46".82T - 0".0006T2 + 0".0018T3, (T in
Julian Centuries from 2000AD)
• north ecliptic pole: 18h +66o33' (J2000)
Reference points
Altitude-Azimuth (theta, phi)
• Theta measured east of north
• Azimuth phi measured from horizon to zenith
Reference points
Galactic (lII, bII)
• (lII, bII) = (0,0) is at α=17h42m24s, δ=-28o55'.
• North galactic pole: (α,δ) =12h49m, +27o24'
(B1950.0).
• The galactic equator is inclined to the celestial
equator by 62.6o.
When
• Solar time
• Terrestrial time
• Sidereal time
The Second
• The atomic second is the duration of 9,192,631,770 periods
of the radiation corresponding to the transition 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 duration, a consequence of the
irregular and unpredictable rotation 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 time
• Local time.
• The Sun transits (crosses the meridian) at
noon, local time.
• The length of the day varies throughout the
year.
Civil Time
• the mean angular velocity of the Sun is 15o per hour.
• Civil time consists of 24 time zones, each nominally 15o
wide, centered on lines of longitude which are
multiples of 15o (there are local variations).
– The Eastern time zone is centered on 75o west longitude.
Noon EST occurs when the fictitious mean Sun crosses the
75th degree of longitude.
• The fictitious mean Sun differs from the true Sun in
that it has a constant angular velocity across the sky.
The difference (in time) between the true Sun and the
fictitious mean Sun, the Equation of Time, reaches
nearly +/-15 minutes.
The Equation of Time
Universal Time
• UT is the civil time at 0o longitude (the standard meridian), which
passes through Greenwich, England.
• UT is also known as Greenwich mean time (GMT), and is military
time Zulu (Z).
• UT is based on the fictitious mean Sun. UT = 12h + the Greenwhich
hour angle (GHA) or Right Ascension of the fictitious mean Sun.
• UT1 is UT corrected for the motion of the geographic poles (the
Chandler wobble and similar phenomena).
• UT2 is UT1 with an extrapolated correction for the spindown of the
Earth.
• UTC (Coordinated Universal time) 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 time on the seismograph
in the ESS lobby.
Atomic Time
• Kept by atomic clocks since 1958
• Stable to 1 part in 1014
• Unaffected by the vagaries of the Solar System
Ephemeris Time
• ET based on the fictitious mean Sun, with the angular
velocity of the Sun on 1900 0.5 January. The RA of the
fictitious mean Sun =
RA=18h38m45.836s + 8,640,184.542s TE + 0.0929s TE2
• ET-UT = 24.349s + 72.318sTE + 29.950sTE2
• Ephemeris time was formally abolished in 1984, and
replaced with Terrestrial Time (TT; formerly Terrestrial
Dynamical Time (TDT) and Terrestrial Barycentric Time
(TBT).
• For all practical purposes, TT = UT1.
• TT - TAI = 32s.184
• TE = (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 time (up to
8.3 minutes)
Terrestrial Barycentric Time
• TDB = TT + 0.001658 sin(g) + 0.000014 sin(2g) seconds,
where
– g = 357o.531 + 0o.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 time calculated for an ideal Earth in a circular orbit
around the Sun.
• The 1.7 ms periodic deviation is a general relativistic effect
due to the variation in the gravitational potential around
the Earth's orbit.
• TCB: ideal time corrected for GR effects in a flat space-time
frame far from the Solar System. Due to gravitational time
dilation, 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 -6.14x10-6T 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
ecliptic.
365.25636042 + 1.11x10-7T days
• Anomalistic Year: The time between successive perihelia.
365.25964134 + 3.04x10-6T days
The Anomalistic 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 12h 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 rotation period (rotation with respect to the stars).
sidereal day = 24 sidereal hours, or 23h56m4s Solar time. The difference is due to the
angular motion of the earth around the Sun.
• The sidereal time is a measured locally.
• The local sideral time (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 0h UT = 24110.54841 + 8640184.812866 TU
+ 0.093104TU2 - 6.2x10-6TU3 seconds
• GAST (Greenwich Apparent Sidereal Time) = GMST + the equation of the equinoxes.
The Equation of the Equinoxes is the total nutation in longitude time the cosine of the
true obliquity of the ecliptic. It ranges from +0.8 to +1.2 seconds.
• LAST (Local Apparent Sidereal Time): hour angle of the ascending node of the ecliptic.
• LMST (Local Mean Sidereal Time) = GMST - geodetic 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 - 0.586x10-10TE
Note 2: TU = (JD-2451545.0)/36525 is the number of Julian Centuries since J2000.0
The Inconstancy of Time
Ephemeris time, which is referred to the fictitious mean Sun and the mean
Equinox is uniform.
True local time varies from ephemeris time because of:
• Periodic variations in the Sun-Earth distance.
• Secular changes, including:
– Tidal friction, which causes the length of the day to increase by 0.0016
sec/century.
dt/t = 4.5x10-8 sec/day, with an acceleration term proportional to t2.
– Irregular variations in the Earth's rotation due to small changes in the moment
of inertia.
The effect is cumulative but unpredictable.
Relative to 1972, the effect was -.005 seconds in 1871, and +0.002 seconds in
1907.
– Seasonal variations in I due to weather.
– man-made changes from reservoirs (increasing I)
– sea-level changes
How Time Affects Position
•
Because of
– motions of the measurement frame (the precession of the equinoxes) and
– intrinsic motions (proper motions),
•
coordinates specified in the Equatorial coordinate system are strictly valid at only
one instant of time.
Therefore, it is necessary to supplement the coordinates with two more pieces of
information:
– the epoch of the measurement. This is the time at which the position was measured. If one
knows the intrinsic motions of a moving object, one can then extrapolate to predict the
position at other epochs.
– the equinox of the coordinates, which makes the RA and DEC of a stationary object change
with time. One reduces the measured position to a standard equinox (e.g., B1950 or J2000),
essentially by adding or subtracting the expected precessional shifts. Equinox B1950 was
standard prior to about 1980; now J2000 is the standard epoch.
Note that the terms "equinox" and "epoch" are often confused; the correct term can
often be discerned from its context. An observation made in 1984 and precessed to
J2000 coordinates should be referred to as Epoch 1984, Equinox J2000, but is often
simply referred to as "Epoch 2000". If proper motions are negligable, the difference is
inconsequential.
How Bright
• Later…