file: SIDEREAL.TXT
June 96 / APB
SIDEREAL TIME
Alan Buckman, AWR Technology
INTRODUCTION
Sidereal Time us used by Astronomers to keep track of 'Star
Time'. It runs faster than Greenwich Mean Time by about 3 minutes
56 seconds a day to complete an extra 24 hours in one year. This
rate matches that of the Sidereal Heavens and so the time, once
set, will show the Right Ascension of the object passing the
observer's Meridian (due South).
This display of Sidereal Time is useful in knowing what is in the
sky at any time by reference to star atlases; for setting drive
systems in Equatorial telescopes; and for use in calculations,
typically for converting coordinates of stars to horizon
coordinates so that an Alt-Azimuth telescope can be pointed
directly at an object. It is also very easy to predict rising
times of objects and useful in locating planets in the daytime.
Sidereal time clocks can be purchased in the form of Observatory
Clocks from AWR Technology or computer programmes running on
personal computers. Most planetarium programmes will have a real
time display of Sidereal Time. Observatory clocks are designed to
be left running permanently and so will require very little re-
setting. A good clock will include battery back-up in the event
of mains. A quartz crystal is used in preference to the mains as
a reference frequency as the mains frequency wanders unacceptably
through the day, dropping at periods of heavy load and speeding
up at night.
DETERMINING SIDEREAL TIME
Setting up of Sidereal Time can be done by several different
methods but the end result is the same. All tables and
calculation methods tell the Sidereal Time at Greenwich
(Longitude 0 degrees) ie Greenwich Sidereal Time (G.S.T.). The
time should be set to Local Sidereal Time which is unique to the
position of your observatory. Thus it is important to obtain the
longitude of your observatory as it is used in several of these
methods.
L.S.T. = G.S.T. - L
Where L is the longitude measured positively westwards from
Greenwich. Convert degrees to angle expressed in hours,
minutes and seconds (15 degrees = 1 hour).
The accuracy required depends on what purpose the Sidereal Time
is to be used for. If it is for locating objects within a medium
power telescopic field then about 1/8th degree in angle is
required, corresponding to a 30 second accuracy on Sidereal time.
Look up Table.
The table below gives the sidereal time throughout any year but
it is accurate to +/- 3 minutes only. It has been compiled from a
mean table from the Astronomical Ephemeris.
GREENWICH SIDEREAL TIME AT 00.00HRS
DAY JAN FEB MAR APR MAY JUN
1 6 41 8 44 10 34 12 36 14 35 16 37
6 7 01 9 03 10 54 12 56 14 54 16 57
11 7 21 9 23 11 14 13 16 15 14 17 16
16 7 41 9 43 11 33 13 36 15 34 17 36
21 8 00 10 03 11 53 13 55 15 53 17 56
26 8 20 10 22 12 13 14 15 16 13 18 15
DAY JLY AUG SEP OCT NOV DEC
1 18 35 20 37 22 40 0 38 2 40 4 38
6 18 55 20 57 22 59 0 58 3 00 4 58
11 19 15 21 17 23 19 1 17 3 20 5 18
16 19 34 21 36 23 39 1 37 3 39 5 37
21 19 54 21 56 23 58 1 57 3 59 5 57
26 20 14 22 16 0 18 2 16 4 19 6 17
Standard Stars.
If the telescope can be accurately set to run on the meridian, ie
due North through the Zenith to due South, then when a standard
star of known position transits in the telescope the clock should
be adjusted to this value. This gives Local Sidereal Time
directly.
Star RA (1988.5) DEC Mag 1 yr
PREC. (RA)
h m s o ' s
Alpha And (Alpheratz) 00:07:47 +29 02 2.06 +3.07
Beta Cet (Diphda) 00:43:01 -18 03 2.04 +2.94
Beta Per (Algol) 03:07:25 +40 55 2.12v +3.84
Delta Ori (Mintaka) 05:31:25 -00 18 2.23 +3.07
Alpha CMi (Procyon) 07:38:42 +05 15 0.34 +3.07
Alpha Hya (Alphard) 09:27:01 -08 36 1.98 +2.88
Beta Leo (Denebola) 11:48:28 +14 38 2.14 +3.15
Alpha Vir (Spica) 13:24:35 -11 06 0.97 +3.15
Alpha Sco (Antares) 16:28:42 -26 24 0.96 +3.66
Alpha Oph (Rasalhague) 17:34:24 +12 34 2.08 +2.76
Alpha Aql (Altair) 19:50:13 +08 50 0.77 +2.88
Alpha Cyg (Deneb) 20:41:02 +45 14 1.25 +2.04
This method is not without its drawbacks as the position of a
star changes with the passing of years and a correction must be
added for Precession to maintain the accuracy. See Norton's Star
Atlas & Reference Handbook. Use the value in the table above and
multiply by the number of years since 1988.5
Annual Handbook.
In a publication such as the British Astronomical Association
Handbook produced annually, there is a tabulation of Sidereal
Time at Greenwich (0 degrees longitude) for 00:00hr every fifth
day. There is also an interpolation table for days and parts of
days. This will give an accuracy of +/- 3 seconds, sufficient for
most uses.
Calculation Method 1.
Using a formula involving the number of days from January 0 and a
table of constants (Sidereal Time at Jan 0.0) it can be computed
to an accuracy of +/- 0.2 seconds. A correction must then be
applied for the longitude.
G.S.T. = K + n * d
Where K is tabulated
n = 236.55536 seconds
d = number of days (including decimal parts of)
since January 0.0
Year K Year K
1995 6.612651 1998
1996 6.596736 1999
1997 6.646532 2000
Note. The longitude correction must be better than 0.1 seconds
accuracy corresponding to knowing where your observatory is to
the nearest 33 yards (at latitude 50 degrees).
Calculation Method 2.
This method involves calculation like method 1 but the constant
is computed first. Again it must be corrected for longitude. See
Practical Astronomy with your Calculator for the details.
References.
1) Norton's Star Atlas & Reference Handbook.
For general information on Sidereal time
,setting up a telescope, precession
2) Practical Astronomy with your Calculator - P Duffett-Smith
Calculation methods 1, 2 and coordinate
conversion.
3) British Astronomical Association Handbook (Annual)
Annual positions of bright stars and sidereal
time every fifth day
USING SIDEREAL TIME
Visibility of objects.
For any given latitude any object will be above the horizon for a
given time. The time from horizon to culmination on the meridian
is called the Semi-Diurnal Arc and is tabled below for various
declinations and latitudes. Pick out the nearest that matches the
object/your latitude and this will tell you the range of Right
Ascensions that are visible when added/subtracted from the
Sidereal Time shown. A realistic horizon of +5 degrees in
altitude is used. This table works for northern and southern
latitudes.
TABLE OF SEMI DIURNAL ARCS
Dec NORTHERN LATITUDES HORIZON = +5 DEGREES
35 45 50 52 54 56 58 60
50 8:47 11:59 0:00 0:00 0:00 0:00 0:00 0:00
45 8:13 9:42 11:59 0:00 0:00 0:00 0:00 0:00
40 7:46 8:50 9:41 10:11 10:56 0:00 0:00 0:00
35 7:24 8:13 8:47 9:05 9:26 9:51 10:27 11:59
30 7:05 7:43 8:08 8:20 8:34 8:50 9:08 9:32
25 6:48 7:17 7:35 7:44 7:54 8:05 8:17 8:31
20 6:32 6:53 7:07 7:13 7:20 7:27 7:36 7:45
15 6:17 6:32 6:41 6:45 6:49 6:54 6:59 7:05
10 6:03 6:11 6:16 6:18 6:21 6:23 6:26 6:29
5 5:49 5:51 5:52 5:53 5:53 5:53 5:54 5:54
0 5:35 5:31 5:28 5:27 5:25 5:24 5:22 5:19
-5 5:21 5:11 5:04 5:01 4:57 4:53 4:48 4:43
-10 5:06 4:49 4:38 4:33 4:27 4:20 4:13 4:04
-15 4:50 4:26 4:10 4:02 3:54 3:44 3:32 3:19
-20 4:33 4:01 3:38 3:27 3:15 3:00 2:43 2:21
-25 4:14 3:31 3:00 2:44 2:25 2:01 1:27 0:00
-30 3:52 2:55 2:09 1:42 1:00 0:00 0:00 0:00
-35 3:26 2:06 0:00 0:00 0:00 0:00 0:00 0:00
-40 2:53 0:00 0:00 0:00 0:00 0:00 0:00 0:00
For SOUTHERN LATITUDES reverse the Declination sign.
Rising Time.
For a particular declination look up the semi-diurnal arc.
Subtract this from the object's Right Ascension to obtain the
sidereal time at which the object will be rising. A glance at the
clock will show how much longer to wait.
Use with an Alt-Azimuth telescope mounting.
Using an application of spherical triangles to transform
coordinate systems you can adjust the Right Ascension,
Declination of an object to horizon coordinates of Altitude and
Azimuth using the value of Sidereal time. This makes it easy to
set up an Alt-Azimuth telescope when fitted with fixed setting
circles for altitude and azimuth.
For an object of Right Ascension R, Declination d, azimuth A,
Altitude a with the observer at latitude lat:
1) Hour Angle H = L.S.T. - R
2) Convert to degrees H = H * 15
3) Altitude sin a = sin d sin lat + cos d cos lat cos H
4) Azimuth cos A' = (sin d - sin lat sin a)/(cos lat cos a)
If the value of sin H is positive the true azimuth is 360 - A'
else true azimuth = A'
Use with equatorially mounted telescopes.
For setting up equatorial telescopes with setting circles two
methods can be used for driven and non-driven polar axes:
1) For driven polar axis set the central meridian on the
Sidereal circle to the time shown on the Sidereal Clock, then
switch on the drive.
2) For non-driven polar axis use a fixed setting circle on this
axis calibrated in hours and minutes and fix 00:00hr on the
central meridian ie due south. To find the position of an object
it is necessary to calculate the hour angle of the object by
reference to its catalogued position and the Sidereal Time shown.
The telescope can then be set at this hour angle.