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.