Astronomy Principles and Practice Fourth Edition.pdf

96 The celestial sphere: timekeeping systems
Table 9.1. Conversion of mean solar time into sidereal time.
24 h mean solar time ≡ (24 h + 3 m 56·s556) sidereal time
1 h mean solar time ≡ (1 h + 9·s8565) sidereal time
1 m mean solar time ≡ (1 m + 0·s1643) sidereal time
1 s mean solar time ≡ (1 s + 0·s0027) sidereal time
Table 9.2. Conversion of sidereal time into mean solar time.
24 h sidereal time ≡ (24 h − 3 m 55·s910) mean solar time
1 h sidereal time ≡ (1 h − 9·s8296) mean solar time
1 m sidereal time ≡ (1 m − 0·s1638) mean solar time
1 s sidereal time ≡ (1 s − 0·s0027) mean solar time
More exactly,
1 mean solar day = 24 h 03 m 56·s5554 of sidereal time
1 sidereal day = 23 h 56 m 04·s0905 of mean solar time.
Tables for the conversion of mean solar time to or from sidereal time are printed in several
almanacs. Any conversion, however, can be performed using tables 9.1 and 9.2.
Alternatively, we may proceed as in the following example: convert 6 h 42 m 10 s MST to sidereal
time.
10 s = 10/60 m = 0·m1667 42·m1667 = 42·1667/60 h = 0·h702 78.
Hence,
6 h 42 m 10 s MST = 6·h702 78 MST = 6·h702 78 × 366 1 4 /365 1 4 ST = 6·h721 13 ST.
Now
0·h721 13 = 0·721 13 × 60 m = 43·m2678 0·m2678 = 0·s2678 × 60 = 16·s1.
Hence, the required interval of sidereal time is 6 h 43 m 16·s1.
9.5 The civil day and timekeeping
The Greenwich meridian is regarded as the standard meridian on the Earth for timekeeping using mean
solar time. Just as for any other observer’s meridian, the Greenwich hour angle of the mean sun is zero
when the mean sun transits across the meridian through the zenith at Greenwich; i.e. at mean noon
GHAMS = 0 h
while at mean midnight,
GHAMS = 12 h .
For convenience, however, a civil day begins at midnight. The Greenwich Mean Time (GMT) is
then zero hours. But the GHAMS is then 12 hours in value. By the time the GHAMS is 24 hours or
zero hours once more (i.e. by mean noon) the GMT is 12 h .