Astronomy Principles and Practice Fourth Edition.pdf

The relationship between mean solar time and sidereal time 95
For navigational purposes based on solar positional measurements, it is, therefore, accurate enough to
rewrite equation (9.7) as
Ephemeris transit = 12 h − (9.9)
since the equation of time is a slowly varying quantity and T is only of the order of 66 seconds at
present (2000).
Hence, by equation (9.6),
GHA⊙ = GHAMS + 12 h − Ephemeris transit. (9.10)
9.4 The relationship between mean solar time and sidereal time
We have seen that the mean solar day is about 4 minutes longer than the sidereal day. A more precise
relationship will now be developed.
Equation (9.4) gives
LST = HAMS + RAMS. (9.11)
Let the values of these quantities be T 1 , H 1 and R 1 at a particular epoch and T 2 , H 2 and R 2 one
mean solar day later.
Then by equation (9.11), we have
Subtracting, we obtain
T 1 = H 1 + R 1
T 2 = H 2 + R 2 .
But H 2 − H 1 = 24 h , since 1 mean solar day has elapsed.
The Sun’s mean angular rate is n, where
T 2 − T 1 = (H 2 − H 1 ) + (R 2 − R 1 ). (9.12)
n = 360 ◦ /365 1 4 days
or
n = 24 h /365 1 4 days
so that the increase in the mean sun’s right ascension in 1 mean solar day is 24 h /365 1 4
. This must be
the quantity (R 2 − R 1 ). Hence, equation (9.12) becomes
T 2 − T 1 = 24 h + 24 h /365 1 4
= 24 h (1 + 1/365 1 4 )
= 24 h (366 1 4 /365 1 4
) of sidereal time.
This interval of sidereal time is equal to 24 hours of mean solar time so that we obtain the relation:
Alternatively,
24 h mean solar time = 24 h × 366 1 4
365 1 4
24 h sidereal time = 24 h × 365 1 4
366 1 4
sidereal time.
mean solar time.