Astronomy Principles and Practice Fourth Edition.pdf

90 The celestial sphere: timekeeping systems
Figure 9.2. The relation between local sidereal time and Greenwich sidereal time.
Then the Greenwich hour angle of X is GPX which is the longitude λW of the observer.
The Greenwich hour angle of the vernal equinox is GP which is equal to the hour angle
XP plus the longitude λW of the observer.
Or
GHA = HA + λW.
But the hour angle of is the LST, therefore we may write
GAST = LST + λW.
If were any celestial object ⋆, we would have
GHA⋆ = HA⋆ + λW.
It is easily seen that if the longitude of the local observer had been east we would have written
GHA⋆ = HA⋆ − λE.
If we agree that a western longitude is positive and eastern is negative, we may combine these
relations to give
GHA⋆ = HA⋆ + λ (9.2)
a very important expression often remembered by the mnemonic:
Longitude east, Greenwich least,
Longitude west, Greenwich ‘best’.
The sidereal day at a given place begins when the vernal equinox transits across the observer’s
meridian and ends 24 sidereal hours later when is once more on the meridian. Thus, one sidereal
day is the time taken for one rotation of the Earth about its axis with respect to the stellar background.
The sidereal clock in an observatory should, therefore, read 0 h when is on the meridian. We have
the following table:
1 sidereal day = 24 sidereal hours
1 sidereal hour = 60 sidereal minutes
1 sidereal minute = 60 sidereal seconds.