Astronomy Principles and Practice Fourth Edition.pdf

98 The celestial sphere: timekeeping systems
Figure 9.6. The Greenwich date and zone time.
sailors when they arrived home one day too late by their reckoning, and which enabled Jules Verne’s
character Phileas Fogg to win his wager to journey round the World in 80 days.
In many problems it is necessary to convert from a particular zone time and date to the
corresponding GMT and date. The Greenwich Date isthenamegiventoaGMTplusthedateat
Greenwich and we now consider the relationship between a Greenwich Date and a zone time and date.
9.6 The Greenwich date and zone time (with date)
In figure 9.6 the Earth is seen as viewed from above the North Pole P, the meridian of longitude PGA
through Greenwich G meeting the equator in A. The International Date Line PL cuts the equator at
L, its southern half being, of course, unseen.
The standard meridian PB, of longitude λ ◦ E, likewise meets the equator at B, whereAPB =
λ ◦ E.
Let a civil day, for example November 3rd, begin at the Date Line. It does so when the HAMS is
12 h for that meridian, i.e. the mean sun is at M 1 , above the point A on the equator.
November 3rd will not begin for places in the zone keeping the zone time of the standard meridian
PB until the mean sun has moved round the celestial sphere to be at M 2 , above D, whereD is 180 ◦
distant from B round the equator.
For the Greenwich meridian and Zone 0, November 3rd will begin even later, when the mean sun
has revolved until it is above L, atM 3 .
The Greenwich Date is then November 3rd, GMT 00 h 00.
But the zone time with date at B is by then November 3rd, ZTλ h ,sinceDPL = APB = λ E.
The required relation is thus
GMT = ZT − λE
where λ is now expressed in hours.
By taking a western standard meridian at F, say,whereAPF = λW, it is easily shown that the
relation is given by
GMT = ZT + λW
λ being expressed in hours.
We may, therefore, combine these rules by adopting as before the convention that a western
longitude is positive and an eastern one is negative. Thus,
GMT = ZT + λ. (9.15)