Astronomy Principles and Practice Fourth Edition.pdf

104 The celestial sphere: timekeeping systems
Table 9.3. The lengths of the northern hemisphere seasons in the year 1999 to 2000.
Season Days Hours
Winter 88 23·86
Spring 92 18·21
Summer 93 15·66
Autumn 89 20·17
Comparison of each of the seasons’ lengths shows that there are variations amounting to a few
minutes from year to year as a result of irregularities in the motion of the apparent Sun relative to the
equatorial coordinate frame. For the year covering 1999 to 2000, the lengths of the seasons are given
in table 9.3.
A simple and only slightly less accurate way of determining the lengths of the seasons involves
calculations of the equation of time, , on the dates corresponding to the equinoxes and solstices.
Consider the development of the general formula for such calculations by taking spring as an example.
From earlier we had
= RAMS − RA⊙ (9.3)
where is the equation of time.
Let the values of the equation of time at the beginning and end of spring be 1 and 2 while the
values of the RAMS at those times are R 1 and R 2 . The corresponding values of the RA⊙ are 0 h and
6 h by definition. Then by equation (9.3),
1 = R 1 − 0 h ,
2 = R 2 − 6 h
giving
R 2 − R 1 = 2 − 1 + 6 h .
But the mean sun increases its right ascension by 24 h in close to 365 1 4
days. Therefore the length
of spring in days is given by ( )
2 − 1 + 6
× 365 1
24
4 . (9.17)
Values of the equation of time precise to 1 s may be derived from The Astronomical Almanac.
Using equation (9.9), namely
ephemeris transit = 12 h − equation of time (9.9)
and taking the relevant values of the ephemeris transit from the almanac at the beginning of the day
when the Sun achieves 0 h and 6 h , we find for the year 2000 that
2 − 1 = 5 m 33·s6 = 0·h092 67.
The expression (9.17) can then be evaluated and it is found that the length of spring in the northern
hemisphere in 2000 is 92 d 17·h3, a value not very different to that given in table 9.3. Values for the
lengths of the other seasons can be obtained by obtaining the difference of the equations of time,
2 − 1, at the end and beginning of each season.
The amount of heat received from the Sun and the average daily temperature have very little to do
with the varying distance of the Earth from the Sun. In the northern hemisphere, in fact, the Earth is