## Rising and Setting Times

instants when the altitude of the Moon is —34' — s + n, where s is the apparent radius (15.5' on the average) and n the parallax (57' on the average). The latter quantity is explained in Sect. 2.9.

Finding the rising and setting times of the Sun, planets and especially the Moon is complicated by their motion with respect to the stars. We can use, for example, the coordinates for the noon to calculate estimates for the rising and setting times, which can then be used to interpolate more accurate coordinates for the rising and setting times. When these coordinates are used to compute new times a pretty good accuracy can be obtained. The iteration can be repeated if even higher precision is required.

From the last equation (2.16), we find the hour angle h of an object at the moment its altitude is a:

sin a

cos S cos p

This equation can be used for computing rising and setting times. Then a = 0 and the hour angles corresponding to rising and setting times are obtained from cos h = — tan S tan p .

If the right ascension a is known, we can use (2.11) to compute the sidereal time &. (Later, in Sect. 2.14, we shall study how to transform the sidereal time to ordinary time.)

If higher accuracy is needed, we have to correct for the refraction of light caused by the atmosphere of the Earth (see Sect. 2.9). In that case, we must use a small negative value for a in (2.20). This value, the horizontal refraction, is about —34'.

The rising and setting times of the Sun given in almanacs refer to the time when the upper edge of the Solar disk just touches the horizon. To compute these times, we must set a = —50' (= —34'—16').

Also for the Moon almanacs give rising and setting times of the upper edge of the disk. Since the distance of the Moon varies considerably, we cannot use any constant value for the radius of the Moon, but it has to be calculated separately each time. The Moon is also so close that its direction with respect to the background stars varies due to the rotation of the Earth. Thus the rising and setting times of the Moon are defined as the

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