Page:Practical astronomy (1902, John Wiley & Sons).djvu/30

12 PRACTICAL ASTRONOMY. from which v can be found; i is found from either of equations (18), when v is known. To find L, m, e, and p, we proceed as in the determination of the table of epochs in the case of the sun, using a similar equation, thus : L -j- m T t = v 1 2 e sin (v 1 p), L -f m T 3 = v s 2 e sin (v, p), r L + m T^ = # 4 2 e sin (# 4 ^?), in which v = v + tan' 1 an ^ 7 r ). /23) cos* and similar values for # 2 , v a , and v 4 . To find the ecliptic longitude of perigee V 0, represented by p l , we have from the right-angled triangle NP 0, tan N = tan (p v) . cos i, (24) from which p l = v -(- tan' 1 (tan (/? r) . cos i). (25) Similarly the mean ecliptic longitude of the moon, L l , at the epoch is L l = v -f tan" 1 (tan (L v) . cos t). (26) To find the sidereal period, s, we have in which s is the length of the sidereal period in mean solar days. 2. The Ephemeris of the Moon. The motion of the moon is much more irregular and complicated than the apparent motion of the sun, owing mainly to the disturbing action of this latter body. But this and other perturbations have been computed and tabulated, and from these tables, including those of the node and inclination, the places of the moon in her orbit are found in fche same way as those of the sun in the ecliptic. The mean orbit longitude of the moon and of her perigee are first found and corrected ; their differ- ence gives her mean anomaly, opposite to which in the appropriate table is found the equation of the center, and this being applied