The Lunar Apsides

Cover The Lunar Apsides
The Lunar Apsides
Elias Colbert
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73957057 2 = -0030139854 97-47914/11416 e 4 = -0000090841 94-9582823 gC = -0000000274 92-4374 e 8 = -00000000008 89-92 t p 0-9969860146 9-9986890662 Then, for the averages on radius vector we have: (r 4- ) = 1-00904 53630 5' 0-00391 06910 (r 4- a) 4 = 1-01508 69601 8 0-00650 44721 7 Also for the inclination we have: 8 a _:_ 3 = _:_ 8 __ _|_ 339627 /' ' - - ^4- 0"804 sin 2 y' = 0-00804069057 97-90529335 sin 4 y ^ = . V 6 46^27 \ 9^105867 sin 8 y 42 91-6212 When n is % $n even power, the average ...value of sin" y is \ (n 1 ) . (n 2) . . . '. ($n + 1) . 2(1 . 2 ; 3 . 4 . . . !* . _ Jw) Giving ( 1 4- 2 ) for sin 2 ; (3^-8) for sin 4 ; (5 4- 16) for sin 6 ; (35 4- 128) for sin*; etc.
Cos 2 ]> 's latitude = 1 sin 2 y sin 2 longitude. Hence we get the following values, not for the latitude at any particular point but the average cos, cos 2, etc. , of the D 's latitude: cos lat. =1 sin 2 y - sin 4 y sin 6 y ' sin y .
4 64 256 16384 cos 2 lat. = 1 J sin 2 y.
395 105 cos 3 lat. = 1 - sin 2 y 4- sin 4 y 4- sin 6 y 4- sin 8 y.


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