Page:Practical astronomy (1902, John Wiley & Sons).djvu/29

 EPHEMERI8. Declinations, corrected for refraction, semi-diameter, parallax, and perturbations, then converted into the corresponding latitudes and longitudes, and finally referred to the mean equinox of the epoch, by correcting for aberration, nutation, and precession. Kef erring to the figure, assume the following notation: v = V N, the longitude of the node; i = C N B, the inclination of the orbit; ^ = V0 l9 the longitude of J/,; 2 = V a, the longitude of Jf a ; A,= M l O l, the latitude of J/,; A a = Jf a O a, the latitude of Jf a ; v, = VEN+ NE M l, the orbit longitude of Mj p = V E N -- N E P, the orbit longitude of perigee, = PE M l = v l p, the true anomaly of Jf, ; e eccentricity of orbit; m = mean motion of moon in its orbit; t l = time since epoch for M 1 ; L = mean orbit longitude at epoch. To find v and i, we have from the right-angled spherical tri- angles M l N O l and Jf, N O a , sin (Zj v) = cot i tan Aj / sin (Z a ^) = cot i tan A f and by division, sin (1. v) tan A. sin ft - r) = i^T; Adding unity to both members, reducing, then subtracting each member from unity, again reducing, and finally dividing one result by the other, we obtain sin (? 2 v) -- sin (?, v) _ tan A 2 -f- tan A, sin (7, -r) sin (/. - v) ~ tan A,- tan A/ or by reduction formulas, page 4 (Book of Formulas),
 * j stained as in case of the sun by observed Eight Ascensions and