Page:Practical astronomy (1902, John Wiley & Sons).djvu/32

 14 PRACTICAL ASTRONOMY. r = E S, be the earth's radius vector; r' S P, be the planet's radius vector; A = V S O f be the heliocentric longitude of planet; A' = V E 0, be the geocentric longitude of planet; 6 P 8 0, be the heliocentric latitude of planet; 6' = P E 0,be the geocentric latitude of planet; S = S E, be the commutation ; = S E, be the heliocentric parallax; E = 8 E be the elongation; L = V E S, be the longitude of the sun; r" = E P, be the distance of planet from the earth. To find the geocentric longitude, S = r' cos 6, (28) VS T = VES = 360 - L, (29) 8 = 180 - (360 - L) - A = L - 180 - A, (30) from which S is known. In the plane triangle E S, we have r' cos 0+ r: r' cos 6 - r : : tan t(E+0): tan (E 0). (31) E= 180, (32) 9) = 90-, (33) hence 7* r*oQ r/ ^* tan 4 (^ - 0) = cot i tf, a , , (34) ^ /' cos B r and placing _r' cos ft . . r ' we have - 0) = ooti# . = cotjtftan (j? - 45) (36)