पृष्ठम्:महाभास्करीयम्.djvu/२४९

164 To begin with, the time of geocentric conjunction is taken as the first approximation to the time of apparent conjunction and the corres- ponding lambana is obtained by the following formula: lambana = Moon's drggatijyä x Earth's semi-diameter Moon's true distance in yojanas Sun's drggatijyä x Earth's semi-diameter minutes. Sun's true distance in yojanas This formula may be derived as follows: Consider Fig.18.CS is the ecliptic, C and S being the central ecliptic point and the Sun at the time of geocentric conjunction (treated as the time of apparent conjunction). K is the pole of the ecliptic and Z the zenith. S' is the position of the Sun as observed from the local place. ZA and S'B are perpendiculars on the secondary to the ecliptic passing through S' (i.e., on KS); S'D is perpendicular to the ecliptic. But ECLIPSES But Rsin (arc BS')= Sun's lambana- Fig. 18 In the triangle S'DS right-angled at D, SS' denotes the Sun's parallax in zenith distance and SD denotes the Sun's parallax in longitude (lambana). Hence From the triangles SBS' and SAZ, right-angled at B and A respectively, we have Rsin (arc BS')= Z Rsin (arc SS)= Rsin (arc AZ) x Rsin (arc SS') Rsin (arc ZS) BS' or SD approximately. Therefore, (Sun's drggatijyä) x Rsin (arc SS') Rsin (arc ZS) Sun's lambana== approx. Earth's semi-diameter x Rsin (arc ZS) Sun's true distance in yojanas K Sun's drggatijyä x Earth's semi-diameter Sun's true distance in yojanas (1)