पृष्ठम्:महाभास्करीयम्.djvu/२११

126 TRUE LONGITUDE OF A PLANET of the centre for each individual planet determines its own eccentric (pratimandala). In Fig. 13, SK and TW are perpendiculars to the apse line EU. TW (which is equal to MA) is the Rsine of the bhuja (or bahu) MU, and SK is the Rsine of the true bhuja (called spasta-bhuja) SU. Comparing the similar triangles SKE and TWE, we have SK SE SK = giving or Rsin (arc SU) Therefore, arc SU Rsin-¹ TW TE TWXSE TE Rsin (bhuja)xR Sun's true distance = "" Rsin (bhuja) xR Sun's true distance (1) Now let be the first point of Aries. (See Fig. 13). Then, if the Sun is in the first anomalistic quadrant (as in the figure), Sun's true longitude arc Ts arc TU + arc SU. longitude of the Sun's apogee + arc SU. When the Sun (i.e., the true Sun) is in the second quadrant, say at Q, the expression on the right hand side of (1) turns out to be the value of arc QN. Hence, in this case. Sun's true longitude arc TQ = arc TU + (180⁰. - arc QN). Similarly, in the remaining quadrants. The method for finding the Moon's true longitude is similar. A rule for finding the Sun's bhujantara correction under the eccentric theory: 24. The (mean) daily motion (of the Sun) multiplied by the difference between the (Sun's) true and mean longitudes computed for the local place¹ and (the product then) divided by the number of minutes in a circle (i.e., by 21600) gives, as before, the (Sun's) bhujantara.² ¹ What is meant here is the svanirakṣa place, i.e., the place where intersects the equator. the local 2 This rule occurs also in BrSpSi, xiv. 19.