The Siddhāntasundara of Jñānarāja: An English Translation with Commentary

16 Chapter on Mathematical: Astronomy Section 10 Conjunctions of Planets

16. Chapter on Mathematical Astronomy Section 10: Conjunctions of Planets This section investigates the occurrence of conjunctions of planets, including computation of the time for a conjunction. (1–2b ) After applying the visibility correction and the ayanavalana to the corrected [longitudes of two given] planets based on the given directions, the minutes of arc in the difference [of the longitudes] divided by the difference of the [true] velocities [of two planets] yield [the time of] the conjunction of the planets. If one planet is retrograde, [but not the other, the time of conjunction is found] by means of the days resulting from the sum of their [true] velocities. The visibility correction and the ayanavalana have already been discussed; see Siddhāntasundara 2.7.7 and 2.5.22–32, respectively . The results are the actual position of the planets in the sky, as seen from a given location on the surface of the earth. The formula given is straightforward. The difference of the true longitudes of the two planets gives the angular distance to be traversed, while the difference of the true velocities gives the velocity by which the two planets approach (or move away from) each other. Time is then found as distance over velocity. The formula assumes that the two planets are moving in the same direction, that is, that they either both have direct motion or both have retrograde motion. If one of the planets in question is retrograde and the other is not, the two planets move in opposite directions and it is therefore necessary to use the sum of their velocities for the computation described in the previous verse rather than the difference. 317 318 16. Chapter on Mathematical Astronomy, Section 10 (2c–d ) When the retrograde planet has the smaller velocity or the smaller [longitude of the two planets], [the conjunction] has already occured; [if it is the] opposite, [the conjunction] will occur in the future. If the planet with retrograde motion has the smallest longitude , the two planets are moving away from each other, so that the conjunction has already occurred. However, it is not correct that just because the retrograde planet has a smaller velocity than the planet with direct motion, the conjunction has occurred; the planets could be close and moving toward each other. (3) When both planets are retrograde, they advance separately according to the obtained days [from the computation given before]. The latitudes of the planets are the same in this case. The computed latitude of the moon is corrected by the latitudinal parallax. The meaning of the verse is unclear. In particular, the latitudes of two retrograde planets are not necessarily equal, and there is no reason to limit a correction by the latitudinal parallax to the moon alone. (4–5b ) The distance between [the centers of] two planets [with equal longitudes], which are located in the directions given by their respective celestial latitudes, is [found as] the difference or the sum of their latitudes when they are [respectively] the same or different. When the apparent latitude, which is the distance [between the centers of the two planets], is less than half the sum of [the diameters of] the disks [of the planets], then there is a [conjunction known as] bhedayoga, just as in the case of a solar eclipse. A conjunction means that the two planets in question occupy the same position with respect to the ecliptic at the same time. A bhedayoga conjunction (sometimes also called bhedayuti), however , occurs when the disks of the planets actually overlap in the sky, rather than merely having the same position. As such, 16. Chapter on Mathematical Astronomy, Section 10 319 a bhedayoga is what most people understand by “a conjunction of two planets,” namely, that one of the planets obscures the other. (5c –6) In the case of Mars, [when it is at its mean distance from the earth,] its disk extends 1,885 yojanas. The measure of the disk of Mercury is 289 [yojanas]. [That] of Jupiter is 16,602 [yojanas]. The disk of Venus is 1,112 [yojanas]. [That] of Saturn is 29,646 [yojanas]. The diameters in yojanas of the disks of the five star-planets at their mean distances from the earth are given; these are called mean diameters. The results are summarized in Table 18. Jñānarāja has already, in Siddhāntasundara 2...