The Siddhāntasundara of Jñānarāja: An English Translation with Commentary

13 Chapter on Mathematical Astronomy: Section 7 Rising and Setting of Planets

13. Chapter on Mathematical Astronomy Section 7: Rising and Setting of Planets This section deals with the rising and setting of planets, including the conditions for it to happen, computing the time until the next rising or setting, and so on. (1) A planet with a velocity less than [that of] the sun rises [heliacally] in the east when the sun passes in front of it, and [a planet] with a greater velocity [than that of the sun] rises [heliacally] in the west when it is in front of the sun, [in both cases] according to the [appropriate] time degrees. [The planet] sets [heliacally] in the opposite manner [i.e., when slower than the sun it sets in the west and when faster than the sun it sets in the east]. The heliacal rising of a planet in the east occurs when the planet is visible just before sunrise after not having been visible for some time due to its proximity to the sun. If the velocity of the planet is less than that of the sun, the heliacal rising in the east occurs after the sun has overtaken the planet. If the planet has a velocity greater than that of the sun, the heliacal rising in the west occurs after the planet has overtaken the sun. Similarly, if the planet has a velocity less than that of the sun, it sets in the west when the sun catches up with it; and if it has a velocity greater than the sun, it sets in the east when it catches up with the sun. The time degrees mentioned give the distance of the planet from the sun in order for the heliacal rising to occur; they will be given below in verse 9. (2) Mars, Jupiter, and Saturn, [the velocities of] which 293 294 13. Chapter on Mathematical Astronomy, Section 7 are less than [that of] the sun, rise [heliacally] in the east [when] their śı̄ghra anomalies are 28, 14, and 17 degrees, respectively. [Their heliacal] setting in the west is said [to occur when their śı̄ghra anomalies have longitudes measured] by these [values] subtracted from 360◦ [i.e., 332◦, 346◦, and 343◦, respectively]. The superior planets, that is, Mars, Jupiter, and Saturn, move slower than the sun. The Indian astronomical tradition gives the values that their śı̄ghra anomalies must have for the heliacal risings or settings to occur. Here values of the śı̄ghra anomalies of Mars, Jupiter, and Saturn (the superior planets) are given; more values are given in the next verse. Table 13 shows the vales of the śı̄ghra anomalies given in verses 2–4. (3–4b ) Venus and Mercury, [whose] velocities [can be] greater or less than the velocity of the sun, rise and set in the west, by means of 24, 50, 177, and 155 [degrees of their śı̄ghra anomalies]. In the east, the two [inferior planets rise and set] by 183, 205, 336, and 310 degrees. The two inferior planets, namely, Venus and Mercury, sometimes move faster than the sun and sometimes slower. In the west, the planet Venus has a heliacal rising when its śı̄ghra anomaly is 24◦, and Mercury has a heliacal rising when its anomaly is 50◦; the settings occur when the śı̄ghra anomalies are 177◦ and 155◦, respectively. Similarly, in the east, Venus has a heliacal rising when its śı̄ghra anomaly is 183◦, and Mercury has a heliacal rising when its anomaly is 205◦; the settings occur when the śı̄ghra anomalies are 336◦ and 310◦, respectively. Table 13 shows the vales of the śı̄ghra anomalies given in verses 2–4. (4c–d ) The minutes of arc [in the current śı̄ghra anomaly] increased or decreased by the given values and [then] divided by the velocity of the śı̄ghra anomaly yield the days elapsed or remaining [since or until the next phenomenon ]. 13. Chapter on Mathematical Astronomy, Section 7 295 Planet Rise, east Rise, west Set, east Set, west Mars 28◦ 332◦ Mercury 205◦ 50◦ 310◦ 155◦ Jupiter 14◦ 346◦ Venus 183◦ 24◦ 336◦ 177◦ Saturn 17◦ 343◦ Table 13: Śı̄ghra anomalies for heliacal risings and settings The verse gives a simple proportion. The śı̄ghra anomaly is the angular distance between the mean planet and the śı̄ghra apogee. Let κσ be the śı̄ghra anomaly, a be one of the given values (depending on what planet...