Chapter on True Positions—2

The Apogees—

The apogee mandocca: the point in a planet's orbit furthest from the Earth where its motion appears slowest of the Sun is 78 degrees original: 'gajādrbhāgā' — gaja (8), adri (7) = 78. For Mars and the others, the values are: 128 and a half; 225; 172 and a half; 81; and 261 respectively. ॥ 1 ॥

Sumatiharṣa's Commentary:—

The apogee of the Sun is 78 degrees, which is 2 signs and 18 degrees In Indian astronomy, 1 sign = 30 degrees. Thus 78° = 2 signs (60°) + 18°. The apogee of the Moon was already stated in the section beginning with "The group [of planets] is twofold."

For Mars Bhauma, the value "128 and a half" original: 'sadalāṣṭasūryāḥ' — sūrya (12), aṣṭa (8), and dala (half) means 128 degrees and 30 minutes, which is 4 signs and 8 degrees and 30 minutes.

For Mercury Budha, the value "twenty-five and two hundred" original: 'tattvāśvinaḥ' — tattva (25), aśvin (2) means 225 degrees, which is 7 signs and 15 degrees.

For Jupiter Guru, the value "half-added two, seven, and one" original: 'sārddhayama-adri-candrāḥ' — yama (2), adri (7), candra (1) means 172 degrees and 30 minutes, which is 5 signs, 22 degrees, and 30 minutes.

For Venus Śukra, the value is 81 degrees original: 'kvaṣṭau' — ku (1), aṣṭa (8), which is 2 signs and 21 degrees.

For Saturn Śani, there are two readings of the text. The reading "moon, limbs, and twins" original: 'śaśāṅka-aṅga-yamāḥ' — śaśāṅka (1), aṅga (6), yama (2) gives 261 degrees, which is 8 signs and 21 degrees. Alternatively, there is a reading "elephants, fire, and twins" original: 'matanga-agni-yamāḥ' — matanga (8), agni (3), yama (2) which gives 238 degrees.

The reason for this is explained in the Siddhānta Śiromaṇi: In the school that holds there are 54 revolutions bhagaṇa of Saturn's apogee in a Kalpa an immense cycle of time, the reading 238 is used. In the school that holds there are 41 revolutions kusāgara, the value 261 is produced. The school asserting 54 revolutions follows the Ārya Siddhānta The astronomical system of Āryabhaṭa, as it is said: "The apogees of the Sun and these others were created by Brahmā..." and so on. Similarly, in the Sūrya Siddhānta, the value for Saturn's apogee is given as 7 signs, 28 degrees, and 37 minutes, which agrees with Āryabhaṭa.

However, in the Mṛgāṅka Karaṇa Pradīpa and other commentaries, the value 238 is adopted. This is expressed in the mnemonic verse: "Planetary positions: mountains, elephants, kings, and zero (7-28-56-0)... the apogee of Saturn is elephants, fire, and twins (238)." The Teacher has accepted the value 238 for Saturn as a specific variant of his own school. As it is said:

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1. "Elephants, fire, and twins" (238) is a textual variant.

"Astronomy is a traditional science āgama-śāstra; it is not proper for us to argue when there is disagreement. We should not simply choose by our own will, but I shall state the opinions of many." ॥ 1 ॥

Sudhākara's Commentary:—
This is for the sake of clarity. Since the apogees are essentially stationary They move extremely slowly over millennia, the Teacher calculated and recorded them for his own time. The underlying logic is clear.

The Fast Points (Conjunctions)—

The values are 81, 44, 23, 87, and 13 respectively. For Mars and the others, the mean Sun is the "Fast Point" śīghrocca: for outer planets, this point corresponds to the Sun's position for Jupiter, Mars, and Saturn. ॥ 2 ॥

Sumatiharṣa's Commentary:—

81, 44, 23, 87, and 13 are the maximum values parākhyāḥ for Mars and the others. These are the "Greatest Equations" parama-phala in the form of a Sine jyā. Their corresponding arcs—the maximum "Fast Corrections"—are: for Mars 42° 40'; for Mercury 22° 30'; for Jupiter 11° 0'; for Venus 46° 15'; and for Saturn 6° 15'.

Now he describes the "Fast Point" śīghrocca of the planets: The Fast Points for Mercury and Venus were already stated in the chapter on mean motion. For the others—Jupiter, Mars, and Saturn—the Mean Sun should be understood as their Fast Point. ॥ 2 ॥

Positive and Negative Values of the Slow and Fast Anomalies—

By subtracting the planet from its Slow Apogee and Fast Point, the Slow Anomaly and Fast Anomaly are produced. These should be divided into quadrants of three signs each. The resulting correction phala is positive or negative depending on whether the anomaly starts in Aries or Libra. ॥ 3 ॥

Sumatiharṣa's Commentary:—

When the Mean Planet (purified by corrections for longitude and the bīja factor) is subtracted from its Slow Apogee mandocca and its Fast Point śīghrocca, the results are respectively the Slow Anomaly manda-kendra and the Fast Anomaly śīghra-kendra. The twelve signs of the zodiac are divided into four quadrants pada. The first and third quadrants are called "odd," while the second and fourth are...