Delight of Mathematicians

The Eight Types of Motion

Verse: Retrograde, starting retrograde, leaving retrograde, slow, very slow, mean; as well as fast and very fast—these are the eight-fold motions of the planets. original: vakrā-anuvakrā vikalā-mandā manda-tarā-samā | tathā śīghrā-atiśīghrākhya grahāṇām-aṣṭadhā gatiḥ ||

Interpretation: Vakra—known as retrograde motion; Anuvakra—the beginning of retrograde motion; Vikala—the abandonment or exit from retrograde motion; Manda—slow motion; Mandatara—exceedingly slow motion; Sama—mean or average motion. Tatha—likewise; Shighra—fast motion; Atishighra—exceedingly fast motion. Ashtavidha—these eight types; Gati—of motions; Jneya—should be understood. In ancient Indian astronomy, planets do not actually move backward; "retrograde" (vakra) describes the optical illusion where a planet appears to move backward against the stars because of the Earth's own movement in its orbit.

Regarding Direct Motion

Verse: Among these, very fast, fast, slow, very slow, and mean—these five are known as direct motion Rjvistraight or forward motion. I shall now explain with care how planets, through the power of their various movements, daily reach a state where their observed positions match the calculations. original: tatrātiśīghra śīghrākhya mandā mandatara samā | ṛjvīti pañcadhā jñeyā yā vakrā sānuvakritā | tattadgativaśān-nityam yathā dṛktulyatāṃ grahāḥ | prayānti-tatpravakṣyāmi sphuṭīkaraṇam-ādarāt ||

Interpretation: Rjvi—regarding direct motion; Tatra—likewise; Atishighra—exceedingly fast; Shighrakhya—named fast; Manda—very slow The Telugu commentary here slightly swaps the intensity of 'manda' and 'mandatara' compared to common usage, but the intent remains a hierarchy of slowness.; Mandatara—slow; Sama—mean; Panchadha—these five types of motion; Jneya—are to be known. Yavakra—that which is retrograde; Asanuvakrita—that which is direct; Tattat-gativashat—by the power of those respective motions; Nityam—always; Grahah—the planets; Drktulyatam—the state where observation matches calculation original: dṛktulyatva; Yatha—in which manner; Prayanti—they attain; Tat—that; Sphutikaranam—method of correction The process of turning a 'mean' position into a 'true' observed position.; Adharat—with care; Pravakshyami—I am telling you.

A Simple Method for the Eight Types of Motion

Verse: Conjoined with the Sun and others, fast in the second; mean in the third, slow in the fourth; retrograde in the fifth and sixth, highly retrograde in the seventh; in the ninth or tenth their motion is tortuous; in the eleventh or twelfth, they become fast and exceedingly fast in sequence. original: sūryamuktādiryaṃte śīghragāśca-dvitīyake | samaṃ tṛtīyake-yānti mandagatyāś-caturthake | vakra pañcama ṣaṣṭheke ativakroṣṭha-saptame | navame daśame-vāpi eteṣāṃ-kuṭilā gatiḥ | ekādaśe dvādaśevā śīghrātī-śīghratarā kramāt ||

Interpretation: This is how you should understand it:
1. A planet joined with the Sun is "extinguished" astamaya: invisible due to the Sun's glare.
2. When it leaves the Sun, it "rises" udaya and moves at a fast speed.
3. In the third position, it moves at a mean (average) speed.
4. In the fourth, it moves at a slow speed.
5. In the fifth, it is in a steady state.
6. In the sixth, it is retrograde.
7. In the seventh, it is retrograde.
8. In the eighth, it is highly retrograde.
9. In the ninth, it returns to direct motion.
10. In the tenth, it has a tortuous or irregular motion.
11. In the eleventh, it moves at a fast speed.
12. In the twelfth, it moves at an exceedingly fast speed.