The “rotations of the fixed stars” in this table is the “rotations of the earth on
its axis” according to A ̄ryabhat.a, because he thought that the earth was moving
while the stars were fixed. But no Indian astronomers followed his idea until
Nı ̄lakan.t.ha of the sixteenth century. The different behaviors of the outer planets
(Saturn, Jupiter, and Mars) and the inner planets (Venus and Mercury) were
known to Indian astronomers. The numbers given for the outer planets are their
sidereal rotations and those of their s ́ı ̄ghra(literally “swift one”) are equal to that
of the Sun. Those numbers for the inner planets are the rotations of the s ́ı ̄ghra,
while their sidereal rotations are equal to that of the Sun. From modern astro-
nomical point of view, therefore, the s ́ı ̄ghracan be interpreted as the mean Sun.
Since, however, ancient Indian planetary theory was geocentric, they regarded
thes ́ı ̄ghraas rotating on the geocentric orbit of the planet and constantly
drawing the planet in its direction.
After computing the longitude of the mean planets as the function of time
since epoch, the true position was obtained by means of the eccentric-epicyclic
theory. Here is a remarkable difference from Ptolemy’s theory. Ptolemy combined
two effects which cause the irregular motions of planets, namely, that of eccen-
tricity and that of anomaly, and put them together in a single geometric model.
In doing so he had to introduce a controversial point, which was later called the
“equant,” outside the center of the eccentric circle. In India, on the other hand,
the two effects were kept separate and no unified model was conceived. One was
called the manda(literally “slow one”) epicycle which explains, in modern words,
the combined effects of the eccentricities of the Sun and the planet, the other
was called the sı ̄ghra epicycle as mentioned above. The effects of these two ele-
ments for each planet were separately tabulated. The procedures of using the
two tables in order to get the final equation (antyaphala) show some variations
depending on the school. Thus we can say that Indian planetary theory is not
totally geometrical. Once they introduced geometrical models from the west,
they developed their own functional method.
It is worth mentioning that A ̄ryabhat.a’s school survived in south India, espe-
cially in Kerala, and was revived as the Ma ̄dhava school in the fourteenth
century. The culmination of this school is Nı ̄lakan.t.ha (1444 to after 1542), who
tried to combine the two effects in a single geometrical model, and the result was
quite similar to the partial heliocentric model of Tycho Brahe.
Notes
1 I follow Dr. Ohashi’s interpretation. Cf. Yukio Ohashi, 1993.
2 Yugapura ̄n.a, a part of the Ga ̄rgya-jyotis.a, was edited and translated by John E.
Mitchiner, Calcutta 1986.
3 MBh.2.11.20; 3.3.19; 6.3.11–17; 13.151.12 etc. Thanks are due to my friend, Prof.
M. Tokunaga by whom the whole text of the Maha ̄bha ̄rata has been digitalized.
4 Some other examples are: Ra ̄ma ̄yana1.17 (Ra ̄ ma’s horoscope), Mudra ̄ra ̄ks.asa4.19
(horoscopic prediction), and a part of the Atharvaveda-paris ́is.t.a.
5 The time when the longitude ofaVirginis was 180°. Cf. Chatterjee 1998.
calendar, astrology, and astronomy 391