ब्राह्मस्फुटसिद्धान्त (ब्रह्मगुप्त - शून्य, कुट्टक, बीजगणित एवं सम्पूर्ण २१ अध्याय सान्वय सटीक)

8 ASTRONOMY IN ANCIENT NATIONS
Earth as a Sphere
The astronomers of the Siddhāntas taught that the Earth
is a sphere, unsupported in space, and they reject the ancient my-
thological notion that it is supported by some animal like śeṣanā-
ga (serpent), kacchapa (tortoise), or diggajas (elephants) which
in turn rest on another, and so on, until the support of the last
one after all has to be left unexplained. Bhāskara II, about
A.D. 1150, who comments on the absurdity of this, also rejects
the idea that the Earth is perpetually falling, since it would fall
faster than an arrow shot upwards, on account of being heavier,
so that an arrow could never again reach the Earth.¹ Round the
Earth the planets are moving, all with the same linear velocity.
The diameter of the Earth is 1600 yojanas, the distance of the
Moon is 51,570 yojanas (or 64.5 times the radius of the Earth,
nearly equal to Ptolemy's greatest distance, 64⅙), while the dis-
tances of the other planets result from the assumption of
equal velocities.² The equation of centre of the planets
is found by an epicycle and to this arrangment the Hindus
add one of their own invention, by assuming that the epi-
cycle had a variable circumference, greatest when the planet is
at apogee or perigee and least at 90° from these, when the equa-
tion reaches its maximum. This contrivance of an oval epicycle
was by some astronomers applied to all the planets, by others
(Brahmagupta and Bhāskara) only to Mars and Venus, by others
it was altogether rejected.³ Why they complicated the calculation
in this way is not clear. Āryabhaṭa I of Kusumapura or Pāṭali-
putra, born A.D. 476, made another deviation from the Alexand-
rian doctrines, as appears in the Brahma-sphuṭa-siddhānta of
Brahmagupta, wherein he quotes the following from Āryabhaṭa:
"The sphere of the stars is stationary, and the Earth, making a
revolution, produces the daily rising and setting of stars and
planets." Brahmagupta rejects this idea, saying: "If the Earth
moves a minute in a prāṇa, then whence and what route does it
proceed? If it revolves, why do not lofty objects fall?" But his
commentator Caturveda Pṛthudaka Svāmi replies: "Āryabhaṭa's

1. As. Res. XII. p. 229 (Essays, II, p. 394).
2. The distances are proportional to the orbital periods of revolution, but for
   Mercury and Venus to the periods in the epicycles.
3. For further details see As. Res. II. p. 251 (Davis) and XII. p. 236
   (Colebrooke, also Essays, II. p. 401).