सिद्धान्तशिरोमणि: गणिताध्याय (भास्कराचार्य - ग्रहगणित, मध्यमाधिकार व स्पष्टाधिकार सटीक)

126
gave the clue to arrive at an approximate estimate of their
sidereal revolutions. But the correct estimates were arri-
ved at not by observing their conjunctions with stars, for,
that would take a very long period of observation in the
case of Saturn, but, by observing a good number of their
heliacal risings or settings. The interval between two
consecutive heliacal risings or settings being a little grea-
ter than an year, ten or fifteen observations could be done
very easily by a single person. Then the aforesaid argu-
ment given in the case of finding the sidereal revolution of
the Sun, was also advanced in the case of these three
planets Mars, Jupiter and Saturn. Let x° be the arc that
the planet covers during the course of a day. Let a° be the
arc covered by the Sun during the same period which was
previously known and that correctly. So, during the
course of a day the Sun overtakes the planet by (a - x)°.
Hence to overtake 360°, the period S was computed. This
period was observed as the interval between two consecu-
tive heliacal risings or settings and known as the synodic
period. So, from the equation 360 / (a - x) = S, the value of x
could be arrived at, wherefrom p the sidereal period was
determined. This sidereal period could be also determined
in another way. Noting the distance covered among stars
by a planet during the course of a synodic period, using
rule of three, the sidereal period could also be arrived at
with a good accuracy, for, the retrograde motion affects
equally each synodic period. An average of such determi-
nations made in two ways could give the sidereal periods
of Mars, Jupiter and Saturn with a good amount of accu-
racy. It will be noted here, that the average of a good
number of geocentric sidereal periods in the case of these
planets (called Superior) is also the heliocentric sidereal
period (for a proof of this statement reference may be made
to page 80 of the author's 'A critical study of the ancient
Hindu astronomy, published by the Karnatak University
Dharwar). It is why the sidereal periods of these planets