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