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

168 situated within particular limits from the Sun, they will be invisible in the rays of the Sun. As these superior planets will be near the Sun, near the moment of conjunction, they will not be seen at conjunction and within particular limits from the position of the Sun. The limits cited above mostly depend upon their respective brilliance and to some extent upon their distances from the Sun too. Their brilliance again depends upon the extent of their gibbosity. The formula given for the phase in modern astronomy is phase = (1 + cos EpS) / 2 and noting that Êps = E₂ = the Śīghraphala, phase = (1 + cos E₂) / 2. Hence the Supe- rior planets are always gibbous ie. the disc illuminated will be always greater than ½. Though at conjunction E₂ = 0 and the entire discs of the major planets will be illumina- ted, we cannot see them as they are immersed in the rays of the Sun. As they emerge out of conjunction gradually E₂ will be increasing so that the discs will be illuminated lesser and lesser gradually. But K decreasing, the brilli- ance will not be so much effected. Along the arc acb (figs. 11, 12) the planets gradually gain in illumination and will be brightest when they are in opposition both as cos E in- creases and K decreases. In other words the Superior planets appear more and more brilliant when they are retrograding, being most brilliant at ‘C’. The spherical radii of Jupiter Saturn and Mars being in decreasing order, their brilliance will be in decreasing order so that they will be rising at distances from the Sun which are in increasing order. The inverse square law of courses works here but combining the two factors (1) the spherical radius of the planet and (2) the inverse square law, we may take it that Bhāskara’s numbers cited above namely 28°, 17° and 14° for Mars, Saturn and Jupiter respectively accord with truth, for, these numbers are given by Bhāskara or his authority Brahmagupta only after observing the planets rising heliacally.