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

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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.