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

156
Lallāchārya formulates the Mandasphutagati in a
different manner which is equally correct (Ref. verse 45
Spaṣtādhikāra Śiṣyadhī Vriddhida “त्रिज्याहता ग्रहगतिः
मृदुकर्णभक्ता मन्दस्फुटा भवति ” i. e. (δm × R) / K = Mandasphuta-
gati where δm = Madhyagati or mean motion and K is the
Manda Karṇa equal to √(R² + r² ± 2 R r cos m)
∴ Mandasphutagati =
(δm × R) / √(1 ± 2 (r / R) cos m + r² / R²) = δm ( 1 ± (2r / R) cos m )⁻¹⁄₂
= δm ( 1 ∓ (r / R) cos m ) neglecting the smaller term
− r² / (2R²) within brackets
= δm ∓ (r H cos m δm) / R² = δm ∓ (r H cos m / R) × (δm / R)
= δm ∓ (Kotiphala × Mandakendragati) / — as given by
Bhāskara.
Verse 38. In the case of the Moon, obtaining the true
Moon for a particular moment and his daily motion for the
day, the ending moment of the tithi near at hand is to be
computed with that daily motion, and the method of suc-
cessive approximations is to be used to rectify the ending
moment. In the case of the ending moment of the tithi be-
ing sufficiently far away, then it does not matter even if
the above daily motion is applied to get the approximate
ending moment. In as much as the Moon’s daily motion is
great and varies from moment to moment the motion
at the moment is to be used.
Comm. Strictly speaking the ending moment of every
tithi is to be computed by the method of successive approxi-
mation. That is why in the computation of eclipses,