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

163 H̄ cos 225 = R and H sin 225 = 225 which is rather crude. Bhāskara of course improved on this crudeness by taking δm to be an increment in E. In the commentary under this verse, Bhāskara, having misinterpreted Lallācharya's phrase आशुचाप as meaning आशुकेन्द्रचाप and not as आशुफलचाप which was in the mind of Lallācharya, goes on recounting examples where the wrong formula attributed to him would give wrong results. So, we need not enter into those details. Now we shall correlate Bhāskara's formula with its modern counterpart. Assuming coplanar heliocentric cir- cular orbits for planets, let us see at what points two planets appear mutually stationary, that is, have a Zero relative angular velocity before they appear mutually retrograde. Let S = Sun, E = Earth, J = Jupiter, u = Earth's linear velocity, v = Jupi- ter's linear velocity r and R the orbital radii of the Earth and Jupiter respe- ctively. Let EE' and JJ' be perpendiculars to EJ so that when the relative velo- city of Jupiter with respect to the Earth perpendicular to EJ is Zero, Jupiter will appear stationary as seen from the Earth. This Fig. 17 means that u cos θ + v cos ξ = 0 I ∴ u / v = - cos ξ / cos θ II But from triangle ESJ, R cos ϕ + K cos θ = r III and r cos ϕ + K cos ξ = R IV