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80, Physics ) QUICK BOOK, Here, Lis angular momentum and m is mass of planet., Third law T-r, where r is semi-major axis of elliptical path., Note Circle is a special case of an ellipse. Therefore, second and third laws can also be applied for circular, path. In third law, r is radius of circular path., • Moat of the problems of planetary motion are solved by two conservation laws:, ) conservation of angular momentum about centre of the sun and, i) conservation of mechanical (potential + kinetic) energy, Hence, the following two equations are used in most of the cases,, mur ain e- conatant, GMm, ...), mu-, - constant, ---(i), At aphelion (or M) and perihelion (or N) positions, 90., Hence, Eq. @ can be written as, mur sin 90° - constant, ... fi), mor - constant, Further, since mass of the planet (m) also remains constant, so, Eę can also be, or, written as, Ur ain e- conatant, ..(iv), :0-90), or, • If the law of force obeys the inverse square law, then, (F- F., dU, The same is true for eloctron-nucleus aystem because there also, the electrostatic, force F, =.