Question

Derive keplers law of planetary motion from netwons law of gravitation

Answer 1

Answer:

F= GMm/(r^2)

F = m(v^2)/r= m( w^2 )(r^2)/r= m (w^2) r= (4π^2) m r/ (T^2)

so, by equating both above equations, we will get

GMm / (r^2)= 4 (π^2) m r /( T^2)

so, T^2= 4 (π^2)(r^3 )/ GM

T^2 is directly proportional to r^3

which is Kepler's third law

Answer 2

Answer:

Newtonian Gravitation and the Laws of Kepler Thus, Kepler's laws and Newton's laws taken together imply that the force that holds the planets in their orbits by continuously changing the planet's velocity so that it follows an elliptical path is (1) directed toward the Sun from the planet, (2) is proportional to the product of masses for the Sun and planet, and ( ...

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