Kepler’s Third Law Provides a Key
Kepler’s 3rd Law: P2 = k R3
But, period = P = 2? R / v ? 4?2 R2 / v2 = k R3
Therefore, v2 = 4?2 / k R
Substituting this form for v2 into Newton’s 2nd Law:
Uniform Circular Motion: a = v2 / R
Newton’s 2nd Law: F = ma = mv2 / R
- This is the force that the Sun must exert on a planet of mass m , orbital radius R, in order that the planet obey Kepler’s Laws in the circular motion approximation.