Newton's Law of Gravitation states: F=GMm/r^2, where G is the gravitational constant (6.67×10−11m^3kg^−1s^−2). Kepler's Third Law, states t^2=kR^3. The mass of the sun is 1.99x10^30kg. Find the value of k and its units
F=GMm/r2=mv2/r, v=2pir/t
equating the two values for F and remembering to include the equation for v, GMm/r^2 = m(2pir/t^2)^2/r. Rearranging to find t^2, t^2 = 4pi^2r^3/GM where 4pi^2/GM equals the constant k. Therefore for the purpose of the question, k = 2.97x10^-19s^-2m^-3.
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