Question

In this problem, you are going to explore three different ways to determine the gravitational constant G.

Part (a) By observing that the centripetal acceleration of the Moon around the Earth is a_c = 2.65 × 10^-3 m/s², what is the gravitatonal constant G, in cubic meters per kilogram per square second? Assume the Earth has a mass of M_E = 6.02 × 10²⁴ kg, and the mean distance between the centers of the Earth and Moon is r_m = 3.83 × 10⁸ m.

Part (b) Measuring the centripetal acceleration of an orbiting object is rather difficult, so an alternative approach is to use the period of the orbiting object. Find an expression for the gravitational constant in terms of the distance between the gravitating objects r_m, the mass of the larger body (the earth) M_E, and the period of the orbiting body T.

Part (c) The gravitational constant may also be calculated by analyzing the motion of an object, launched from the surface of the earth at an initial velocity of v_i. Find an expression of the gravitational constant from the initial velocity, mass of the earth M_E, and the initial and final heights. Use the parameter φ = 1/r_initial - 1/r_final to simplify your final answer.

Answer 1