September 2015 saw the historic discovery of gravitational waves, almost exactly 100 years after Einstein predicted their existence as a consequence of his theory of general relativity. Gravitational waves are a literal stretching and compressing of the fabric of space. Even the most sensitive instruments--capable of sensing that the path of a 4-km-long laser beam has lengthened by one-thousandth the diameter of a proton--can detect waves created by only the most extreme cosmic events. The first detection was due to the collision of two black holes more than 750 million light years from earth. Although a full description of gravitational waves requires knowledge of Einstein's general relativity, a surprising amount can be understood with the physics you've already learned.


Question 1:
Consider two equal masses M that interact gravitationally and revolve at angular velocity ω about their center of mass. Let the distance between them be 2r , so that each is distance r from the center of mass. Apply Newton's second law for circular motion to one of the masses to find an expression for ω2 (not ω ) in terms of G , M , and r .
Express your answer in terms of the variables M , r , and the gravitational constant G .