The figure below shows two large masses, M, that each have a mass of 3.0 x 106 kg. These masses ar fixed in place along the y-axis, as shown. Each is a distance l = 5m from the center of the figure. A thir mass m = 2kg is placed on the x-axis at an initial distance r = 0.045m from the origin. The constan of gravitation is G = 6.67 × 1o-11Nm²kg¯2 (a) What is the magnitude of the gravitational force on the smaller mass m? м (fixed in place) (free to move) х-ахis (path of m) M (fixed in place) (b) If the small mass m is allowed to freely move, it will end up oscillating back and forth. What is the frequency of this oscillation? (Recall that for very small angles, sin 0 z 0). (c) What is the amplitude of this oscillation? (Note that you don't need to know the froquonoU dotormino thigl)

A 765-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. 5588.1 m/s (b) Find the period of its revolution. 1.9 Enter Anumber. differs from the correct answer by more than 10%. Double check your calculations.h (c) Find the gravitational force acting on it. 1874.25

The force of gravity  between two masses is originally 480N.  If the masses are moved to a new distance that is six times farther apart than the initial separation distance, the new force of gravity will be

The earth orbits the sun at an approximate velocity v = 30 km/s and radius r = 150*10^6 km. (a) Assuming a circular orbit for the earth, what is the approximate mass of the sun? (b) If the mass of the sun was doubled, what would the new length of a year be? Assume the Earth remains in circular orbit about the sun at its usual orbital radius. Answer in terms of current years. (Hint: you do not need to plug in the value of G.)