3. You are a person with incredible arm strength. You throw a ball of mass m = 2 kg horizontally with initialy velocity vo. (a) How quickly would you have to throw the ball so that the ball enters a perfectly circular orbit around Earth? (Assume your height is much less than Earth's radius). (b) How long would the ball take to complete one orbit? (c) Let's say you throw the ball with 1.2x the speed found in (a). What is the semi-major axis of the new elliptical orbit of the ball?

The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.

Some of the most spectacular objects in the universe are fairly small: neutron stars are spheres with a diameter that's about 10km (they are remnants of old stars). Their spectacular nature is indicated by the fact that they are about as massive as the sun, i.e. 2 x 1030kg. What is the gravitational acceleration on the surface of such an object? Express your result as a multiple of g.

Two satellitess, and S, orbit around a planet P in circular orbits of radil r, = 5.15 x 106 m, and r, = 8.40 x 106 m respectively. If the speed of the first satellite S, is 1.65 x 10 m/s, what is the speed of the second satellite S,? m/s