A Last Look at Gravity

1) When is it necessary to use General Relativity instead of Newton’s theory of gravity?

2) Suppose you were to take your spaceship to a place just outside the event horizon of a black hole (burning enormous amounts of fuel to keep from falling in). You hover there for a while, then go back to join your twin on the mother ship, far away. How would your ages compare when you got back?

3) Why can our sun never become a black hole?

4) How far would a bullet fired horizontally here on Earth drop in one second? How far would a beam of light here on Earth drop in one second?

5) The simplest equation that gives the radius of a black hole’s event horizon is r = 2GM/c², where M is the mass of the singularity. The mass of our sun is 1.99 × 10³⁰ kg and its radius is 6.96 × 10⁸ m. How many solar masses would a black hole need, to have an event horizon equal to the radius of the sun?

6) Spaghettification is caused by a black hole exerting a great deal more force on one side of an object than the other. This is sometimes referred to as a tidal effect, since the tides are caused by the moon pulling harder on the closer side of Earth. Let’s say the distance from the center of the moon to the closest surface of Earth is 3.79 × 10⁸ m, the diameter of Earth is 12.76 × 10⁶ m, and the mass of the moon is 7.35 × 10²² kg. Find the difference in gravity pulling on a 75 kg person on the closest and the farthest side of Earth.

7) Mass #1 is 3100 kg, mass #2 is 6200 kg and mass #3 is 4800 kg. Distance #1 is 0.85 m and distance #2 is 0.55 m. It’s a right triangle. Find the net force acting on mass #3.