The gravity of the situation - Newton's Law of Gravitation

First, a link to a description of the Cavendish experiment that determined the magnitude of the Gravitational constant to be 6.67 x 10^-11 N*m^2/kg^2.

Homework Solutions:
Questions:
6. The apple exerts a force on the Earth equal to the magnitude of its weight, by Newton's Third Law. This is independent of whether the apple is falling or sitting still. Newton's law of gravitation applies whenever you have two objects with mass, regardless of what they are actually doing.

7. The acceleration due to gravity would be greater since g = GMp/R^2. If the distance was the same (and the orbit was still circular) this would mean that the moon would have a greater speed as it orbits, so it would change phases from new to full more quickly.

16. The question is better answered by saying the gravity force keeps the satellite "down" in its orbit, as it keeps the satellite moving in a circular path. Without the gravity force, satellites would travel in straight line paths.

Problems:
26. using g = GM/r^2, the acceleration is 1.619 m/s^2

30. Calculate the acceleration due to gravity to show the strength of the gravity.

g = 8.938 m/s^2

32. g = .98 m/s^2 = GMp/r^2 so r = 2.017 x 10⁷ m, or at an altitude of 1.379 x 10⁷ m above the surface of the Earth.

34.
a) 9.789 m/s^2
b) 4.346 m/s^2