Physics Worksheet on Kepler’s Laws and Newton’s Universal Law of Gravity

1. In Blue Physics Book pg. 172 (1,5,6,8,12,14,16,19,24,26,27) Just Click on the number for the solution to that problem.

2. Three billiard balls, each of mass 0.3kg, are placed on a table at the corners of a right triangle, Find the net gravitational force on the m₁ due to the forces exerted by the other two balls.

CLICK ON IMAGE FOR SOLUTION

3. Use the gravitational force law to find an approximate value for the mass of the Earth. (Solution)

4. A satellite of mass m moves in a circular orbit about the Earth with a constant speed of v, at a height h = 1000 km about the Earth’s surface. Find the orbital speed of the satellite. The Earth radius is 6.38 X 10⁶ m, and it’s mass is 5.98 X 10²⁴ kg. (Solution)

5. The mean distance of Jupiter from the sun is 5.20 astronomical units (AU), where

1 AU = 1.5 X 10¹¹m = 93.0 X 10⁶ mi

What is the Period of Jupiter?

(Solution)

6. A satellite orbits the earth in a circular orbit. Find its period (a) if the satellite is just about the surface of the Earth and (b) if the satellite is at an altitude of 300km. (Solution)

7. The gravitational potential with U = 0 at the Earth’s surface is:

With this in mind, a projectile if fired straight up form the surface of the earth, the potential energy of the projectile is zero and its kinetic energy is ½(mv²). When the object is at a height of h = r – R_E, it potential energy is given by the above equation. Find the height for which this objects final speed is zero. (HINT: Use conservation of Energy)(Solution)