Chapter 6

1. (p.153 prob.50) What is the distance form the Earth's center to a point outside the Earth where the gravitational acceleration due to the Earth is 1/10 of its value at the Earth's surface?

   Answer.

2. (p.153 prob.55) The rings of Saturn are composed of chunks of ice that orbit the planet. The inner radius of the rings is 73,000km, while the outer radius is 170,000km. find the period of an orbiting chunk of ice at the inner radius and the period of a chunk at the outer radius. Compare your numbers with Saturn's mean rotation period of 10 hours and 39 minutes. The mass of Saturn is 5.69  x 10²⁶kg.

   Answer.

3. (p.154 prob.61) The planet Jupiter is about 320times as massive as the Earth. Thus, it has been claimed that pa person would be crushed by the force of gravity on Jupiter since people can't survive more than a few g's. Calculate the number of g's a person would experience if she could stand on the equator of Jupiter. Use the following astronomical data for Jupiter: mass = 19 x 10²⁷kg, equatorial radius = 7.1 x 10⁴km, rotation period 9 hr 55 min. Take the centripetal acceleration into account.

   Answer.

4. *(p.153 prob.46) Two identical particles, each of mass m, are located on the x axis at x = + x₀ and x = - x₀. (a) Determine a formula for the gravitational field due to these two particles for points on the y axis; that is, write g as a function of y, m, x₀, and so on. (b) At what point (or points) on the y axis is the magnitude of g a maximum value, and what is its value there? [Hint: Take the derivative dg/dy.]

   Answer.