Chapter Questions
Compared with the strength of Earth's gravity at its surface, how much weaker is gravity at a distance of 10 Earth radii from Earth's center? At 20 Earth radii?
Compare the force of lunar gravity on the surface of the moon with the force of Earth's gravity at Earth's surface.
If a small lead ball falls from a high tower on Earth, what will be its velocity after 2 seconds? After 4 seconds?
What is the circular velocity of an Earth satellite $1000 \mathrm{km}$ above Earth's surface? (Hint: Earth's radius is $6380 \mathrm{km}$.)
What is the circular velocity of an Earth satellite 36,000 km above Earth's surface? What is its orbital period? (Hint: Earth's radius is 6380 km.)
What is the orbital period of an imaginary satellite orbiting just above Earth's surface? Ignore friction with the atmosphere.
Repeat the previous problem for Mercury, Venus, the moon, and Mars.
Describe the orbit followed by the slowest cannonball on page 88 on the assumption that the cannonball could pass freely through Earth. (Newton got this problem wrong the first time he tried to solve it.)
If you visited an asteroid $30 \mathrm{km}$ in radius with a mass of $4 \times 10^{17}$ kg, what would be the circular velocity at its surface? A major league fastball travels about 90 mph. Could a good pitcher throw a baseball into orbit around the asteroid?
What is the orbital period of a satellite orbiting just above the surface of the asteroid in Problem 9?
What would be the escape velocity at the surface of the asteroid in Problem 9 ? Could a major league pitcher throw a baseball off of the asteroid?