1. An evil genius puts a spherical rock (made of ordinary stone) in the earth’s orbit, but moving around the sun the other way. It collides with the earth, and destroys a city. It is estimated that the destruction is about the same as would have been caused by a one-megaton hydrogen bomb. How big was the rock?
2. Halliday Ch 14, problem 48 – and is it possible to place a satellite in a hovering orbit above Charlottesville? Explain why or why not.
3. In deep space, an astronaut is marooned ten meters from his four-ton spacecraft. If he is exactly at rest relative to the craft, and there are no other gravitational fields close by, estimate how long it will be before he’s back on board. How fast will he be moving when he hits the craft (which is 5 meters in diameter)?
4. The escape speed from the moon is 2.38 km/sec. Suppose you had on the moon a cannon that could fire shells at 2.4 km/sec. Obviously, if you fired a shell vertically upwards, it would escape the moon’s gravity. But what if you fired it almost horizontally, just elevated enough so it cleared the mountains? Describe its trajectory in this situation.
5. Open the Planet Spreadsheet. You can see the components of the velocity by moving the chart over. Take the mass of the “planet” to be one.
(a) Show that, with reasonable accuracy, both total energy and angular momentum are the same at the closest approach to the “sun” as they were at the beginning.
(b) Measure the semimajor axis of the elliptical path. Now change the initial variables until you have a circular orbit with the radius equal to the original ellipse semimajor axis. Check that the total energy in this new orbit is the same as the original orbit.