Physics 2210 (Schroeder) Name
spring 2006
Problem Set 10
(due Wednesday, March 22)
1. Estimate the gravitational force between you and a person sitting 2 m away from you.
(You should find that the attraction is negligible. As Einstein once said, “Gravity
cannot be held responsible for people falling in love.”)
2. The planet Mars has a satellite (moon), called Phobos, which travels in an approxi-
mately circular orbit of radius 9.4×106m with a period of 7 hours, 39 minutes. From
this information and Newton’s law of gravity, determine the mass of Mars.
3. Communication satellites are placed in circular orbits above the earth’s equator at
such a height that they orbit exactly once every 24 hours, and therefore appear to
remain fixed in our sky. How far above earth’s surface is such a satellite? Please solve
this problem from first principles (not from Kepler’s third law).
4. A projectile is fired vertically from Earth’s surface with an initial speed of 10 km/s.
Neglecting air drag, how far above Earth’s surface will it go?
5. An asteroid of mass 3×1015 kg is observed to be heading straight toward the earth. At
the time of observation, the asteroid is ten million kilometers away and has a speed
(relative to the earth) of 8.5 km/s. What is its kinetic energy just before hitting
earth? Compare your result to the energy released by a 1 megaton nuclear bomb
(about 4 ×1015 J). What forms might this energy take after the asteroid hits earth?
6. Calculate “escape speed” from the moon’s surface, that is, the minimum speed needed
for an unpowered projectile to escape rather than falling back.
7. While prospecting for titanium among the asteroids (in order to find raw materials for
building more spaceships, so more people can go prospecting for titanium, and so on),
you discover a spherical asteroid with a radius of 3 km. You put your spaceship into a
circular orbit around this asteroid, at a height of 2 km above the surface, then descend
to the surface on your handy jet-pack. Upon arriving at the surface, you discover that
the asteroid is made of solid titanium (which has a density of 4.54 g/cm3)! You are
overjoyed by this discovery—so overjoyed, that while jumping up and down for joy,
you accidentally land on your jet-pack, demolishing it. Fortunately, you have a back-
up jet-pack, but unfortunately, that’s exactly where it is: back up on the spaceship.
However, all hope is not lost. Because the asteroid’s gravitational pull is so much less
than earth’s, you wonder whether you might be able to jump up to your spaceship.
You know that on earth, while wearing your cumbersome spacesuit, you can jump
only 0.5 meters (as measured by your center of mass). Given this information, can
you jump to your spaceship? Please explain carefully.
8. You are the commander of the starship Elliptica, orbiting an unexplored planet (mass
3.0×1024 kg) in a circular orbit of radius 1.0×107m. (a) What is your current orbital
speed? (b) The scientists on your crew are having another argument: one wants to
