Links to answers and explanations are at the are at the end of the problem set.
Use 6400 km as the radius of the earth, and 1600 km as the radius of the moon.
1. A man's weight on earth is 800 N. Find his weight at
(a) a point 6400 km above the earth's surface,
(b) a point 12,800 km above the earth's surface,
(c) a point 19,200 km above the earth's surface.
2. Find the man's acceleration at the three points in problem 1.
3. A women's weight on the moon is 100 N.
(a) Find her weight at a point 3200 km above the moon's surface.
(b) Find her weight at a point 5000 km above the moon's surface.
4. Given that the acceleration on the moon's surface is 1.7 m/s2, find the acceleration at the two points in problem 3.
5. Find the weight of the same woman when she is in an earth satellite, orbitting at a height of 200 km above the earth's surface. Use the fact that her weight on the earth's surface is 618 N.
6. Using data given in class for the orbits of earth and Jupiter around the sun, verify the inverse square relation in the law of gravitation.
7. Two of the satellites of Jupiter are Io and Europa. The distance from Jupiter to Io is 422,000 km and the distance from Jupiter to Europa is 671,000 km. The acceleration of Io in its orbit around Jupiter is 0.7124 m/s2. The acceleration of Europa is 0.28l6 m/s2. Verify that these numbers are consistent with the law of universal gravitation.
8. A space probe discovers a new satellite of Jupiter at a distance of 1,120,000 km from the planet. What is its acceleration expected to be? (Use data from problem 7.)
9. An asteroid is in orbit about the sun. Its distance from the sun is twice the distance of Mars from the sun. Find its acceleration, using the data on Mars given in class.
10. An asteroid is in orbit about the sun, between the orbits of Mars and Jupiter. The asteroid's distance from the sun is 5.0 X 1011 meters. Find its acceleration, using the data on Mars given in class.