PHYS207 Honors

Hints for Problem Set 13

Last revised 1997/11/13

Chapter 14

#5. Call x = m/M. How do you maximize a quantity with respect to x?

#21. "How much does X weigh?" means "How large is the gravitational force on X?"

#23. The problem essentially tells you what to do.

The result of this problem holds also if the density is the average density of a spherically-symmetric planet. In practice, however, a planet spinning this fast would be neither spherical nor spherically symmetric, but would have an equatorial radius much larger than its polar radius. A careful analysis of the maximum possible rotation rate of a planet would take distortion of the planet into account.

#53. The problem contains a hint, but even so it is not easy. Note that in the frame of reference in which the masses are at rest at the beginning, the velocity of the two masses are never the same again unless m = M.

#74. If you want an accurate answer, you have to do this problem symbolically. Let the initial orbital radius be R and the higher radius be R + delta-R, and use the fact that delta-R << R. What is the ratio of the orbital speed and the speed of the (changing) point on Earth directly below the satellite?

#80. Use symbols!