Homework 9. Due Wednesday, June 6.

This homework is a pretty long one and involves at least 3 different sorts of problems, so I thinking it could be best not to try to do them all at once?
1. One type involves calculations of little g, the acceleration near the surface of a planet, using G and M, the mass of the planet. (Also R)
2. Another type involves orbital motion and the relationship between the acceleration need to maintain a circular orbit and the force of gravity (e.g., exerted by the sun on an orbiting planet).  (see video below)
3. A third type of problem involves gravitational force vectors, and how to calculate components and add them. (see other video below).
4. Problem 13.73 involves negative gravitational potential energy (-GMm/r). When the comet is closer to the sun, its potential energy is lower and it will speed up as it gets closer to keep the total energy of the comet-Sun system unchanged. (Don't accidentally use -GMm/r^2 by mistake like i did the first time.) Roughly, U=-5... at the far location, and U= -25... at the close-to-the-sun location, so the KE must increase by +20... in order to keep the total energy constant. Does that make sense?
Problem 13.17 also involves gravitational potential energy. Weirdly, the potential energy of the rocket-earth system is highest when the rocket is very far away from the earth (at which point, its value is basically zero!) Zero potential energy, however, is higher than the large negative potential energy that the system has when the rocket is closer to the earth.
Solutions follow: