I'm stuck on 2 problems. T5.11.96) One big question is planetary science is whether each of the rings of Saturn is solid or composed of many smaller satellites. There is a simple observation that can now be made to resolve this issue. Measure the velocity of the inner and outer portion of the ring: if the inner portion of the ring moves more slowly than the outer portion, then the ring is solid; if the opposite is true, then it is composed of many seperate chunks. a) If the thickness of the ring is r, the average distance of the ring from the center of Saturn is R, and the average velocity of the ring is v, show that v(out)-v(in) ~ rv/R if the ring is solid. Here, v(out) is the speed of the outmost portion of the ring, v(in) is the speed of the outermost portion, and v is the average velocity of the ring. b) If, however, the ring is composed of many small chunks, show that v(out)-v(in) ~ -.5(rv)/R. (Assume that r<<R.) I tried integration, which didn't work. I tried using linear equations of motion to solve, but that got me nowhere either. This problem is a level 3 question, which is the toughest in the book. I've tried...but to no avail. I know that the rings closer to Saturn have a higher velocity...but that didn't help me much either. T5.11.101.) United Federation Spaceship Excelsior is dropping two robot probes to the surface of a neutron star for exploration. The mass of the star is the same as that of the sun, but the star's diameter is only 10 km. The robot probes are linked together by a 1-m-long steel cord, and are dropped vertically(that is, one always above the other). a) Explain why there seems to be a "force" trying to pull the robots apart. b) How close will the robots be to the surface of the star before the cord breaks? Assume that the cord has a breaking tension of 25000N and that the robots each have a mass of 1kg. I know this question seems stupid because a neutron star would crush these probes in a matter of seconds. I'd figure since there is so much massin such a small area that the force of gravity would pull down on them more. But I also know that the force of gravity increases with a shorter radius...so wouldn't an object farther out be less affected? b) For part b, do I just plug in the equation for gravitational force? I know the answer is 220km...but I'm unsure how to get it. I thought it was more like setting the force to 25000N and then solving for "r^2"...but somehow it went wrong. Am I doing something wrong here or maybe it's just calculations error? Thanks.