1. If a comet has an eccentricity of 0.98 and a semimajor axis of 12 AU, what are the apehlion and perihelion distances? What is the period? How does the velocity at perihelion compare to the velocity at aphelion? In this problem, I used the perihelion and aphelion equations to solve for them, where P=(1-e)a and A=(1=e)a. Perihelion = 0.24 and Aphelion = 23.76. I don't know how to calcuate the velocity, and am confused by that. And since I have the eccentricity and semimajor axis, do I use the equation P(years) = R(A.U.)^3/2? 2. If this comet appeared to have a brightness of one at its nearest point to Earth, how bright would it appear at its maximum distance? Assume incorrectly that is does not change in luminosity as it approaches the Sun and use the inverse square law. I know to use the inverse square law on this one, but how can I relate that to brightness and distances? 3. If an asteroid is in a 5:2 resonance with Jupiter, what is its semimajor axis? The next two problems are the same and I don't have any equations for resonance but I will keep looking. 4. If an asteroid is in a 2:5 resonance with mars, what is its semimajor axis?