1. The problem statement, all variables and given/known data The Earth's distance from the sun varies from 1.471 x 108 km to 1.521 x 108 km during the year. Determine the difference in (a) the potential energy, (b) the earth's kinetic energy, and (c) the total energy between these extreme points. Take the sun to be at rest. 2. Relevant equations FGrav = (GMm)/r2 U = integral(a→b)(GMm/r2)dr KE = .5mv2 Law of the Conservation of energy: Ei = Ef ac = v2 / r 3. The attempt at a solution I got (a) easily. I need help with b and c, though. I tried taking the average distance from the sun, which is just the length of the semi-major axis, which is 1.521 x 108 km - 1.471 x 108 km = 5.00 x 109 m = rave Then I used the centripetal acceleration formula to get Fa = FG = (GMsun / (rave)2) = (v2)ave/rave. Solving for vave I get vave = 2.7 x 1010 m/s. I then calculated average kinetic energy to be .5 * mearth * (vave)2 = 2.1 * 1045 J. Average gravitational energy would be -GMm/rave = -1.6 * 1035 J. Average total energy would be average kinetic + average potential. Since energy is constant the average energy is constant for instantaneous energy. Therefore, at perihelion and aphelion, I would have average total energy - potential energy at the point, correct? Any help would be appreciated, thanks.