1. The problem statement, all variables and given/known data Comet Halley approaches the Sun to within 0.570 AU, and its orbital period is 75.6 years. (AU is the symbol for astronomical unit, where 1 AU = 1.50 x 1011 m is the mean Earth‐Sun distance.) How far from the Sun will Halleyʹs comet travel before it starts its return journey? 2. Relevant equations There are none given, though I believe some of these are probably relevant. T=2π√(a^3/(GM)) which is the equation relation period to the semi-major axis and a gravitational constant Ke(perihelion) + Kp(perihilion)=Ke(aphelion) + Kp(aphelion) L= mvrsinθ 3. The attempt at a solution This question is legitimately driving me insane. I feel like I am on the brink of solving it, but I just keep going around in circles. Now, I understand that if I had the semi-major axis, to solve this would be relatively easy...but I don't. Given this, I attempted to rearrange T=2π√(a^3/(GM)) to solve for a. My calculus can be a bit dodgy but I came up with, a is equal to the cube root of t^2/2π(GM) or a=3√(T2/2π(GM) Angular momentum and total energy for the system are conserved and thus are equitable at the perihelion and aphelion. At the aphelion sinθ=1 So angular momentum is mvr at angles 0 and 180, which both lie on the major axis. at the perihelion gravitational potential energy = 0 and kinetic energy is 100% Inversely, at the aphelion, the energy in the comet is 100% gravitational potential. Which I guess means acceleration = 0. I am really lost on this one guys. please. Please. anything!