Find the period T of the space shuttle 1. The problem statement, all variables and given/known data (See image of problem statement for nice layout; the questions are stated below) A space shuttle of mass m is in a circular orbit of radius r around a planet of mass M in an alternate universe. In this alternate universe the laws of physics are exactly the same as in our universe, except the force of gravity between these two objects has magnitude F=HMm/r3 where H is the alternate universe gravitational constant. The associated potential energy function is U=−(1/2)HMm/r2. (a) Find the period T of the space shuttle's orbit. (b) The astronauts want to launch a long-range probe from their shuttle. What is the minimum initial speed needed by this probe so that its trajectory will never return near the planet? (The probe does not have its own engines.) 2. Relevant equations H is gravitational constant in this universe T2 = 4π2α3/HM (where α is the semi-major axis) F = Gm1m2/r2 except on this planet it is F=HMm/r3 in this universe--> U=−(1/2)HMm/r2 E = KE - U = 0.5mv2 − (1/2)HMm/r2 vescape = sqrt(2MplanetG/rplanet) not sure how escape velocity would change in this universe 3. The attempt at a solution This question threw me off, and I'm not sure how to proceed with it. My first guess for T was just to plug in the gravitational constant for this universe, H, into the orbital period relationship like so T2 = 4π2α3/HM But that isn't right. Will appreciate any guidance on getting started on this problem! I'm struggling a bit with the Gravity/Orbits section I'm on and will appreciate learning the correct approach.