The orbit of an asteroid extends from the Earth’s orbit to Jupiter’s orbit, just touching both. Assume that the planetary orbits are circular and co-planar and that Newton’s constant G, the mass of the sun Ms, the mass of the asteroid ma and the radii of the Earth’s and Jupiter’s orbit respectively, (LE, LJ ), are known.
1. Find the orbital period of the asteroid.
Express all of your answers in terms of the given quantities of the problem: G, Ms, ma,LE and LJ
T = 2π (a3/μ)1/2 where T is the period, a is the semi-major axis of the orbit and μ is the gravitational mass of the sun (μ = GMs)
The Attempt at a Solution
I'm actually really stuck on this one though it seems simple. It seems like the answer is T = 2π (LJ3/μ)1/2 but I am almost certain that is wrong. It just seems to easy to me.
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