What is the orbital period of an asteroid between Earth and Jupiter?

[TheBigDig]

Homework Statement

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 M_s, the mass of the asteroid m_a and the radii of the Earth’s and Jupiter’s orbit respectively, (L_E, L_J ), 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, M_s, m_a,L_E and L_J

Homework Equations

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 = GM_s)

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 (L_J³/μ)^1/2 but I am almost certain that is wrong. It just seems to easy to me.

 

[Isaac0427]

3. 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.

That is because for a you used the orbital radius of Jupiter's orbit. What you found was the period of Jupiter's orbit. What you need here is the semi-major axis. Try a diagram.

 

[gneill]

Make a sketch of the orbit and identify the major axis.