# Orbital period of an asteroid

## 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 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

## 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 = 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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## Answers and Replies

Isaac0427
Gold Member
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
Mentor
Make a sketch of the orbit and identify the major axis.