Calculate the maximum and minimum distances between the Earth and the Moon

[Alexanddros81]

Homework Statement

14.100 Calculate the maximum and minimum distances in kilometres between
the centers of the Earth and moon, taking the eccentricity of the moon's orbit into
account. Use the data given in Prob. 14.99

Homework Equations

The Attempt at a Solution

Can you check my solution?
The book gives as solutions Rmin=343074 km and Rmax= 383009 km.

 

[gneill]

I would be a bit leery about using formulas that were derived assuming that the mass of the body in orbit is negligible w.r.t. the "central" mass. The Moon's mass is not entirely negligible in the Earth-Moon system, so setting the gravitational parameter $\mu = GM_E$ might not be entirely kosher if accuracy is important.

Unfortunately, on the other hand, I can't think of another expedient way to relate the eccentricity and period to the orbit size that doesn't assume a negligible mass for one of the objects.