Compute the distance between the Earth and the Moon

[Alexanddros81]

Homework Statement

14.99 Assuming that the orbit of the moon around the Earth is a circle (its
eccentricity is actually 0.055), and knowing that the period of the orbit is 27.3
days, compute the distance in kilometres between the centers of the Earth and moon.

Homework Equations

The Attempt at a Solution

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Can you check my solution?

 

[PeroK]

Have you ever heard of a thing called "algebra"?

 

[berkeman]

Have you ever heard of a thing called "algebra"?

Well, 240,000 miles is about 384,000 km, so the answer looks close to right. Are you seeing algebra errors?

 

[PeroK]

Well, 240,000 miles is about 384,000 km, so the answer looks close to right. Are you seeing algebra errors?

The numerical answer looks correct. It just looks like "plug and chug" gone mad to me.

It would have been nice to see a formula for $r$ in terms of $G,M, T$.

Am I expecting too much?

 

[berkeman]

Ah, got it. Yeah, I only checked the final answer because I was having some trouble following his equations and work. Nice job converting units, though...

 

[PeroK]

@Alexanddros81 your solution is neat, tidy and logical. But, algebra was invented - among other things - to avoid working with many lines of ten digit numbers.

If there were an error in your arithmetic it would be difficult to track down.