Expert: Philip Stahl - 8/19/2010

Question
QUESTION: Dear expert,

A website claimed that if Earth-Moon system were isolated from Sun's gravity, Moon's orbit around Earth wouldn't be elliptic as today but would be almost a perfect sphere.

In that hypothetic condition, mean moon's speed would be lower than 3680km/h according to them.

They calculated this new value by doing:
V'= 3680*(1-(2*e))=3278km/h   where 'e' is the eccentricity of actual Moon's orbit and '2*e' the variation ratio.

Consequently, the circumference of Moon's orbit would become:

L=V'*T=3278* 655hour= 2,147,682km


My question is: are their calculations and claims accurate?


Thank you

ANSWER: Hello,

You don't cite a source or link for these calculations, but I have never seen anything like them before.

What I did is obtain the putative radius for the Moon's orbit (given their circumference) and assume circularity - then apply the force balance equation:

mv^2/ r = GMm/r^2

where M is the mass of Earth, m the mass of moon, and r the radius - to get:

v =  [GM/r]^1/2

which comes out to v = 3.43 x 10^4 m/s which is not the same as their value.

In any case, the computation of 3680*(1-(2*e))=3278km/h is not correct using their formula, but would be 3562 km/h (given e = 0.016). So I am not sure you have cited the correct formula, or they haven't.

If you can locate the actual original source or link and send it, we can examine the claims in more detail.

---------- FOLLOW-UP ----------

QUESTION: Thank you for your reply,


"In any case, the computation of 3680*(1-(2*e))=3278km/h is not correct using their formula, but would be 3562 km/h (given e = 0.016)."

3280km/h seems on the contrary to be correct with their formula because here 'e' is the eccentricity of Moon's orbit not Earth's, so e=0.0549.

I located the source of it. All the assumptions and formulas come from an article written by a researcher called Dr. Muhammad Doudah:          http://www.eajaz.org/Arabic/ejaz_pdf/issue/8.pdf

It's obvious his article has a little religious content,
but let's analyze only the science-related claims therein and let's not mind the rest.



         Sincerely

Answer
Hello,

Yes, I examined the paper and it looks like mostly gobbledegook to me. Most of his celestial mechanics "relations" look like pure inventions as when he relates the mass ratio of two mutually orbiting bodies to the cubes of the velocity ratios. The V*(1-(2*e)) also looks like another fiction. I've perused my old celestial mechanics notes and there is absolutely nothing to even remotely suggest such a relationship.

The kicker was at the end of the paper when he claims the "dynamics" of the Earth-Moon-Sun system existed *before* they actually did physically (which would mean even in nebular form). Then somewhat further he gives his agenda away by referencing a "6 day creation" criterion.

I will say he had me semi-convinced at least for a brief (~ 15 minute) interval!

Hope this helps!