Moon's orbit

[ganon]

Hello!

A website (attempting to find modern Science in religious scriptures) states that
if Earth-Moon system were isolated from Sun's and other planets' gravitationnal influences, Moon's orbit around the Earth would eventually become almost a perfect circle (whereas with the Sun it's an ellipse).

In that condition, they claim that the radius R' of Moon's new orbit
would be: R'= actual semi-major axis*(1-2e)

and mean moon's speed would become equal to V'= 3680*(1-2e)

where "e" is the actual excentricity of Moon (about 0.0549) and "2e" the variation ratio.



Link to image of maths: http://img40.imageshack.us/img40/9568/1dtp.jpg



Are their claims and calculations accurate?

[Swift]

ganon,

Since you seem to be "just asking" and you are not advocating any such claims, I've moved your thread to Q&A.

[jfribrg]

I'm not an expert, but a few things seem odd. First, they start with the common definition of acceleration, not the physical definition. Acceleration is the change in velocity, not the change in speed. Velocity incorporates both speed and direction of motion, and so does acceleration. However, after a roundabout explanation in that first sentence ("it is known...."), they settle on an acceptable definition of acceleration. I don't understand the next sentence which implies that eccentricity is the result of the sun's gravitational influence on the Earth-Moon system. The moon revolves around the Earth in an ellipse where the Earth is at one focus (Technically it is the barycenter of the two-body system that is at the ellipse, but that point is inside the Earth, so we can ignore that technicality). Newton proved this. The eccentricity is the result of the angular momentum of the system. The sun does have an influence, but if we remove that influence, the eccentric orbit will not disappear. Eventually, the moon and Earth will become tidally locked (many billions of years from now), which means that the day and the month will have the same length, and I believe it would also result in a circular orbit, but the sun's influence is not what is causing the eccentricity. This all seems to be based on the unproven assertion that the term 2e is based on the suns influence. The reason it is unproven is because it is wrong. The moon's speed varies throughout the month to a small degree because of the sun's gravitational pull, but it is mainly because of the inverse square law of gravitational attraction between the Moon and Earth.

The other thing that seems odd is the various definitions and formulae. The definitions are not used in the narrative. It seems to be just fluff with no bearing on the discussion. The Earth's inclinclination with respect to the ecliptic is termed " in relation to vacuum" which makes no sense. Seems to me that it was written by someone who remembered some of their high school physics (but not too much), looked up some seemingly related mathematical and astronomical definitions, and put it together with some handwaving to "prove" something that is simply wrong.

[Jeff Root]

I expect that the forces between Earth and Moon which cause tides,
lock the Moon's rotation, slow Earth's rotation, and move the Moon
gradually away from Earth would also circularize the Moon's orbit if
not for the influence of the Sun and other planets.

-- Jeff, in Minneapolis