Sorry I could not pollute a real thread...

[MKruer]

Sorry I could not pollute a real thread, but when I was reading http://celestiaproject.net/forum/viewtopic.php?t=11692

And came upon

Good Doctor,

Can the Brain-Dead ask WHY the Moon is different? What makes it
so different from any other orbiting body in the Solar System?

Just curious...

Thanks, Bob

Bob,

first you should recall what VSOP87 qualitatively does. It is some kind of "perturbation expansion", as we say, which successively takes into account the cumulative effects of all sources of a gravitational field (other planets, moons,...) around a given body in form of hundreds of "perturbative" terms. [It's precisely the analog of the so-called Hartree-Fock method in atomic physics.]. These correction terms due to the other bodies are relative to elliptical Keplerian orbits which are assumed as a starting approximation.

The specific problem with the Moon is quite intuitive and more general than VSOP87, actually:

The Moon moves noticeably differently from a simple Keplerian ellipse, because of the competing gravitation of the Earth and the Sun.. So many more correction terms are actually needed. That and many other more technical issues form the basis for why the Moon orbits are difficult to calculate at high accuracy. You will perhaps also recall that the gravitational force is a long-range force (decreasing relatively slowly with distance) and its strength is proportional to the masses of the bodies under consideration. So the Sun is still very competitive at the location of the Moon. And so is the Earth, of course.

Bye Fridger

I though, so all we need to do is solve the unsolved n-body problem in physics, and we should be able to get rid of all the custom orbits right? Sounds simple enough.
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Sorry could not resist.

[t00fri]

I though, so all we need to do is solve the unsolved n-body problem in physics, and we should be able to get rid of all the custom orbits right? Sounds simple enough.
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Sorry could not resist. Embarassed

While you are of course free to write whatever you could not restist to...your remark is not very qualified.

The often stated impossibility to solve the n-body problem is not a general "impossibility", but precisely refers to the method of first integrals of motion in classical mechanics. You surely know that mechanical problems can often be solved ("integrated") via their "first integrals" (energy-momentum conservation!). Since the n-body problem involves 6n variables, namely 3 space and 3 velocity components per particle, the issue was simply whether there are enough first integrals to solve for these 6n variables algebraically The statement is NO. It could be proven that there are ONLY 10 independent such "first integrals". That's all! Of course you can treat the n-body problem very precisely via a perturbative series expansion and by means of numerical methods! That's precisely what's being done in our custom orbits

Bye Fridger