Questions tagged [celestial-mechanics]

The part of classical mechanics which deals with the motion of planets and satellites.

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Newton and affine curvature

This is a reference request for the following modern formulation of one of the central results of mathematical physics—Newton’s deduction of the inverse square law from Kepler’s description of the ...
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A.e. global existence of solution to 'encased' n-body problem already somewhere in the literature?

In the study of the Newtonian n-body problem, it seems that Von Zeipel's theorem and Saari's theorem concerning the improbability of collision singularities ought to lend themselves to a nice ...
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Decidability of 3 body problem

Is there a result showing that something along the lines of the three body problem is undecidable? Or are they known to be decidable or neither? I mean problems along the lines of the following ...
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Transport theorem in space craft control: tracking a reference angular velocity

I am reading the book named "Analytical mechanics aerospaces systems" by Schaub and Junkins. In section 7.2, the task is to control the spacecraft to track a specified angular velocity $w_r$ ...
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36 votes
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Euler's Master's Thesis

At the age of 16, Leonhard Euler defended his Master's Thesis, where he discussed and compared Descartes' and Newton's approaches to planet motion. I don't know anything else about it. In particular, ...
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restricted three body problem equations of motion using particle distances and one angle variable

If we solve numerically a three (or $N$) body planar problem, it's easy to calculate the distances of the bodies as function of time. Conversely if we know the interparticle distances as functions of ...
9 votes
1 answer
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Status of the three-body problem

I find many numerical results on the three-body problem, but what is rigorously proved? Especially I would be interested in the parameter domains for which we have rigorous lower bounds on the ...
14 votes
0 answers
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Precise form of the mean motion theorem

Consider an exponential polynomial $$f(t)=\sum_{k=1}^na_k\exp(i\lambda_kt),$$ where $a_k$ are complex and $\lambda_k, t$ real. The usual form of the Mean Motion Theorem says that the limit $$\lim_{t\...