# Questions tagged [celestial-mechanics]

Use this tag for questions about the branch of astronomy dealing with motions of celestial objects.

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### Relationship between lifetime of tech civilisations and time taken for a roundtrip between two such civilisations

Here is a statement of the question, which is taken from Chaisson and McMillan's Astronomy: A Beginner's Guide to the Universe. Assume that the number of (technological) civilisations in the Milky Way ...
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### Dominated splitting in dynamical system

I am studying paper '' A (SHORT) SURVEY ON DOMINATED SPLITTING '' by MART´IN SAMBARINO It is mentiend that on page 2 '' Nevertheless, since the action of Df on the invariant subbundles might not have ...
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### how to solve single nonlinear algebraic equation in two variables?

(I am not a mathematician; I am having physics background.) How to solve a single nonlinear algebraic equation in two variables, $x$ and $y$? (I know that - if there are two variables, one needs two ...
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### Do Kepler's laws (really) solve the Kepler problem? And should the terms of the central force problem be treated as dependent variables?

See the bottom for an added definition and discussion. Context Note: I've never had a course in differential equations, so my question may demonstrate gross ignorance. When the distinction is clear, I ...
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### Finding area of a circle from circular motion

We can find the change in area by $$dA=1/2 |r⃗ ×dr⃗|$$ $$dA = 1/2 r dr \sin(θ) = 1/2 r dr$$ since velocity vector is orthogonal to r $$dA = 1/2 r vdt$$ T =2πr/v $$A = 1/2\int_t^T r vdt$$ couldn'...
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### Deriving a second-order system of differential equations that describes the motion of a planet (in cartesian coordinates)

I got a question that’s probably very basic but I just can’t figure it out. I want to derive a system of second order differential equations that describes the motion of a planet in (x,y)-coordinates (...
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### How off is my understanding of Lambert's theorem to solve Lambert's Problem?

Math Overflow-ites! Hopefully, this question fits here better than places like Space and Physics. And sorry if I ramble a little - I'm rather new to this all. My understanding of Lambert's theorem is ...
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### Periodic Behavior of a Two-Body Problem?

Given the following equations and parameters: does the orbit repeat? If not, why? and what would make it repeat? Any clarification on what makes an orbit periodic would be greatly appreciated! I ...
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### A very simple question on motion in a circle.

Question A spacecraft of mass m orbits Earth at a radius R and speed $v_0$ as shown below. An aerospace engineer decides it should orbit at a radius of $\frac{2R}{3}$ instead. The mass of Earth is M. ...
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### Normal distance

Recently, I saw a paper "G. H. Darwin, Periodic Orbits" and I don't undertand the concept of "normal displacement $\delta$p". "... Now suppose that x, y are the coordinates of a point on an orbit, ...
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### Equation of Motion of a particle

I've tried this question over and over, and I'm getting nowhere. I've even tried looking for a solution to help make sense of how to get there, but I've had no luck. Can anyone help me please? A ...
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