# Questions tagged [celestial-mechanics]

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### Why is the orbital resonance of the Galilean moons stable?

It is well known that the orbits of Ganymede, Europa and Io are in a 4:2:1 resonance. Most online sources (including but not limited to Wikipedia) say that such an orbital resonance, along with the 3:...
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### Why does planetary spin affect the stability of orbits?

Reading about the Hill Sphere I notice that "the region of stability for retrograde orbits at a large distance from the primary, is larger than the region for prograde orbits at a large distance from ...
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### Horseshoe orbit cycle times

I asked on Worldbuilding originally, but was directed here instead I've been working on a habitable moon system for a story, and I'm now trying to populate the other moons around the parent planet. ...
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### Why do the orbit equations have to be symmetric about two axes even the orbit is not bounded?

In the book of Classical Mechanics by Goldstein, at page 88, it is given that However, the orbit might not be bounded, so there might not be two turning point; just one. In such a case, how can we ...
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### A question about almost stationary orbits

For an orbit around the earth with period equal to a sidereal day with eccentricity $e=0$ and inclination $i=0$, the path on earth would be a single point on the equator. I have done some simulations ...
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### Proof of unsolvability of $n$-body problem for $n\geqslant 3$ in general

We know there are general solutions for 1-body problem and 2-body problem and also we know in some "special cases" there are some possible solutions for $n$-body problem for $n \geqslant 3$ and there ...
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### Calculating stable orbital resonance and other factors into orbits

Firstly here is a brief summary of what I trying to accomplish. From a predetermined total solar system mass , star count in that system, per-star classification and mass I am building a system of ...
1answer
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### Coexistence at Lagrange points

I was wondering how precise the location of an object in a Lagrange point needs to be to maintain stability, since it seems that several natural objects (asteroids) exists together in some of these ...
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### What is the difference between Saddle points and Lagrangian points between Earth and the Sun?

I am studying MOND bubble effects in the Solar System (Paper). In "mond habitats.." (last reference) first page, the author says MOND bubbles reside on the saddle points but I fail to understand the ...
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### How to calculate orbital eccentricity from the ratio of satellites' velocities?

I have a problem with working out how to calculate the orbital eccentricity from the ratio of two satellites' linear velocities. We know that two satellites encircles the Earth in two elliptical ...
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### Story about a mathematician, a dinner party, and the three-body problem

I remember dimly hearing a story, coincidentally also at a dinner party, and I was trying recently to track the details down with no success. I was hoping someone here might have also heard this story ...
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### For two planets in a 2:1 mean motion resonance , where will their periastron and apastron points be?

I want to animate the changing orbits of planets when they enter a mean motion resonance. Using a 2:1 resonance, I want to show a low-mass inner planet and a low-mass outer planet being tugged by a ...
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### Why are so few inclined circumbinary planets known?

For a research project I'm studying the orbits of circumbinary planets, most of these planets orbits are coplanar. However I was wondering if orbits with a high inclination could be stable. I made a ...
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### Two bodies orbiting around common barycenter

Assume $2$ bodies of mass $M_1$ and $M_2$ orbiting in a plane around their common barycenter $G$. It means the axis $(M_1M_2)$ is rotating in the plane around a vertical axis through $G$. [Please ...
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### Mass distributions within two bodies such that the orbit is no longer Keplerian?

The trajectories of two point masses or spherically symmetric masses with respect to their center of mass are conic sections or Kepler orbits. Consider that the bodies have finite size with respect ...
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### Restricted 3-body problem - Rotating coordinate system

I'm trying to follow the formulation of the restricted 3-body problem in Taff's "Celestial Mechanics" book as I'm writing an essay on Lagrange points and am confused by the transformation into the ...
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### The shape characteristics of gravitational wells given different masses and spread of objects

I am curious as to research that calculates the shape of gravitational wells, and their limits, and affect on time, for different masses and spread of mass. The actual question is st the end. For ...
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### Good sources to get velocity/position vectors for all planets and moons in the Solar System for building an orbital simulator?

I’m building an $N$-body simulator, and I have everything ready to begin simulating. But my issue is is that I have no idea how to get all the starting positions and velocities for the celestial ...
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### Stability of solar system

As far as I understand, the stability of the Solar system means that planets do not collide and will not in near future. The only thing that is stated on Wikipedia is that scientists are concerned ...