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This sounds like a homework problem so I'll give you most of it but you'll have to work out the details yourself. Newton's shell theorem tells us that for any spherical mass distribution, the potential at a distance $r_0$ from the center is the same as if all the mass within the shell of radius $r_0$ were at $r=0$, and all the mass outside of the shell didn'...


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I think this is what you want: Simon et al. 1994 You can find Meeus formula in it.


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Perhaps you are looking for Lagrange’s planetary equations? Given some perturbation $H_1$ to the Hamiltonian, they give six equations to calculate the change of the orbital elements over time; a thorough discussion is given in Goldstein’s textbook on classical mechanics. The equation for $\Omega$ is $$\frac{d\Omega}{dt}=\frac{1}{\sqrt{GMm^2(1-e^2)\sin i}}\...


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I don't have an exact answer, too many factors are involved. If we consider Newtonian orbits, you can have a stable orbit as long as the perihelion is outside the Sun. But by getting closer to the Sun, two other effects start playing a role: tidal interactions and general relativity. I'm not an expert in general relativity, but I know that Mercury is already ...


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The Milky Way's outer halo has many globular clusters with a retrograde orbit (about 40% of all clusters in Milky Way). One of the more prominent example include Kapteyn's star which is highly retrograde due to it being ripped from a dwarf galaxy and merging with the Milky Way. However, the structure of the halo is a topic of an ongoing debate. Several ...


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