# Questions tagged [celestial-mechanics]

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

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### Formula for Stereographic Projection of Celestial Sphere centered at north point of horizon ,not at North Pole.

I'm currently making planetarium on web just for fun, and have problem with finding projection formula. Several search results shows formulas for projection of upper celestial sphere(centered at north ...
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### Interval of convergence of Lagrange's infinite series

I am reading a book on Orbital Mechanics for Engineering Students by Howard D. Curtis. In that book it was mentioned (in page 119) that there is no closed form solution for $E$ as a function of the ...
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### what is the math for gravity causing different kinds of orbit ( ellipse, parabola ,straight line ) for an object in different cases?

case-1: the motion or you can say the orbit of a projectile is parabolic because gravity acts on it. case-2: the motion or the orbit of an object ...
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### northmost latitude

From the book Astronomy, principles and practice. I cannot solve the second part. Assuming the Earth to be a sphere of radius 6378 km calculate the great circle distance in kilometers between London (...
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### Getting started on Celestial Mechanics

I am searching for a math-accurate book on this subject, in particular for this topics: $n$-body problem, getting more detailed when $n=2$. Efeméride calculation. Orbit determination. Perturbation ...
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### multyplication of 2 vectors forming a matrix - meaning

I am trying understand an algorithm used to determine orientations. Knowing a cross product of 2 vectors gives you a third vector which is orthogonal. What does the multiplication of a 3x1 and 1x3 ...
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### Keplerian orbits and closest approaches to Earth.

This question arose out of a discussion on Space.SE, but I think it will appeal to mathematicians more than astronomers: Let's consider a small astronomical object following an ideal elliptic ...
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### planetary motion: Particle describes an ellipse as a central orbit about a focus

A particle describes an ellipse as a central orbit about a focus. Show that the velocity at the end of the minor axis is the geometric mean between the greatest and least velocities. My attempt: I ...
I'm investigating further into my orbital overlap problem. I've already looked into the overlap ($0°$ angle between the two orbits) of two planets in a circular orbit around the sun. I'm now trying ...