Celestial mechanics

Celestial mechanics is a division of astronomy dealing with the motions and gravitational effects of celestial objects. The field applies principles of physics, historically Newtonian mechanics, to astronomical objects such as stars and planets.

Examples of problems

Celestial motion without additional forces such as thrust of a rocket, is governed by gravitational acceleration of masses due to other masses. A simplification is the n-body problem, where we assume n spherically symmetric masses, and integration of the accelerations reduces to summation.

Related Topics:
Thrust - Rocket - N-body problem

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Examples:

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• 4-body problem: spaceflight to Mars (for parts of the flight the influence of one or two bodies is very small, so that there we have a 2- or 3-body problem; see also the patched conic approximation)
• 3-body problem:
• quasi-satellite
• spaceflight to, and stay at a Lagrangian point

In the case that n=2 (two-body problem), the situation is much simpler than for larger n. Various explicit formulas apply, where in the more general case typically only numerical solutions are possible. It is a useful simplification that is often approximately valid.

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Examples:

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• a binary star, e.g. Alpha Centauri (approx. the same mass)
• a double planet, e.g. Pluto with its moon Charon (mass ratio 0.147)
• a binary asteroid, e.g. 90 Antiope (approx. the same mass)

A further simplification is based on "standard assumptions in astrodynamics", which include that one body, the orbiting body, is much smaller than the other, the central body. This is also often approximately valid.

Related Topics:
Standard assumptions in astrodynamics - Orbiting body - Central body

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Examples:

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• Solar system orbiting the center of the Milky Way
• a planet orbiting the Sun
• a moon orbiting a planet
• a spacecraft orbiting Earth, a moon, or a planet (in the latter cases the approximation only applies after arrival at that orbit)

Either instead of, or on top of the previous simplification, we may assume circular orbits, making distance and orbital speeds, and potential and kinetic energies constant in time. Notable examples where the eccentricity is high and hence this does not apply are:

Related Topics:
Circular orbit - Orbital speed - Eccentricity

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• the orbit of Pluto, ecc. = 0.2488 (largest value among the planets of the Solar System)
• the orbit of Mercury, ecc. = 0.2056
• Hohmann transfer orbit
• Gemini 11 flight
• suborbital flights

Of course, in each example, to obtain more accuracy a less simplified version of the problem can be considered.

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Perturbation theory

Perturbation theory comprises mathematical methods that are used to find an approximate solution to a problem which cannot be solved exactly, by starting from the exact solution of a related problem

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