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Celestial motion, without additional forces such as drag forces or the thrust of a rocket, is governed by the reciprocal gravitational acceleration between masses. A generalization is the n-body problem, [3] where a number n of masses are mutually interacting via the gravitational force.
Until the rise of space travel in the twentieth century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik , the field was termed 'space dynamics'. [ 1 ] The fundamental techniques, such as those used to solve the Keplerian problem (determining position as a function of time), are therefore the same in ...
A space vehicle's flight is determined by application of Newton's second law of motion: =, where F is the vector sum of all forces exerted on the vehicle, m is its current mass, and a is the acceleration vector, the instantaneous rate of change of velocity (v), which in turn is the instantaneous rate of change of displacement.
Carl Runge and Wilhelm Lenz much later identified a symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law.
The three-body problem is a special case of the n-body problem. Historically, the first specific three-body problem to receive extended study was the one involving the Earth, the Moon, and the Sun. [2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three ...
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The thermal energy is dissipated mainly by compression heating the air in a shockwave ahead of the vehicle using a blunt heat shield shape, with the aim of minimising the heat entering the vehicle. Sub-orbital space flights, being at a much lower speed, do not generate anywhere near as much [further explanation needed] heat upon re-entry.
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