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[1] [2] [3] In classical mechanics for instance, in the action formulation, extremal solutions to the variational principle are on shell and the Euler–Lagrange equations give the on-shell equations. Noether's theorem regarding differentiable symmetries of physical action and conservation laws is another on-shell theorem.
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.
A rocket acting on a fixed object, as in a static firing, does no useful work on the rocket; the rocket's chemical energy is progressively converted to kinetic energy of the exhaust, plus heat. But when the rocket moves, its thrust acts through the distance it moves. Force multiplied by displacement is the definition of mechanical work. The ...
The space rendezvous before docking normally takes multiple precisely calculated engine firings in multiple orbital periods, requiring hours or even days to complete. To the extent that the standard assumptions of astrodynamics do not hold, actual trajectories will vary from those calculated.
The shell theorem is an immediate consequence of Gauss's law for gravity saying that ∫ S g ⋅ d S = − 4 π G M {\displaystyle \int _{S}{\mathbf {g} }\cdot \,d{\mathbf {S} }=-4\pi GM} where M is the mass of the part of the spherically symmetric mass distribution that is inside the sphere with radius r and
The parachute is located at the apex of the back shell and slows the spacecraft during EDL. The pyrotechnic control system releases devices such as nuts, rockets, and the parachute mortar. The inertial measurement unit reports the orientation of the back shell while it is swaying underneath the parachute.
A space rendezvous is a sequence of orbital maneuvers during which two spacecraft, one of which is often a space station, arrive at the same orbit and approach to a very close distance (e.g. within visual contact).
Space exploration is about reaching the destination safely (mission enabling), quickly (reduced transit times), with a large quantity of payload mass, and relatively inexpensively (lower cost). The act of reaching the destination requires an in-space propulsion system, and the other metrics are modifiers to this fundamental action.