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The specific orbital energy associated with this orbit is −29.6 MJ/kg: the potential energy is −59.2 MJ/kg, and the kinetic energy 29.6 MJ/kg. Compared with the potential energy at the surface, which is −62.6 MJ/kg., the extra potential energy is 3.4 MJ/kg, and the total extra energy is 33.0 MJ/kg.
The formula for an escape velocity is derived as follows. The specific energy (energy per unit mass) of any space vehicle is composed of two components, the specific potential energy and the specific kinetic energy. The specific potential energy associated with a planet of mass M is given by =
In its basic form, it is the sum of the 'opposing' centrifugal potential energy with the potential energy of a dynamical system. It may be used to determine the orbits of planets (both Newtonian and relativistic ) and to perform semi-classical atomic calculations, and often allows problems to be reduced to fewer dimensions .
the kinetic energy of the system is equal to the absolute value of the total energy; the potential energy of the system is equal to twice the total energy; The escape velocity from any distance is √ 2 times the speed in a circular orbit at that distance: the kinetic energy is twice as much, hence the total energy is zero. [citation needed]
The central body and orbiting body are also often referred to as the primary and a particle respectively. In the specific cases of an elliptical or circular orbit, the vis-viva equation may be readily derived from conservation of energy and momentum. Specific total energy is constant throughout the orbit.
By substituting the vis-viva equation into the kinetic energy component, the orbital energy of a circular orbit is given by: = + = Where G is the gravitational constant, M E is the mass of the central body and m is the mass of the orbiting satellite. We take the derivative of the orbital energy with respect to the radius.
A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red. The height of the kinetic energy decreases asymptotically toward zero as the speed decreases and distance increases ...
A low energy transfer, or low energy trajectory, is a route in space which allows spacecraft to change orbits using very little fuel. [ 8 ] [ 9 ] These routes work in the Earth - Moon system and also in other systems, such as traveling between the satellites of Jupiter .