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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.
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.
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 .
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
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.
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]
This is defined as the distance from a satellite at which its gravitational pull on a spacecraft equals that of its central body, which is = /, where D is the mean distance from the satellite to the central body, and m c and m s are the masses of the central body and satellite, respectively. This value is approximately 66,300 kilometers (35,800 ...