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Specific orbital energy - Equation forms for different orbits | | Specific orbital energy - Equation forms for different orbits: Encyclopedia II - Specific orbital energy - Equation forms for different orbits | | For an elliptical orbit specific orbital energy equation simplifies to:
where:
is the standard gravitational parameter
is semi-major axis of the orbiting body
For a parabolic orbit this equation simplifies to:
For a hyperbolic trajectory this specific orbital energy equation takes form:
In this case the specific orbital energy is also referred to as characteristic energy (or ) and is equal to the ...
See also:Specific orbital energy, Specific orbital energy - Equation forms for different orbits, Specific orbital energy - Rate of change, Specific orbital energy - Additional energy, Specific orbital energy - Examples, Specific orbital energy - Applying thrust | | | Specific orbital energy, Specific orbital energy - Additional energy, Specific orbital energy - Applying thrust, Specific orbital energy - Equation forms for different orbits, Specific orbital energy - Examples, Specific orbital energy - Rate of change | | |
| | | Specific orbital energy: Encyclopedia II - Specific orbital energy - Equation forms for different orbits
Specific orbital energy - Equation forms for different orbits
For an elliptical orbit specific orbital energy equation simplifies to:
where:
- is the standard gravitational parameter
- is semi-major axis of the orbiting body
For a parabolic orbit this equation simplifies to:
For a hyperbolic trajectory this specific orbital energy equation takes form:
In this case the specific orbital energy is also referred to as characteristic energy (or ) and is equal to the excess specific energy compared to that for an escape orbit (parabolic orbit).
It is related to the hyperbolic excess velocity (the orbital velocity at infinity) by
It is relevant for interplanetary missions.
Thus, if orbital position vector () and orbital velocity vector () are known at one position, and is known, then the energy can be computed and from that, for any other position, the orbital speed.
Other related archivesAstrodynamics, Celestial mechanics, International Space Station, Specific energy change of rockets, astrodynamics, atmospheric drag, characteristic energy, delta-v, eccentricity, elliptical orbit, escape orbit, gravity drag, hyperbolic trajectory, kinetic energy, km, orbital, orbital distance, orbital energy conservation equation, orbital position vector, orbital speed, orbital velocity, orbital velocity vector, orbiting body, parabolic orbit, periapsis distance, potential energy, s, semi-major axis, space, specific relative angular momentum, standard assumptions, standard gravitational parameter, thrust, trajectory
 Adapted from the Wikipedia article "Equation forms for different orbits", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
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