Difference between revisions of "Specific energy"
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==Circular and ellipticla orbits<ref name=SME>J.R. Wertz, D.F. Everett & J.J. Puschell - ''Space mission engineering: The new SMAD''. 2011. pp. 963-970. ISBN 978-1-881883-15-9</ref>== | ==Circular and ellipticla orbits<ref name=SME>J.R. Wertz, D.F. Everett & J.J. Puschell - ''Space mission engineering: The new SMAD''. 2011. pp. 963-970. ISBN 978-1-881883-15-9</ref>== | ||
| − | <math>\epsilon = - \frac{\mu}{2a} = \frac{V^2}{2} - \frac{\mu}{ | + | <math>\epsilon = - \frac{\mu}{2a} = \frac{V^2}{2} - \frac{\mu}{r} < 0</math> |
where <math>a < 0</math> is the [[semi-major axis]], <math>\mu</math> is the gravitational parameter for the body being orbited, <math>r</math> is the distance to the body being orbited at some point in time and <math>V</math> is velocity at that time. This relationship comes about because <math>\frac{V^2}{2}</math> is the kinetic energy and <math>- \frac{\mu}{2a}</math> the potential energy of the system. | where <math>a < 0</math> is the [[semi-major axis]], <math>\mu</math> is the gravitational parameter for the body being orbited, <math>r</math> is the distance to the body being orbited at some point in time and <math>V</math> is velocity at that time. This relationship comes about because <math>\frac{V^2}{2}</math> is the kinetic energy and <math>- \frac{\mu}{2a}</math> the potential energy of the system. | ||
Revision as of 20:08, 5 February 2013
In orbital mechanics, specific energy (symbol ) is the total orbital energy per unit mass of an orbiting body.
Contents
Circular and ellipticla orbits[1]
where is the semi-major axis, is the gravitational parameter for the body being orbited, is the distance to the body being orbited at some point in time and is velocity at that time. This relationship comes about because is the kinetic energy and the potential energy of the system.
Parabolic orbits[1]
- to do: a more in-depth explanation of why orbital energy is defined in such a way that is relative to the parabolic orbit.
Hyperbolic orbits[1]
where is the semi-transverse axis, is the gravitational parameter for the body being orbited, is distance to the body being orbited at some point in time and is velocity at that time.
