Difference between revisions of "Specific energy"
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<math>\epsilon = - \frac{\mu}{2a} = \frac{V^2}{2} - \frac{\mu}{r} < 0</math> | <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. |
==Parabolic orbits<ref name=SME />== | ==Parabolic orbits<ref name=SME />== | ||
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<math>\epsilon = - \frac{\mu}{2a} = \frac{V^2}{2} - \frac{\mu}{r} > 0</math> | <math>\epsilon = - \frac{\mu}{2a} = \frac{V^2}{2} - \frac{\mu}{r} > 0</math> | ||
| − | where <math>a < 0</math> is the [[semi-transverse axis]], <math>\mu</math> is the gravitational parameter for the body being orbited, <math>r</math> is distance to the body being orbited at some point in time and <math>V</math> is velocity at that time. | + | where <math>a < 0</math> is the [[semi-transverse axis]], <math>\mu</math> is the [[gravitational parameter]] for the body being orbited, <math>r</math> is distance to the body being orbited at some point in time and <math>V</math> is velocity at that time. |
==References== | ==References== | ||
Revision as of 08:09, 16 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]
Since orbital mechanics only concerns itself with changes in orbital energy, the zero could be chosen arbitrarily. It is computationally most convenient to choose the value at escape velocity (i.e. parabolic orbit). This choice makes the semi-major axis inversely proportional to the specific energy and if the mass does not change also to the total orbital energy.
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.
