Difference between revisions of "Specific energy"
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In [[orbital mechanics]], '''specific energy''' (symbol <math>\epsilon</math>) is the total orbital energy per unit mass of an orbiting body. | In [[orbital mechanics]], '''specific energy''' (symbol <math>\epsilon</math>) is the total orbital energy per unit mass of an orbiting body. | ||
| − | ==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}{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" />== |
<math>\epsilon = 0</math> | <math>\epsilon = 0</math> | ||
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]]. | 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<ref name=SME />== | + | ==Hyperbolic orbits<ref name="SME" />== |
<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. | ||
| + | |||
| + | == Mars orbit == | ||
| + | for Mars, | ||
| + | |||
| + | == Earth Orbit == | ||
==References== | ==References== | ||
Revision as of 14:43, 27 April 2019
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.
Mars orbit
for Mars,
