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In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.
Velocity
Under standard assumptions the orbital velocity (<math>v\,<math>) of a body traveling along circular orbit can be computed as:
- <math>v=\sqrt{\mu\over{r}}<math>
where:
Conclusion:
- Velocity is constant along the path.
Orbital period
Under standard assumptions the orbital period (<math>T\,\!<math>) of a body traveling along circular orbit can be computed as:
- <math>T={2\pi\over{\sqrt{\mu}}}r^{3\over{2}}<math>
where:
Conclusions:
Energy
Under standard assumptions, specific orbital energy (<math>\epsilon\,<math>) is negative and the orbital energy conservation equation for this orbit takes the form:
- <math>{v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2r}}=\epsilon< 0\,\!<math>
where:
The virial theorem applies even without taking a time-average:
- the potential energy of the system is equal to twice the total energy
- the kinetic energy of the system is equal to minus the total energy
Thus 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.
Equation of motion
Under standard assumptions, the orbital equation becomes:
- <math>r={{h^2}\over{\mu}}<math>
where:
Delta-v to reach a circular orbit
Maneuvering into a large circular orbit, e.g. a geostationary orbit, requires a larger delta-v than an escape orbit, although the latter implies getting arbitrarily far away and having more energy than needed for the orbital speed of the circular orbit. It is also a matter of maneuvering into the orbit. See also Hohmann transfer orbit.
See also
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