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# The Online Encyclopedia and Dictionary   ## Encyclopedia ## Dictionary ## Quotes  # Circular orbit

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0.

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## Velocity

Under standard assumptions the orbital velocity ( $v\,$) of a body traveling along circular orbit can be computed as: $v=\sqrt{\mu\over{r}}$

where:

• $r\,$ is radius of orbit equal to radial distance of orbiting body from central body,
• $\mu\,$ is standard gravitational parameter.

Conclusion:

• Velocity is constant along the path.

## Orbital period

Under standard assumptions the orbital period ( $T\,\!$) of a body traveling along circular orbit can be computed as: $T={2\pi\over{\sqrt{\mu}}}r^{3\over{2}}$

where:

• $r\,$ is orbit radius equal to radial distance of orbiting body from central body,
• $\mu\,$ is standard gravitational parameter.

Conclusions:

• The orbital period is the same as that for an elliptic orbit with the semi-major axis ( $a\,\!$) equal to orbit radius .

## Energy

Under standard assumptions, specific orbital energy ( $\epsilon\,$) is negative and the orbital energy conservation equation for this orbit takes the form: ${v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2r}}=\epsilon< 0\,\!$

where:

• $v\,$ is orbital velocity of orbiting body,
• $r\,$ is radius of orbit equal to radial distance of orbiting body from central body,
• $\mu\,$ is standard gravitational parameter.

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: $r={{h^2}\over{\mu}}$

where:

• $r\,$ is radial distance of orbiting body from central body,
• $h\,$ is specific angular momentum of the orbiting body,
• $\mu\,$ is standard gravitational parameter.

## 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.  