thumb|right|[[Newton's cannonball|Isaac Newton's Cannonball. Path C depicts a circular orbit.]]
A circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle.
In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version.
Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the orbital plane.
Circular acceleration
Transverse acceleration (perpendicular to velocity) causes a change in direction. If it is constant in magnitude and changing in direction with the velocity, circular motion ensues. Taking two derivatives of the particle's coordinates concerning time gives the centripetal acceleration
:<math> a\, = \frac {v^2} {r} \, = {\omega^2} {r} </math>
where:
- <math>v\,</math> is the orbital velocity of the orbiting body,
- <math>r\,</math> is radius of the circle
- <math> \omega \ </math> is angular speed, measured in radians per unit time.
The formula is dimensionless, describing a ratio true for all units of measure applied uniformly across the formula. If the numerical value <math> \mathbf{a}</math> is measured in meters per second squared, then the numerical values <math>v\,</math> will be in meters per second, <math>r\,</math> in meters, and <math> \omega \ </math> in radians per second.
Velocity
The speed (or the magnitude of velocity) relative to the centre of mass is constant:
:<math> v = \sqrt{ GM\! \over{r = \sqrt{\mu\over{r </math>
where:
- <math>G</math>, is the gravitational constant
- <math>M</math>, is the mass of both orbiting bodies <math>(M_1+M_2)</math>, although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
- <math> \mu = GM </math>, is the standard gravitational parameter.
- <math>r</math> is the distance from the center of mass.
Equation of motion
The orbit equation in polar coordinates, which in general gives r in terms of θ, reduces to:
:<math>r=</math>
where:
- <math>h=rv</math> is specific angular momentum of the orbiting body.
This is because <math>\mu=rv^2</math>
Angular speed and orbital period
:<math>\omega^2 r^3=\mu</math>
Hence the orbital period (<math>T\,\!</math>) can be computed as: