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.

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

where:

The formula is dimensionless, describing a ratio true for all units of measure applied uniformly across the formula. If the numerical value ${\displaystyle \mathbf {a} }$ is measured in meters per second squared, then the numerical values ${\displaystyle v\,}$ will be in meters per second, ${\displaystyle r\,}$ in meters, and ${\displaystyle \omega \ }$ in radians per second.

The speed (or the magnitude of velocity) relative to the centre of mass is constant:

where:

The orbit equation in polar coordinates, which in general gives r in terms of θ, reduces to:^{[clarification needed][citation needed]}