TheInfoList

A circular orbit is the orbit with a fixed distance around the barycenter, that is, in the shape of a circle.

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 plane of motion.

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.

## Circular acceleration

Transverse acceleration (perpendicular to velocity) causes 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 with respect to time gives the centripetal acceleration

${\displaystyle a\,={\frac {v^{2}}{r}}\,={\omega ^{2}}{r}}$

where:

• ${\displaystyle v\,}$ is orbital velocity of orbiting body,
• ${\displaystyle r\,}$ is radius of the circle
• ${\displaystyle \omega \ }$ 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 of ${\displaystyle \mathbf {a} }$ is measured in meters per second per second, then the numerical values for ${\displaystyle v\,}$ will be in meters per second, ${\displaystyle r\,}$ in meters, and ${\displaystyle \omega \ }$ in radians per second.

## Velocity

The speed (or the magnitude of velocity) relative to the central object is constant:[1]:30

${\displaystyle v={\sqrt {GM\! \over {r}}}={\sqrt {\mu \over {r}}}}$

where:

• ${\displaystyle G}$, is the gravitational constant
• ${\displaystyle M}$, is the mass of both orbiting bodies ${\displaystyle (M_{1}+M_{2})}$, although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
• ${\displaystyle \mu =GM}$, is the standard gravitational parameter.

## Equation of motion

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

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

where: