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Concept# Circular orbit

Summary

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 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
where:
is orbital velocity of orbiting body,
is radius of the circle
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 is measured in meters per second per second, then the numerical values for will be in meters per second, in meters, and in radians per second.
The speed (or the magnitude of velocity) relative to the central object is constant:
where:
is the gravitational constant
is the mass of both orbiting bodies , although in common practice, if the greater mass is significantly larger, the lesser mass is often neglected, with minimal change in the result.
is the standard gravitational parameter.
The orbit equation in polar coordinates, which in general gives r in terms of θ, reduces to:
where:
is specific angular momentum of the orbiting body.
This is because
Hence the orbital period () can be computed as:
Compare two proportional quantities, the free-fall time (time to fall to a point mass from rest)
(17.7% of the orbital period in a circular orbit)
and the time to fall to a point mass in a radial parabolic orbit
(7.

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