Circular orbit

Two bodies with a slight difference in mass orbiting around a common barycenter with circular orbits.

For other meanings of the term "orbit", see orbit (disambiguation)

In astrodynamics or celestial mechanics a circular orbit is an elliptic orbit with the eccentricity equal to 0. It is an example of a rotation around a fixed axis: this axis is the line through the center of mass perpendicular to the plane of motion.

Circular acceleration

Transverse acceleration (perpendicular to velocity) causes change in direction. If it is constant in magnitude and changing in direction with the velocity, we get a circular motion. For this centripetal acceleration we have

where:

• is orbital velocity of orbiting body,
• is radius of the circle
• is angular frequency, measured in radians per second.

Velocity

Under standard assumptions the orbital velocity of a body traveling along circular orbit, can be computed as:

where:

• is radius of orbit equal to radial distance of orbiting body from central body,
• is the standard gravitational parameter, which is the product of the gravitational constant G and the central mass M.

Conclusion:

• Velocity is constant along the path.

Orbital period

Under standard assumptions the orbital period () of a body traveling along circular orbit can be computed as:

where:

• is the semi-major axis of the orbit; radius of the central body plus altitude of the orbit
• is standard gravitational parameter.

Energy

Under standard assumptions, specific orbital energy () is negative for a closed orbit and the orbital energy conservation equation (the Vis-viva equation) can take the form:

where:

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

The boundary case is which corresponds to escape from the primary (parabolic orbit), with .

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:

where:

• is radial distance of orbiting body from central body,
• is specific angular momentum of the orbiting body,
• 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.

See also

• Orbit
• Elliptic orbit
• List of orbits
• Two-body problem

v • d • e Orbits   Types General Box · Capture · Circular · Elliptical / Highly elliptical · Escape · Graveyard · Hyperbolic trajectory · Inclined / Non-inclined · Osculating · Parabolic trajectory · Parking · Synchronous (semi · sub) Geocentric Geosynchronous · Geostationary · Sun-synchronous · Low Earth · Medium Earth · Molniya · Near-equatorial · Orbit of the Moon · Polar · Tundra · Two-line elements Other Areosynchronous · Areostationary · Halo · Lissajous · Lunar · Heliocentric · Heliosynchronous   Parameters Classical  Inclination ·  Longitude of the ascending node ·  Eccentricity ·  Argument of periapsis ·  Semi-major axis ·  Mean anomaly at epoch Other  True anomaly ·  Semi-minor axis ·  Linear eccentricity ·  Eccentric anomaly ·  Mean longitude ·  True longitude ·  Orbital period   Maneuvers Bi-elliptic transfer · Delta-v budget · Geostationary transfer · Gravity assist · Gravity turn · Hohmann transfer · Oberth effect  · Inclination change · Phasing · Rendezvous · Transposition, docking, and extraction   Other orbital mechanics topics Apsis · Celestial coordinate system · Epoch · Ephemeris · Equatorial coordinate system · Ground track · Interplanetary Transport Network · Kepler's laws of planetary motion · Lagrangian point · Low energy transfers · n-body problem · Orbit equation · Orbital speed · Orbital state vectors · Perturbation · Retrograde and direct motion · Specific orbital energy · Specific relative angular momentum List of orbits