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A circular orbit is depicted in the top-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy remains constant throughout the constant speed circular orbit.
The mean anomaly at epoch, M 0, is defined as the instantaneous mean anomaly at a given epoch, t 0. This value is sometimes provided with other orbital elements to enable calculations of the object's past and future positions along the orbit. The epoch for which M 0 is defined is often determined by convention in a given field or discipline.
The important special case of circular orbit, ε = 0, gives θ = E = M. Because the uniform circular motion was considered to be normal, a deviation from this motion was considered an anomaly. The proof of this procedure is shown below.
Argument of periapsis (ω) defines the orientation of the ellipse in the orbital plane, as an angle measured from the ascending node to the periapsis (the closest point the satellite body comes to the primary body around which it orbits), the purple angle ω in the diagram. True anomaly (ν, θ, or f) at epoch (t 0) defines the position of the ...
In the case of circular orbits it is often assumed that the periapsis is placed at the ascending node and therefore ω = 0. However, in the professional exoplanet community, ω = 90° is more often assumed for circular orbits, which has the advantage that the time of a planet's inferior conjunction (which would be the time the planet would ...
Circular orbits, having no eccentricity, give no means by which to orient the coordinate system about the focus. [5] The perifocal coordinate system may also be used as an inertial frame of reference because the axes do not rotate relative to the fixed stars. This allows the inertia of any orbital bodies within this frame of reference to be ...
An orbiting body's mean longitude is calculated L = Ω + ω + M, where Ω is the longitude of the ascending node, ω is the argument of the pericenter and M is the mean anomaly, the body's angular distance from the pericenter as if it moved with constant speed rather than with the variable speed of an elliptical orbit.
The following are some of the more common ones. A synchronous orbit around Earth that is circular and lies in the equatorial plane is called a geostationary orbit. The more general case, when the orbit is inclined to Earth's equator or is non-circular is called a geosynchronous orbit.