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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.
Thus mean anomaly is also [6] = . Mean angular motion can also be expressed, = , where μ is the gravitational parameter, which varies with the masses of the objects, and a is the semi-major axis of the orbit. Mean anomaly can then be expanded, = , and here mean anomaly represents uniform angular motion on a circle of radius a. [7]
Instead of the mean anomaly at epoch, the mean anomaly M, mean longitude, true anomaly ν 0, or (rarely) the eccentric anomaly might be used. Using, for example, the "mean anomaly" instead of "mean anomaly at epoch" means that time t must be specified as a seventh orbital element. Sometimes it is assumed that mean anomaly is zero at the epoch ...
mean anomaly (M) The fraction of an elliptical orbit 's period that has elapsed since the orbiting body passed periapsis, expressed as the angular distance from the pericenter which a fictitious body would have if it moved in a perfectly circular orbit in the same orbital period as the actual body in its
Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets.
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.
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 ...
The true anomaly is usually denoted by the Greek letters ν or θ, or the Latin letter f, and is usually restricted to the range 0–360° (0–2π rad). The true anomaly f is one of three angular parameters (anomalies) that defines a position along an orbit, the other two being the eccentric anomaly and the mean anomaly.