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The classical method of finding the position of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly. Define ϖ as the longitude of the pericenter, the angular
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.
Define the angular distance along the plane of the orbit from the ascending node to the pericenter as the argument of the pericenter, ω. Define the mean anomaly, M, as the angular distance from the pericenter which the body would have if it moved in a circular orbit, in the same orbital period as the actual body in its elliptical orbit.
The mean anomaly changes linearly with time, scaled by the mean motion, [2] =. where μ is the standard gravitational parameter. Hence if at any instant t 0 the orbital parameters are (e 0, a 0, i 0, Ω 0, ω 0, M 0), then the elements at time t = t 0 + δt is given by (e 0, a 0, i 0, Ω 0, ω 0, M 0 + n δt).
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.
In orbital mechanics, mean motion (represented by n) is the angular speed required for a body to complete one orbit, assuming constant speed in a circular orbit which completes in the same time as the variable speed, elliptical orbit of the actual body. [1]
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.
In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit , values between 0 and 1 form an elliptic orbit , 1 is a parabolic escape orbit (or capture orbit), and greater than ...