Search results
Results from the WOW.Com Content Network
In celestial mechanics, true anomaly is an angular parameter that defines the position of a body moving along a Keplerian orbit.It is the angle between the direction of periapsis and the current position of the body, as seen from the main focus of the ellipse (the point around which the object orbits).
is the true anomaly of the orbiting body, is the standard gravitational parameter. As the true anomaly θ approaches 180°, the denominator approaches zero, so that r tends towards infinity. Hence, the energy of the trajectory for which e=1 is zero, and is given by:
Shown are mean anomaly and true anomaly for two units of time. (Note that for visual simplicity, a non-overlapping circular orbit is diagrammed, thus this circular orbit with same orbital period is not shown in true scale with this elliptical orbit: for scale to be true for the two orbits of equal period, these orbits must intersect.)
The angle between the direction of periapsis and an asymptote from the central body is the true anomaly as distance tends to infinity (), so is the external angle between approach and departure directions (between asymptotes). Then
The green path in this image is an example of a parabolic trajectory. A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red.
True anomaly defines the position of the orbiting body along the trajectory, measured from periapsis. Several alternate values can be used instead of true anomaly, the most common being M {\displaystyle M} the mean anomaly and T {\displaystyle T} , the time since periapsis.
Because it increases uniformly with time, expressing any other variable as a series in mean anomaly is essentially the same as expressing it in terms of time. Although the true anomaly is an analytic function of M, it is not an entire function so a power series in M will have a limited range of convergence.
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.