# Orbit Equation

## Description

In astrodynamics an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time. Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular orbit, elliptic orbit, parabolic trajectory, hyperbolic trajectory, or radial trajectory) with the central body located at one of the two foci, or the focus (Kepler’s first law).

Consider a two-body system consisting of a central body of mass M and a much smaller, orbiting body of mass m, and suppose the two bodies interact via a central, inverse-square law force (such as gravitation). In polar coordinates, the orbit equation can be written as shown.

## Variables

r | separation distance between the two bodies (m) |

l | angular momentum of the orbiting body about the central body (kg*m^{2}/s) |

m | orbiting body mass (kg) |

γ | for gravitation,it is the standard gravitational parameter (m^{3}/s^{2}) |

e | eccentricity of the orbit (dimensionless) |

θ | angle that separation distance makes with the axis of periapsis (also called the true anomaly) (deg) |