# Elliptic orbit

A small body in space orbits a large one (like a planet around the sun) along an elliptical path, with the large body being located at one of the ellipse foci.
Two bodies with similar mass orbiting around a common barycenter with elliptic orbits.
An elliptical orbit is depicted in the top-right 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 decreases as the orbiting body's speed decreases and distance increases according to Kepler's laws.

In astrodynamics or celestial mechanics, an elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0. In a stricter sense, it is a Kepler orbit with the eccentricity greater than 0 and less than 1 (thus excluding the circular orbit). In a wider sense, it is a Kepler orbit with negative energy. This includes the radial elliptic orbit, with eccentricity equal to 1.

In a gravitational two-body problem with negative energy, both bodies follow similar elliptic orbits with the same orbital period around their common barycenter. Also the relative position of one body with respect to the other follows an elliptic orbit.

Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit, and tundra orbit.

## Velocity

Under standard assumptions the orbital speed (${\displaystyle v\,}$) of a body traveling along an elliptic orbit can be computed from the vis-viva equation as:

${\displaystyle v={\sqrt {\mu \left({2 \over {r}}-{1 \over {a}}\right)}}}$

where:

• ${\displaystyle \mu \,}$ is the standard gravitational parameter,
• ${\displaystyle r\,}$ is the distance between the orbiting bodies.
• ${\displaystyle a\,\!}$ is the length of the semi-major axis.

The velocity equation for a hyperbolic trajectory has either + ${\displaystyle {1 \over {a}}}$, or it is the same with the convention that in that case a is negative.

Other Languages
العربية: مدار إهليجي
فارسی: مدار بیضی
한국어: 타원 궤도
Bahasa Melayu: Orbit eliptik

português: Órbita elíptica
slovenčina: Eliptická dráha
українська: Еліптична орбіта