In astrodynamics or celestial mechanics a elliptic orbit is an orbit with the eccentricity greater than 0 and less than 1.

Specific energy of an elliptical orbit is negative. An orbit with an eccentricity of 0 is a circular orbit. Examples of elliptic orbits include: Hohmann transfer orbit, Molniya orbit and tundra orbit.


Under standard assumptions the orbital velocity ($ v\, $) of a body traveling along elliptic orbit can be computed as:

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



  • Velocity does not depend on eccentricity but is determined by length of semi-major axis ($ a\,\! $),
  • Velocity equation is similar to that for hyperbolic trajectory with the difference that for the latter, $ {1\over{2a}} $ is positive.

Orbital period

Under standard assumptions the orbital period ($ T\,\! $) of a body traveling along elliptic orbit can be computed as:

$ T={2\pi\over{\sqrt{\mu}}}a^{3\over{2}} $




Under standard assumptions, specific orbital energy ($ \epsilon\, $) of elliptic orbit is negative and the orbital energy conservation equation for this orbit takes form:

$ {v^2\over{2}}-{\mu\over{r}}=-{\mu\over{2a}}=\epsilon<0 $



Using the virial theorem we find:

  • the time-average of the specific potential energy is equal to 2ε
    • the time-average of r-1 is a-1
  • the time-average of the specific kinetic energy is equal to -ε

Flight path angle

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Equation of motion

See orbit equation.

Orbital parameters

An elliptic orbit has three degrees of freedom (three spatial dimensions). This means that an orbit, which is defined by the orbiting body's position and velocity, must be represented by at least the the three dimensional Cartesian coordinates (position of the orbiting body represented by x, y, and z) and the similar Cartesian components of the orbiting body's velocity. This set of six variables, together with time, are called the orbital state vectors. Because at least six variables are absolutely required to completely represent an orbit with this set of parameters, then six variables are required to represent an orbit with any set of parameters. Another set of six parameters that are commonly used are the orbital elements.

Solar system

In the solar system planets, asteroids, comets and space debris have elliptical orbits around the Sun.

Moons have an elliptic orbit around their planet.

Many artificial satellites have various elliptic orbits around the Earth.

See also

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