Elliptical Orbit

In astrodynamics or celestial mechanics an elliptic orbit is a Kepler orbit with the eccentricity less than 1; this includes the special case of a circular orbit, with eccentricity equal to zero. 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.

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:

where:

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.

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