Highly elliptical orbit

A highly elliptical orbit (HEO) is an elliptic orbit with a low-altitude (often under 1,000 kilometres (540 nmi)) perigee and a high-altitude (often over 35,786 kilometres (19,323 nmi)) apogee. The 'highly elliptical' term refers to the shape of the ellipse, and to the eccentricity of the orbit, not to the high apogee altitude.

Such extremely elongated orbits have the advantage of long dwell times at a point in the sky during the approach to, and descent from, apogee. Visibility near apogee can exceed twelve hours of dwell at apogee with a much shorter and faster-moving perigee phase. Bodies moving through the long apogee dwell can appear still in the sky to the ground when the orbit is at the right inclination, where the angular velocity of the orbit in the equatorial plane closely matches the rotation of the surface beneath. This makes these elliptical orbits useful for communications satellites.

Sirius Satellite Radio uses HEO orbits to keep two satellites positioned above North America while another satellite quickly sweeps through the southern part of its 24-hour orbit. The longitude above which the satellites dwell at apogee in the small loop remains relatively constant as the earth rotates. The three separate orbits are spaced equally around the Earth, but share a common ground track.

Elliptic 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.

Velocity

Under standard assumptions the orbital speed () of a body traveling along an elliptic orbit can be computed from the Vis-viva equation as:

where:

is the standard gravitational parameter,