To completely describe an orbit mathematically, six quantities must be calculated. These quantities are called orbital elements, or Keplerian elements. They are: Semi-major axis (1) and eccentricity (2), which are the basic measurements of the size and shape of the orbit's ellipse . Recall an eccentricity of zero indicates a circular orbit). The orbit's inclination (3) is the angular distance of the orbital plane from the plane of the planet's equator (or from the ecliptic plane, if you're talking about heliocentric orbits), stated in degrees: an inclination of 0 degree. means the spacecraft orbits the planet at its equator, and in the same direction as the planet rotates. An inclination of 90 degrees indicates a polar orbit, in which the spacecraft passes over the north and south poles of the planet. An inclination of 180 degrees indicates an equatorial orbit in which the spacecraft moves in a direction opposite the planet's rotation (retrograde). The argument of periapsis (4) is the argument (angular distance) of periapsis from the ascending node. Time of periapsis passage (5) and the celestial longitude of the ascending node (6) are the remaining elements. Generally, three astronomical or radiometric observations of an object in an orbit are enough to pin down each of the above six Keplerian elements.

Types of Orbits

Geosynchronous Orbits

A geosychronous orbit (GEO) is a direct, circular, low inclination orbit about Earth having a period of 23 hours 56 minutes 4 seconds . A spacecraft in geosynchronous orbit maintains a position above Earth constant in longitude. Normally, the orbit is chosen and station keeping procedures are implemented, to constrain the spacecraft's apparent position so that it hangs motionless above a point on Earth. In this case, the orbit may be called geostationary. For this reason this orbit is ideal for certain kinds of communication satellites, or meteorological satellites. To attain geosynchronous orbit, a spacecraft is first launched into an elliptical orbit with an apoapsis altitude in the neighborhood of 37,000 km. This is called a Geosynchronous Transfer Orbit (GTO). It is then circularized by turning parallel to the equator and firing its rocket engines at apoapsis.

Polar Orbits

Polar orbits are 90 degrees inclination orbits, useful for spacecraft that carry out mapping or surveillance operations. Since the orbital plane is, nominally, fixed in inertial space, the planet rotates below a polar orbit, allowing the spacecraft low-altitude access to virtually every point on the surface. The Magellan spacecraft used a nearly-polar orbit at Venus. Each periapsis pass, a swath of mapping data was taken, and the planet rotated so that swaths from consecutive orbits were adjacent to each other. When the planet rotated once, all 360 degrees longitude had been exposed to Magellan's surveillance.

To achieve a polar orbit at Earth requires more energy, thus more propellant, than does a direct orbit of low inclination. To achieve the latter, launch is normally accomplished near the equator, where the rotational speed of the surface contributes a significant part of the final speed required for orbit. A polar orbit will not be able to take advantage of the "free ride" provided by Earth's rotation, and thus the launch vehicle must provide all of the energy for attaining orbital speed.

Walking Orbits

Planets are not perfectly spherical, and they do not have evenly distributed mass. Also, they do not exist in a gravity "vacuum"--other bodies such as the sun, or satellites, contribute their gravitational influences to a spacecraft in orbit about a planet. It is possible to choose the parameters of a spacecraft's orbit to take advantage of some or all of these gravitational influences to induce precession, which causes a useful motion of the orbital plane. The result is called a walking orbit or a precessing orbit, since the orbital plane moves slowly with respect to fixed inertial space.

Sun Synchronous Orbits

A walking orbit whose parameters are chosen such that the orbital plane precesses with nearly the same period as the planet's solar orbit period is called a sun synchronous orbit. In such an orbit, the spacecraft crosses periapsis at about the same local time every orbit. This can be useful if instruments on board depend on a certain angle of solar illumination on the surface. Mars Global Surveyor's intended orbit at Mars is a 2-pm Mars local time sun-synchronous orbit. It may not be possible to rely on use of the gravity field alone to exactly maintain a desired synchronous timing, and occasional propulsive maneuvers may be necessary to adjust the orbit.