Characteristic energyIn astrodynamics, the characteristic energy () is a measure of the excess specific energy over that required to just barely escape from a massive body. The units are length2 time−2, i.e. velocity squared, or energy per mass. Every object in a 2-body ballistic trajectory has a constant specific orbital energy equal to the sum of its specific kinetic and specific potential energy: where is the standard gravitational parameter of the massive body with mass , and is the radial distance from its center.
Elliptic orbitIn 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.
Circular orbitA circular orbit is an orbit with a fixed distance around the barycenter; that is, in the shape of a circle. In this case, not only the distance, but also the speed, angular speed, potential and kinetic energy are constant. There is no periapsis or apoapsis. This orbit has no radial version. Listed below is a circular orbit in astrodynamics or celestial mechanics under standard assumptions. Here the centripetal force is the gravitational force, and the axis mentioned above is the line through the center of the central mass perpendicular to the orbital plane.
Specific angular momentumIn celestial mechanics, the specific relative angular momentum (often denoted or ) of a body is the angular momentum of that body divided by its mass. In the case of two orbiting bodies it is the vector product of their relative position and relative linear momentum, divided by the mass of the body in question. Specific relative angular momentum plays a pivotal role in the analysis of the two-body problem, as it remains constant for a given orbit under ideal conditions. "Specific" in this context indicates angular momentum per unit mass.
Specific orbital energyIn the gravitational two-body problem, the specific orbital energy (or vis-viva energy) of two orbiting bodies is the constant sum of their mutual potential energy () and their total kinetic energy (), divided by the reduced mass. According to the orbital energy conservation equation (also referred to as vis-viva equation), it does not vary with time: where is the relative orbital speed; is the orbital distance between the bodies; is the sum of the standard gravitational parameters of the bodies; is the specific relative angular momentum in the sense of relative angular momentum divided by the reduced mass; is the orbital eccentricity; is the semi-major axis.
