Specific orbital energy

Specific orbital energy is the sum of an orbiting body's kinetic and gravitational potential energy per unit mass. In a two-body gravitational system, it is constant along the orbit and determines the orbit's size.

Vis-viva equation: An equation relating orbital speed, distance from the central body, and the orbit's semimajor axis. It calculates speed at a given distance from the same orbital energy that sets the orbit's size.
Newton's law of universal gravitation: The law stating that two masses attract with a force proportional to their product and inversely proportional to distance squared. It supplies the central force assumed in the standard orbital-energy relation.
Orbital transfer: A maneuver or sequence of maneuvers that changes a spacecraft from one orbit to another. A transfer changes the spacecraft's orbital energy to reach a new orbit size.
Orbital angular momentum: The rotational momentum of an orbiting system about a chosen center, conserved in a central force field. Unlike energy, angular momentum chiefly constrains orbital orientation and shape rather than size alone.
Gravitational potential energy: Energy associated with the gravitational interaction between masses, defined relative to a chosen zero point. Its inverse-distance term supplies the potential part of specific orbital energy.
Two-body problem: The problem of predicting the motion of two objects interacting only through their mutual gravitational attraction. The familiar constant-energy formula follows from this idealized system.
Hohmann transfer orbit: An elliptical transfer orbit connecting two coplanar circular orbits using two impulsive velocity changes. Its two burns alter specific energy to move between circular orbit sizes.
Specific orbital energy in the restricted three-body problem: The Jacobi constant is a conserved quantity in the rotating-frame circular restricted three-body problem. In a three-body setting, this replaces simple two-body energy as the useful integral of motion.
Kinetic energy: Energy associated with the motion of an object, equal to one-half its mass times speed squared in classical mechanics. Orbital speed supplies the other term in the specific-energy sum.
Keplerian orbit: An ideal orbit following the conic-section solutions of two-body motion under Newtonian gravity. Its conic shape and size are classified by specific orbital energy.

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