Orbit Definition and Explication:

1. An orbit in general is just a trajectory of an astro-body (including spacecraft) relative to an inertial frame (usually a center-of-mass inertial frame which recall does NOT rotate with respect to the observable universe) under the gravitational force aside from small astrophysical perturbations NOT due to gravity.

   Note an orbit is an accelerated motion by Newton's 2nd law of motion (AKA F=ma) since the gravitational force is a NET EXTERNAL on the astro-body.

2. However, when we say a first astro-body orbits a second astro-body, we usually mean is that the first astro-body goes around the center of mass of the system of astro-bodies to which the two astro-bodies belong and that the second astro-body is close to the center of mass and the "going around" is an angular motion relative to the observable universe.

3. If you have a completely isolated gravitationally bound 2-body system, then Newtonian physics dictates that the 2 astro-bodies will perpetually orbit their mutual center of mass in exact elliptical orbits.

   General relativity dictates some correction to the Newtonian physics behavior. The 2-body system will slowly lose kinetic energy due to energy carried away by gravitational waves and will inspiral to coalescence. In fact, the loss of kinetic energy due to gravitational waves is general to all gravitationally-bound systems. However, the loss is usually extremely slow, and so can be neglected in doing ordinary celestial mechanics.

   There are fast cases of inspiralling. The observed gravitational wave events are among those cases and the only ones observed so far.

4. More generally, in a gravitationally-bound system of 2 or more of astro-bodies, the astro-bodies orbit the center of mass of the gravitationally-bound system in a more or less complicated way. Such a gravitationally-bound system constitutes a center-of-mass inertial frame for analyzing the motions of the astro-bodies. The INTERNAL motions are those relative to the center of mass. The center of mass motion is determined ONLY by the NET EXTERNAL force on the gravitationally-bound system which is usually overwhelmingly the NET EXTERNAL gravitational force. In absolute generality, the EXTERNAL gravitational force due all of the observable universe outside of the center of mass must be considered. However, usually you only need to account for EXTERNAL gravitational forces of relatively nearby sources of gravity in order understand motions relative to those relatively nearby sources of gravity.

5. There are some highly complex orbits with special names: e.g., co-orbital configuration orbits, horseshoe orbits, Kozai mechanism orbits, and Lissajous orbits.

1. The above definition is for what we ordinarily mean by orbit (i.e., orbit unqualified) as opposed to what is called a "geometrical orbit" which is just a rotation around any point taken as an observation point.

2. For example, the Earth orbits the Sun in an unqualified sense, but from the Earth's perspective the Sun "geometrically orbits" the Earth. Now the geometrical "orbit" of the Sun is relative to the observable universe, but the Earth is NOT near the center of mass of the Earth-Sun system: the Sun is.

3. For another example, consider the Pluto-moon system (overwhelmingly dominated in mass by Pluto and its major moon Charon). Exactly speaking, Pluto and Charon orbit the Pluto-moon system center of mass (which is very close to Pluto, but not inside it) or, much less exactly speaking, Charon orbits Pluto. However, clearly Pluto only geometrically "orbits" Charon since Charon is relatively far from the Pluto-moon system center of mass.