Where does orbit collide?

In astronomy and celestial mechanics, an orbit is the gravitationally curved path that one body follows around another, such as a planet around the Sun or a moon around a planet. Under Newton's law of gravitation a bound orbit is a closed conic, an ellipse with the central body at one focus, and its shape and orientation are captured by a small set of orbital elements. Murray and Dermott's Solar system dynamics sets out how these paths are derived and how they are perturbed. The referent is a trajectory traced through space over time, not a socket in the skull, an electron's energy state, or a set of points under a group action.[1]

Unit

A body's closed path around another, described by its orbital elements such as period, semi-major axis, and eccentricity

Recovery means

A bound orbit is periodic: the body returns to the same position relative to the central mass once each period

Measured by

Reconstructed by fitting astrometric positions, or radial-velocity and timing data, to the six Keplerian orbital elements

In the early physics of the atom, an orbit is the path an electron was pictured as following around the nucleus, held in one of a set of allowed circular tracks, each with a fixed energy. Bohr's 1913 On the constitution of atoms and molecules proposed these stationary states to explain why atoms emit and absorb light only at sharp, discrete wavelengths. Later quantum mechanics replaced the definite path with the orbital, a region where the electron is merely likely to be found, so the word survives while the picture behind it has changed. The referent is an electron's energy state in an atom, not a planet's trajectory, a bony socket, or a set under a group action.[2]

Unit

An electron's stationary state in an atom, indexed by a quantum number and its energy

Recovery means

Not applicable

Measured by

Inferred from the discrete wavelengths an atom emits or absorbs as its electrons change states

In mathematics, an orbit is the set of all points that can be reached from a given starting point by applying the elements of a group that acts on a set, or, in a dynamical system, the sequence of points a state passes through as a map or flow is iterated. For a group action, the orbit of a point is everything the group can move it to, and the whole set breaks into disjoint orbits. Dummit and Foote's Abstract algebra defines orbits and relates their size to stabilisers through the orbit-stabiliser theorem. The referent is a set of points closed under a transformation, not a body's path in space, an electron's state, or a socket in the skull.[3]

Unit

A subset of a set, the collection of images of one point under the acting group

Recovery means

Not applicable

Measured by

Found by applying every group element to the point; its size follows from the orbit-stabiliser theorem