Apastron

Apastron is the farthest point in an object's orbit around another body. In the context of celestial mechanics, it refers to the location where the two bodies are most distant from each other during a bound, elliptical orbit, though the term is sometimes used more generally for orbits around any central mass.

In an elliptical orbit with semi-major axis a and eccentricity e, the closest approach is periapsis at distance r_p = a(1 - e), and the farthest point is apastron at distance r_a = a(1 + e). The velocity of the orbiting body is lowest at apastron and highest at periapsis, a consequence of conservation of angular momentum and Kepler's laws. The vis-viva equation can be used to compute speed at any distance: v^2 = μ(2/r − 1/a), where μ is the standard gravitational parameter.

Terminology varies with the central body. The general terms periapsis and apoapsis describe closest and farthest points in any two-body orbit, while the specific forms perihelion/aphelion and perigee/apogee refer to orbits around the Sun or Earth, respectively. Apastron is commonly used for star or binary-star systems or more generic references, whereas apogee or aphelion are used when the central body is Earth or the Sun.

Not all orbits have a well-defined apastron. In unbound orbits (parabolic or hyperbolic), the separation does not remain finite; for hyperbolic trajectories, the distance increases without bound and an apastron is not defined. For elliptical orbits, apastron marks the maximum separation within the orbital cycle. An example is Earth's orbit around the Sun, where the aphelion occurs around early July.

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