In astrodynamics or celestial mechanics a parabolic trajectory is a Kepler orbit with the eccentricity (e) equal to 1 and is an unbound orbit that is exactly on the border between elliptical and hyperbolic. When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a ${\displaystyle C_{3}=0}$ orbit (see Characteristic energy).

Under standard assumptions a body traveling along an escape orbit will coast along a parabolic trajectory to infinity, with velocity relative to the central body tending to zero, and therefore will never return. Parabolic trajectories are minimum-energy escape trajectories, separating positive-energy hyperbolic trajectories from negative-energy elliptic orbits.

In 1609, Galileo wrote in his 102nd folio (MS. Gal 72) about parabolic trajectory calculations, later found in Discorsi e dimostrazioni matematiche intorno a due nuove scienze as projectiles impetus.

The orbital velocity (${\displaystyle v}$) of a body travelling along a parabolic trajectory can be computed as:

where:

At any position the orbiting body has the escape velocity for that position.

If a body has an escape velocity with respect to the Earth, this is not enough to escape the Solar System, so near the Earth the orbit resembles a parabola, but further away it bends into an elliptical orbit around the Sun.

This velocity (${\displaystyle v}$) is closely related to the orbital velocity of a body in a circular orbit of the radius equal to the radial position of orbiting body on the parabolic trajectory: