Hyperbolic trajectory

A hyperbolic trajectory is an unbound path around a gravitating body, with positive orbital energy and eccentricity greater than one. The object approaches and recedes without being captured.

Vis-viva equation: An equation relating orbital speed, distance from a central body, and the orbit’s semimajor axis. It calculates speed along a hyperbolic path when the semimajor axis is negative.
Gravity assist: A spacecraft maneuver that changes heliocentric velocity by passing near a moving celestial body. A flyby follows a hyperbolic path relative to the body and can redirect spacecraft.
Elliptic orbit: A bound orbital path shaped like an ellipse, with eccentricity below one. Unlike a hyperbolic trajectory, it returns repeatedly rather than escaping.
ʻOumuamua: An interstellar object discovered passing through the Solar System in 2017. Its strongly hyperbolic solar trajectory established that it was not bound to the Sun.
Specific orbital energy: The total mechanical energy of an orbiting object per unit mass. Positive specific energy distinguishes an unbound hyperbolic path from a bound orbit.
Escape velocity: The minimum launch speed needed to escape a body's gravity without further propulsion, under idealized conditions. Exceeding local escape speed produces an unbound trajectory.
Parabolic trajectory: The limiting unbound conic orbit with eccentricity exactly one and zero specific orbital energy. It separates bound ellipses from positive-energy hyperbolic paths.
2I/Borisov: An interstellar comet discovered in 2019, the second confirmed interstellar object detected passing through the Solar System. Its hyperbolic orbit revealed an extrasolar origin.
Eccentricity (orbit): A dimensionless measure of how much an orbit deviates from a circle. Values greater than one identify hyperbolic conic sections.
Interstellar object: An astronomical object whose trajectory through the Solar System indicates an origin outside it. Its solar-system passage is hyperbolic because it is not gravitationally bound to the Sun.

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