Escape orbit

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An escape orbit (also known as C3 = 0 orbit) is a high-energy parabolic orbit around the central body. A body in this orbit has at each position the escape velocity with respect to this central body, for this position. If this energy were further increased the orbit would turn to a hyperbolic trajectory.

Position as function of time

Finding the position as function of time corresponds to solving a differential equation. In the theoretical case of a straight escape trajectory there is a rather simple expression for the solution:

where

• μ is the standard gravitational parameter
• corresponds to the extrapolated time of the fictitious starting at the center of the central body.

At any time the average speed from is 1.5 times the current speed, i.e. 1.5 times the local escape velocity.

To have at the surface, apply a time shift; for the Earth (and any other spherically symmetric body with the same average density) as central body this time shift is 6 minutes and 20 seconds; seven of these periods later the height above the surface is three times the radius, etc.

See also

• Capture orbit
• List of orbits

v • d • e Orbits   Types General Box · Capture · Circular · Elliptical / Highly elliptical · Escape · Graveyard · Hyperbolic trajectory · Inclined / Non-inclined · Osculating · Parabolic trajectory · Parking · Synchronous (semi · sub) Geocentric Geosynchronous · Geostationary · Sun-synchronous · Low Earth · Medium Earth · Molniya · Near-equatorial · Orbit of the Moon · Polar · Tundra · Two-line elements Other Areosynchronous · Areostationary · Halo · Lissajous · Lunar · Heliocentric · Heliosynchronous   Parameters Classical  Inclination ·  Longitude of the ascending node ·  Eccentricity ·  Argument of periapsis ·  Semi-major axis ·  Mean anomaly at epoch Other  True anomaly ·  Semi-minor axis ·  Linear eccentricity ·  Eccentric anomaly ·  Mean longitude ·  True longitude ·  Orbital period   Maneuvers Bi-elliptic transfer · Delta-v budget · Geostationary transfer · Gravity assist · Gravity turn · Hohmann transfer · Oberth effect  · Inclination change · Phasing · Rendezvous · Transposition, docking, and extraction   Other orbital mechanics topics Apsis · Celestial coordinate system · Epoch · Ephemeris · Equatorial coordinate system · Ground track · Interplanetary Transport Network · Kepler's laws of planetary motion · Lagrangian point · Low energy transfers · n-body problem · Orbit equation · Orbital speed · Orbital state vectors · Perturbation · Retrograde and direct motion · Specific orbital energy · Specific relative angular momentum List of orbits

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