- Parabolic trajectory
In

astrodynamics orcelestial mechanics ais aparabolic trajectoryKepler orbit with the eccentricity equal to 1. When moving away from the source it is called anescape orbit , otherwise acapture orbit .Under standard assumptions a body traveling along an escape orbit will coast to infinity, with velocity relative to the

central body tending to zero, and therefore will never return. Parabolic trajectory is a minimum-energy escape trajectory.**Velocity**Under standard assumptions the

orbital velocity ($v,$) of a body traveling along parabolic trajectory can be computed as::$v=sqrt\{2muover\{r$where:

*$r,!$ is radial distance of orbiting body fromcentral body ,

*$mu,!$ isstandard gravitational parameter .At any position the orbiting body has the

escape velocity for that position.If the body has the 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 ($v,$) is closely related to the

orbital velocity of a body in acircular orbit of the radius equal to the radial position of orbiting body on the parabolic trajectory::$v=sqrt\{2\}cdot\; v\_O$where:

*$v\_O,!$ isorbital velocity of a body incircular orbit .**Equation of motion**Under standard assumptions, for a body moving along this kind of trajectory an

orbital equation becomes::$r=$h^2}over{mu1}over{1+cos uwhere:

*$r,$ is radial distance of orbiting body fromcentral body ,

*$h,$ isspecific angular momentum of theorbiting body ,

*$u,$ is atrue anomaly of the orbiting body,

*$mu,$ isstandard gravitational parameter .**Energy**Under standard assumptions,

specific orbital energy ($epsilon,$) of parabolic trajectory is zero, so theorbital energy conservation equation for this trajectory takes form::$epsilon=\{v^2over2\}-\{muover\{r=0$where:

*$v,$ isorbital velocity of orbiting body,

*$r,$ is radial distance of orbiting body fromcentral body ,

*$mu,$ isstandard gravitational parameter .**ee also***

Hyperbolic trajectory

*Orbit

*Circular orbit

*Elliptic orbit

*Orbital equation

*List of orbits

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

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