Parabolic trajectory

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.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.) of a parabolic trajectory is zero, so the orbital energy conservation equation for this trajectory takes the form: where: This is entirely equivalent to the characteristic energy (square of the speed at infinity) being 0: Barker's equation relates the time of flightof a parabolic trajectory:[1] where: More generally, the time (epoch) between any two points on an orbit is Alternately, the equation can be expressed in terms of periapsis distance, in a parabolic orbit: Unlike Kepler's equation, which is used to solve for true anomalies in elliptical and hyperbolic trajectories, the true anomaly in Barker's equation can be solved directly forIf the following substitutions are made then With hyperbolic functions the solution can be also expressed as:[2] where A radial parabolic trajectory is a non-periodic trajectory on a straight line where the relative velocity of the two objects is always the escape velocity.
The green path in this image is an example of a parabolic trajectory.
A parabolic trajectory is depicted in the bottom-left quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the parabolic trajectory is shown in red. The height of the kinetic energy decreases asymptotically toward zero as the speed decreases and distance increases according to Kepler's laws.
Projectile Motiongravitational potential wellOrbital mechanicsOrbital elementsArgument of periapsisEccentricityInclinationMean anomalyOrbital nodesSemi-major axisTrue anomalytwo-body orbitsCircular orbitElliptic orbitTransfer orbitHohmann transfer orbitBi-elliptic transfer orbitHyperbolic orbitRadial orbitDecaying orbitDynamical frictionEscape velocityKepler's equationKepler's laws of planetary motionOrbital periodOrbital velocitySurface gravitySpecific orbital energyVis-viva equationCelestial mechanicsBarycenterHill spherePerturbationsSphere of influenceN-body orbitsLagrangian pointsHalo orbitsLissajous orbitsLyapunov orbitsEngineering and efficiencyMass ratioPayload fractionPropellant mass fractionTsiolkovsky rocket equationGravity assistOberth effectOrbital maneuverOrbit insertionastrodynamicsKepler orbitCharacteristic energyparaboliccentral bodyenergyhyperbolic trajectorieselliptic orbitsstandard gravitational parametertrajectoryorbital equationspecific angular momentumorbiting bodyorbital energy conservation equationtrajectory on a straight lineParabolaBibcodeorbitsCircularEllipticalHighly ellipticalHorseshoeHyperbolic trajectoryInclinedNon-inclinedKeplerLagrange pointOsculatingParkingPrograde / RetrogradeSynchronousGeocentricGeosynchronousGeostationaryGeostationary transferGraveyardHigh EarthLow EarthMedium EarthMolniyaNear-equatorialOrbit of the MoonSun-synchronousTransatmosphericTundraVery low EarthAreocentricAreosynchronousAreostationaryDistant retrogradeLissajousLibrationHeliocentricEarth's orbitMars cyclerHeliosynchronousLunar cyclerParametersSemi-minor axisApsidesLongitude of the ascending nodeLongitude of the periapsisEccentric anomalyMean longitudeTrue longitudeMean motionOrbital speedManeuversBi-elliptic transferCollision avoidance (spacecraft)Delta-vDelta-v budgetGravity turnHohmann transferInclination changeLow-energy transferPhasingRocket equationRendezvousTrans-lunar injectionTransposition, docking, and extractionOrbitalmechanicsAstronomical coordinate systemsEphemerisEquatorial coordinate systemGround trackInterplanetary Transport NetworkKozai mechanismLagrangian pointn-body problemOrbit equationOrbital state vectorsPerturbationRetrograde and prograde motionTwo-line elementsList of orbits