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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. There are two cases: the bodies move away from each other or towards each other. There is a rather simple expression for the position as function of time:
The trajectory then generalizes (without air resistance) from a parabola to a Kepler-ellipse with one focus at the center of the Earth (shown in fig. 3). The projectile motion then follows Kepler's laws of planetary motion. The trajectory's parameters have to be adapted from the values of a uniform gravity field stated above.
A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously. The mass might be a projectile or a ...
The following image illustrates a circle (grey), an ellipse (red), a parabola (green) and a hyperbola (blue) A diagram of the various forms of the Kepler Orbit and their eccentricities. Blue is a hyperbolic trajectory (e > 1). Green is a parabolic trajectory (e = 1). Red is an elliptical orbit (0 < e < 1). Grey is a circular orbit (e = 0).
In astrodynamics, an orbit equation defines the path of orbiting body around central body relative to , without specifying position as a function of time.Under standard assumptions, a body moving under the influence of a force, directed to a central body, with a magnitude inversely proportional to the square of the distance (such as gravity), has an orbit that is a conic section (i.e. circular ...
Radial parabolic trajectory, a non-periodic orbit where the relative speed of the two objects is always equal to the escape velocity. There are two cases: the bodies move away from each other or towards each other. Radial hyperbolic trajectory: a non-periodic orbit where the relative speed of the two objects always exceeds the escape velocity ...
This can be shown to result in the trajectory being ideally a conic section (circle, ellipse, parabola or hyperbola) [10] with the central body located at one focus. Orbital trajectories are either circles or ellipses; the parabolic trajectory represents first escape of the vehicle from the central body's gravitational field.
a parabolic trajectory, a trajectory that goes back and forth along a line segment from the centre of attraction to a point at some distance away, a trajectory going in or out along an infinite ray emanating from the centre of attraction, with its speed going to zero with distance