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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 ...
A radial trajectory can be a double line segment, which is a degenerate ellipse with semi-minor axis = 0 and eccentricity = 1. Although the eccentricity is 1, this is not a parabolic orbit. Most properties and formulas of elliptic orbits apply. However, the orbit cannot be closed.
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).
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.
Circular and elliptical orbits are closed. Parabolic and hyperbolic orbits are open. Radial orbits can be either open or closed. Circular orbit: An orbit that has an eccentricity of 0 and whose path traces a circle. Elliptic orbit: An orbit with an eccentricity greater than 0 and less than 1 whose orbit traces the path of an ellipse.
Keeping the energy constant and reducing the angular momentum, elliptic, parabolic, and hyperbolic orbits each tend to the corresponding type of radial trajectory while e tends to 1 (or in the parabolic case, remains 1). For a repulsive force only the hyperbolic trajectory, including the radial version, is applicable.
Furthermore, the equation was derived on the assumption of an elliptical orbit, and so it does not hold for parabolic or hyperbolic orbits. These difficulties are what led to the development of the universal variable formulation , described below.
An animation showing a low eccentricity orbit (near-circle, in red), and a high eccentricity orbit (ellipse, in purple). In celestial mechanics, an orbit (also known as orbital revolution) is the curved trajectory of an object [1] such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such ...