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An elliptic Kepler orbit with an eccentricity of 0.7, a parabolic Kepler orbit and a hyperbolic Kepler orbit with an eccentricity of 1.3. The distance to the focal point is a function of the polar angle relative to the horizontal line as given by the equation ( 13 )
The orbit inside a radial shaft in a uniform spherical body [3] would be a simple harmonic motion, because gravity inside such a body is proportional to the distance to the center. If the small body enters and/or exits the large body at its surface the orbit changes from or to one of those discussed above.
In gravitationally bound systems, the orbital speed of an astronomical body or object (e.g. planet, moon, artificial satellite, spacecraft, or star) is the speed at which it orbits around either the barycenter (the combined center of mass) or, if one body is much more massive than the other bodies of the system combined, its speed relative to the center of mass of the most massive body.
For instance, a small body in circular orbit 10.5 cm above the surface of a sphere of tungsten half a metre in radius would travel at slightly more than 1 mm/s, completing an orbit every hour. If the same sphere were made of lead the small body would need to orbit just 6.7 mm above the surface for sustaining the same orbital period.
Kepler's first law states that: The orbit of every planet is an ellipse with the sun at one of the two foci. Kepler's first law placing the Sun at one of the foci of an elliptical orbit Heliocentric coordinate system (r, θ) for ellipse.
In a two-body problem with inverse-square-law force, every orbit is a Kepler orbit. The eccentricity of this Kepler orbit is a non-negative number that defines its shape. The eccentricity may take the following values: Circular orbit: e = 0; Elliptic orbit: 0 < e < 1; Parabolic trajectory: e = 1; Hyperbolic trajectory: e > 1; The eccentricity e ...
When moving away from the source it is called an escape orbit, otherwise a capture orbit. It is also sometimes referred to as a C 3 = 0 orbit (see Characteristic energy ). 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 ...
In astrodynamics or celestial mechanics, a hyperbolic trajectory or hyperbolic orbit is the trajectory of any object around a central body with more than enough speed to escape the central object's gravitational pull. The name derives from the fact that according to Newtonian theory such an orbit has the shape of a hyperbola.