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An elliptical orbit is depicted in the top-right quadrant of this diagram, where the gravitational potential well of the central mass shows potential energy, and the kinetic energy of the orbital speed is shown in red. The height of the kinetic energy decreases as the orbiting body's speed decreases and distance increases according to Kepler's ...
Geosynchronous (and geostationary) orbits have a semi-major axis of 42,164 km (26,199 mi). [10] This works out to an altitude of 35,786 km (22,236 mi). Both complete one full orbit of Earth per sidereal day (relative to the stars, not the Sun). High Earth orbit: geocentric orbits above the altitude of geosynchronous orbit (35,786 km or 22,236 mi).
Diagram illustrating Newton's derivation. The blue planet follows the dashed elliptical orbit, whereas the green planet follows the solid elliptical orbit; the two ellipses share a common focus at the point C. The angles UCP and VCQ both equal θ 1, whereas the black arc represents the angle UCQ, which equals θ 2 = k θ 1.
All bounded orbits where the gravity of a central body dominates are elliptical in nature. A special case of this is the circular orbit, which is an ellipse of zero eccentricity. The formula for the velocity of a body in a circular orbit at distance r from the center of gravity of mass M can be derived as follows:
In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler in 1609 (except the third law, and was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary ...
The following diagram illustrates the positions and relationship between the lines of solstices, equinoxes, and apsides of Earth's elliptical orbit. The six Earth images are positions along the orbital ellipse, which are sequentially the perihelion (periapsis—nearest point to the Sun) on anywhere from January 2 to January 5, the point of ...
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 ()
Parabolic (1) and hyperbolic (3) orbits are escape orbits, whereas elliptical and circular orbits (2) are captive. The orbital plane of a revolving body is the geometric plane in which its orbit lies. Three non-collinear points in space suffice to determine an orbital plane.