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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 ...
The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this, Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels faster.
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).
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 ()
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:
For elliptical orbits it can also be calculated from the periapsis and apoapsis since = and = (+), where a is the length of the semi-major axis. = + = / / + = + where: r a is the radius at apoapsis (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to the center of mass of the system, which is a focus of the ellipse.
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 ...
Harmonic and subharmonic orbits are special types of such closed orbits. A closed trajectory is called a harmonic orbit if k is an integer, i.e., if n = 1 in the formula k = m / n . For example, if k = 3 (green planet in Figures 1 and 4, green orbit in Figure 9), the resulting orbit is the third harmonic of the original orbit.
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