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Over hundreds of thousands of years, the eccentricity of the Earth's orbit varies from nearly 0.003 4 to almost 0.058 as a result of gravitational attractions among the planets. [3] Luna's value is 0.054 9, the most eccentric of the large moons in the Solar System.
The eccentric anomaly E is related to the mean anomaly M by Kepler's equation: [3] = This equation does not have a closed-form solution for E given M. It is usually solved by numerical methods, e.g. the Newton–Raphson method. It may be expressed in a Fourier series as
However, the actual solution, assuming Newtonian physics, is an elliptical orbit (a Keplerian orbit). For these, it is easy to find the mean anomaly (and hence the time) for a given true anomaly (the angular position of the planet around the sun), by converting true anomaly f {\displaystyle f} to " eccentric anomaly ":
[2] Orbital circularization can be caused by either or both of the two objects in an orbit if either or both are inelastic. Cooler stars tend to be more viscous and circularize objects orbiting them faster than hot stars. [3] If Ω/ω > 18/11 (~1.64) circularization will not occur and the eccentricity will increase. [4]
HD 80606 b was considered the planet with the most eccentric orbit until the recent discovery. HD 80606 b has an eccentricity of 0.93 and a shorter orbit of 111 days, and it orbits in the same ...
From a circular orbit, thrust applied in a direction opposite to the satellite's motion changes the orbit to an elliptical one; the satellite will descend and reach the lowest orbital point (the periapse) at 180 degrees away from the firing point; then it will ascend back. The period of the resultant orbit will be less than that of the original ...
Orbital position vector, orbital velocity vector, other orbital elements. In astrodynamics and celestial dynamics, the orbital state vectors (sometimes state vectors) of an orbit are Cartesian vectors of position and velocity that together with their time () uniquely determine the trajectory of the orbiting body in space.
2017 MB 7 orbits the Sun at a distance of 4.5–3,419 AU once every 70,825 years (semi-major axis of 1712 AU). Its orbit has an eccentricity of 0.9974 and an inclination of 56° with respect to the ecliptic. [2] As it has an eccentricity higher than 0.50, the distant object is labelled an (other) unusual object by the Minor Planet Center. [4]