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Periodic comets have eccentricities mostly between 0.2 and 0.7, [6] but some of them have highly eccentric elliptical orbits with eccentricities just below 1; for example, Halley's Comet has a value of 0.967. Non-periodic comets follow near-parabolic orbits and thus have eccentricities even closer to 1.
HD 80606 b has the most eccentric orbit of any known planet after HD 20782 b.Its eccentricity is 0.9336, comparable to Halley's Comet.The eccentricity may be a result of the Kozai mechanism, which would occur if the planet's orbit is significantly inclined to that of the binary stars.
The planet completes a somewhat eccentric orbit every 131.458 days from a semimajor axis of just over 0.6 AU, only about 3.5 times the semi-major axis between the parent stars. The proximity and eccentricity of the binary star as well as both stars have similar masses results the planet's orbit to significantly deviate from Keplerian orbit. [6]
In orbital mechanics, the eccentric anomaly is an angular parameter that defines the position of a body that is moving along an elliptic Kepler orbit. The eccentric anomaly is one of three angular parameters ("anomalies") that define a position along an orbit, the other two being the true anomaly and the mean anomaly .
With the exoplanet sample known in 2009, a group of astronomers estimated that "(1) around 35% of the published eccentric one-planet solutions are statistically indistinguishable from planetary systems in 2:1 orbital resonance, (2) another 40% cannot be statistically distinguished from a circular orbital solution" and "(3) planets with masses ...
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 ":
The dynamics of a system composed of three bodies system acting under their mutual gravitational attraction is complex. In general, the behaviour of a three-body system over long periods of time is enormously sensitive to any slight changes in the initial conditions, including even small uncertainties in determining the initial conditions, and rounding-errors in computer floating point arithmetic.
[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]