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The mean eccentricity of an object is the average eccentricity as a result of perturbations over a given time period. Neptune currently has an instant (current epoch ) eccentricity of 0.011 3 , [ 13 ] but from 1800 to 2050 has a mean eccentricity of 0.008 59 .
Note that for a given amount of total mass, the specific energy and the semi-major axis are always the same, regardless of eccentricity or the ratio of the masses. Conversely, for a given total mass and semi-major axis, the total specific orbital energy is always the same. This statement will always be true under any given conditions. [citation ...
The eccentricity e is defined as: = . From Pythagoras's theorem applied to the triangle with r (a distance FP) as hypotenuse: = + () = () + ( + ) = + = () Thus, the radius (distance from the focus to point P) is related to the eccentric anomaly by the formula
is the distance of the orbiting body from the center of mass of the central body, is the semi-major axis, is the standard gravitational parameter. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem we find:
Adding mass beyond this point causes the radius to shrink. [39] [40] [41] Even when taking heat from the star into account, many transiting exoplanets are much larger than expected given their mass, meaning that they have surprisingly low density. [42] See the magnetic field section for one possible explanation. Plots of exoplanet density and ...
is the distance of the orbiting body from the central body, is the length of the semi-major axis, is the standard gravitational parameter. Conclusions: For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem to find:
For a hyperbolic trajectory this specific orbital energy is either given by =. or the same as for an ellipse, depending on the convention for the sign of a . In this case the specific orbital energy is also referred to as characteristic energy (or C 3 {\displaystyle C_{3}} ) and is equal to the excess specific energy compared to that for a ...
For Kepler orbits the eccentricity vector is a constant of motion. Its main use is in the analysis of almost circular orbits, as perturbing (non-Keplerian) forces on an actual orbit will cause the osculating eccentricity vector to change continuously as opposed to the eccentricity and argument of periapsis parameters for which eccentricity zero ...