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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, [11] but from 1800 to 2050 has a mean eccentricity of 0.008 59. [12]
Hyperbolic orbit: An orbit with the eccentricity greater than 1. Such an orbit also has a velocity in excess of the escape velocity and as such, will escape the gravitational pull of the planet and continue to travel infinitely until it is acted upon by another body with sufficient gravitational force.
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
When the apocenter distance is close to the pericenter distance, the orbit is said to have low eccentricity; when they are very different, the orbit is said be eccentric or having eccentricity near unity. This definition coincides with the mathematical definition of eccentricity for ellipses, in Keplerian, i.e., / potentials.
where is the orbital inclination, is the eccentricity, is mean motion in degrees per day, is the perturbing factor, is the radius of the earth, is the semimajor axis, and ˙ is in degrees per day. To avoid this expenditure of fuel, the Molniya orbit uses an inclination of 63.4°, for which the factor 4 − 5 sin 2 i {\displaystyle 4-5\sin ...
A highly elliptical orbit (HEO) is an elliptic orbit with high eccentricity, usually referring to one around Earth. Examples of inclined HEO orbits include Molniya orbits , named after the Molniya Soviet communication satellites which used them, and Tundra orbits .
Mars has an orbit with a semimajor axis of 1.524 astronomical units (228 million km) (12.673 light minutes), and an eccentricity of 0.0934. [1] [2] The planet orbits the Sun in 687 days [3] and travels 9.55 AU in doing so, [4] making the average orbital speed 24 km/s.
Selecting the initial mean eccentricity vector as (, ) the mean eccentricity vector will stay constant for successive orbits, i.e. the orbit is frozen because the secular perturbations of the term given by and of the term given by cancel out.