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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. [14]
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.
The eccentricity (e) and either the semi-major axis (a) or the distance of periapsis (q) are used to specify the shape and size of an orbit. The longitude of the ascending node ( Ω ) the inclination ( i ) and the argument of periapsis ( ω ) or the longitude of periapsis ( ϖ ) specify the orientation of the orbit in its plane.
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.
An inclination of 90° is an edge-on orbit, meaning the plane of the exoplanet's orbit is parallel to the line of sight with Earth. Since the word "inclination" is used in exoplanet studies for this line-of-sight inclination, the angle between the planet's orbit and its star's rotational axis is expressed using the term the "spin-orbit angle ...
The proper orbital elements or proper elements of an orbit are constants of motion of an object in space that remain practically unchanged over an astronomically long timescale. The term is usually used to describe the three quantities: proper semimajor axis (a p), proper eccentricity (e p), and; proper inclination (i p).
The planetary orbit is not a circle with epicycles, but an ellipse. The Sun is not at the center but at a focal point of the elliptical orbit. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed (closely linked historically with the concept of angular momentum) is constant.
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