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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]
The United States Naval Observatory states "the Equation of Time is the difference apparent solar time minus mean solar time", i.e. if the sun is ahead of the clock the sign is positive, and if the clock is ahead of the sun the sign is negative. [6] [7] The equation of time is shown in the upper graph above for a period of slightly more than a ...
is the eccentricity of the central body (e.g., 0.081819 for Earth) is the geodetic latitude (the angle between the normal line of horizontal plane and the equatorial plane) ′ is the geocentric latitude (the angle between the radius and the equatorial plane)
As for instance, if the body passes the periastron at coordinates = (), =, at time =, then to find out the position of the body at any time, you first calculate the mean anomaly from the time and the mean motion by the formula = (), then solve the Kepler equation above to get , then get the coordinates from:
where M 0 is the mean anomaly at the epoch t 0, which may or may not coincide with τ, the time of pericenter passage. The classical method of finding the position of an object in an elliptical orbit from a set of orbital elements is to calculate the mean anomaly by this equation, and then to solve Kepler's equation for the eccentric anomaly.
For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem to find: the time-average of the specific potential energy is equal to −2ε the time-average of r −1 is a −1; the time-average of the specific kinetic energy is equal to ε
For a given semi-major axis the specific orbital energy is independent of the eccentricity. Using the virial theorem we find: the time-average of the specific potential energy is equal to ; the time-average of is
The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars.