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The apsides refer to the farthest (2) and nearest (3) points reached by an orbiting planetary body (2 and 3) with respect to a primary, or host, body (1). An apsis (from Ancient Greek ἁψίς (hapsís) 'arch, vault'; pl. apsides / ˈ æ p s ɪ ˌ d iː z / AP-sih-deez) [1] [2] is the farthest or nearest point in the orbit of a planetary body about its primary body.
= | |, the distance between Sun and planet. θ = ∠ z s p , {\displaystyle \theta =\angle zsp,} the direction to the planet as seen from the Sun, the true anomaly . The problem is to compute the polar coordinates ( r , θ ) of the planet from the time since perihelion, t .
Some of these TNOs with an extreme aphelion are detached objects such as 2010 GB 174, which always reside in the outermost region of the Solar System, while for other TNOs, the extreme aphelion is due to an exceptionally high eccentricity such as for 2005 VX 3, which orbits the Sun at a distance between 4.1 (closer than Jupiter) and 2200 AU (70 ...
r a is the radius at apoapsis (also "apofocus", "aphelion", "apogee"), i.e., the farthest distance of the orbit to the center of mass of the system, which is a focus of the ellipse. r p is the radius at periapsis (or "perifocus" etc.), the closest distance.
Historically, the astronomical unit was conceived as the average Earth-Sun distance (the average of Earth's aphelion and perihelion), before its modern redefinition in 2012. The astronomical unit is used primarily for measuring distances within the Solar System or around other stars.
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:
[1] [2] The low eccentricity and comparatively small size of its orbit give Venus the least range in distance between perihelion and aphelion of the planets: 1.46 million km. The planet orbits the Sun once every 225 days [ 3 ] and travels 4.54 au (679,000,000 km; 422,000,000 mi) in doing so, [ 4 ] giving an average orbital speed of 35 km/s ...
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: