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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.
At θ = 90° and at θ = 270° the distance is equal to . At θ = 180°, aphelion, the distance is maximum (by definition, aphelion is – invariably – perihelion plus 180°) = The semi-major axis a is the arithmetic mean between r min and r max:
The ancient Greek astronomer Hipparchus noted the apsidal precession of the Moon's orbit (as the revolution of the Moon's apogee with a period of approximately 8.85 years); [4] it is corrected for in the Antikythera Mechanism (circa 80 BCE) (with the supposed value of 8.88 years per full cycle, correct to within 0.34% of current measurements). [5]
The International Astronomical Union defines it as the angle measured relative to the north celestial pole (NCP), turning positive into the direction of the right ascension. In the standard (non-flipped) images, this is a counter clockwise measure relative to the axis into the direction of positive declination .
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.
This diagram shows various possible elongations (ε), each of which is the angular distance between a planet and the Sun from Earth's perspective. In astronomy, a planet's elongation is the angular separation between the Sun and the planet, with Earth as the reference point. [1] The greatest elongation is the maximum angular separation.
Afternoon analemma photo taken in 1998–99 in Murray Hill, New Jersey, U.S., by Jack Fishburn.The Bell Laboratories building is in the foreground. In astronomy, an analemma (/ ˌ æ n ə ˈ l ɛ m ə /; from Ancient Greek ἀνάλημμα (analēmma) 'support') [a] is a diagram showing the position of the Sun in the sky as seen from a fixed location on Earth at the same mean solar time over ...
Now the problem has become one of finding the nearest point on this plane to the origin, and its distance from the origin. The point on the plane in terms of the original coordinates can be found from this point using the above relationships between and , between and , and between and ; the distance in terms of the original coordinates is the ...