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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 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 procedure for calculating the heliocentric polar coordinates (r,θ) of a planet as a function of the time t since perihelion, is the following five steps: Compute the mean motion n = (2π rad)/P, where P is the period. Compute the mean anomaly M = nt, where t is the time since perihelion.
For instance, the maximum angular speed of the Earth as measured from the Sun varies by a semitone (a ratio of 16:15), from mi to fa, between aphelion and perihelion. Venus only varies by a tiny 25:24 interval (called a diesis in musical terms). [7] Kepler explains the reason for the Earth's small harmonic range:
Log-log plot of period T vs semi-major axis a (average of aphelion and perihelion) of some Solar System orbits (crosses denoting Kepler's values) showing that a 3 / T 2 is constant (green line) In astrodynamics the orbital period T of a small body orbiting a central body in a circular or elliptical orbit is: [1]
The Earth spends less time near perihelion and more time near aphelion. This means that the lengths of the seasons vary. [ 14 ] Perihelion currently occurs around 3 January, so the Earth's greater velocity shortens winter and autumn in the northern hemisphere, and summer and spring in the southern hemisphere.
For illustration, the long axis of the planet Mercury is defined as the line through its successive positions of perihelion and aphelion. Over time, the long axis of most orbiting bodies rotates gradually, generally no more than a few degrees per complete revolution, because of gravitational perturbations from other bodies, oblateness in the ...
The longitudes of perihelion were only 29 degrees apart at J2000, so the smallest distances, which come when inferior conjunction happens near Earth's perihelion, occur when Venus is near perihelion. An example was the transit of December 6, 1882: Venus reached perihelion Jan 9, 1883, and Earth did the same on December 31.