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The superior planets, orbiting outside the Earth's orbit, do not exhibit a full range of phases since their maximum phase angles are smaller than 90°. Mars often appears significantly gibbous, it has a maximum phase angle of 45°. Jupiter has a maximum phase angle of 11.1° and Saturn of 6°, [1] so their phases are almost always full.
Diagram showing the eastern and western quadratures of a superior planet like Mars. In spherical astronomy, quadrature is the configuration of a celestial object in which its elongation is a right angle (90 degrees), i.e., the direction of the object as viewed from Earth is perpendicular to the position of the Sun relative to Earth.
"Inferior planet" refers to Mercury and Venus, which are closer to the Sun than Earth is. "Superior planet" refers to Mars, Jupiter, Saturn, Uranus, and Neptune (the latter two added later), which are further from the Sun than Earth is. The terms are sometimes used more generally; for example, Earth is an inferior planet relative to Mars.
For some objects, such as the Moon (see lunar phases), Venus and Mercury the phase angle (as seen from the Earth) covers the full 0–180° range. The superior planets cover shorter ranges. For example, for Mars the maximum phase angle is about 45°. For Jupiter, the maximum is 11.1° and for Saturn 6°. [1]
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.
The phase curve of the Moon [26] compared to Mercury. [1] The phase curve of the Moon approximately resembles that of Mercury due to the similarities of the surfaces and the lack of an atmosphere on either body. [27] Clementine spacecraft data analyzed by J. Hillier, B. Buratti and K. Hill [28] indicate a lunar opposition surge.
In the Hipparchian, Ptolemaic, and Copernican systems of astronomy, the epicycle (from Ancient Greek ἐπίκυκλος (epíkuklos) 'upon the circle', meaning "circle moving on another circle") [1] was a geometric model used to explain the variations in speed and direction of the apparent motion of the Moon, Sun, and planets.
Conversely, the closed trajectory is called a subharmonic orbit if k is the inverse of an integer, i.e., if m = 1 in the formula k = m/n. For example, if k = 1/3 (green planet in Figure 5, green orbit in Figure 10), the resulting orbit is called the third subharmonic of the original orbit. Although such orbits are unlikely to occur in nature ...
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