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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.
As a consequence the amount of calculation in the simulation goes up with the square of the number of bodies: Doubling the number of bodies increases the work with a factor four. To increase the accuracy of the simulation not only more decimals are to be taken but also smaller timesteps, again quickly increasing the amount of work.
With the development of space travel, as well as in hypothetical observations from other points in space, the notion of phase angle became independent of Sun and Earth. The etymology of the term is related to the notion of planetary phases, since the brightness of an object and its appearance as a "phase" is the function of the phase angle.
The apparent brightness of Mercury as seen from Earth is greatest at phase angle 0° (superior conjunction with the Sun) when it can reach magnitude −2.6. [14] At phase angles approaching 180° ( inferior conjunction ) the planet fades to about magnitude +5 [ 14 ] with the exact brightness depending on the phase angle at that particular ...
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.
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.
The heliocentric ecliptic system describes the planets' orbital movement around the Sun, and centers on the barycenter of the Solar System (i.e. very close to the center of the Sun). The system is primarily used for computing the positions of planets and other Solar System bodies, as well as defining their orbital elements .