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The evolution of the apparent diameter and phases of Venus. A planetary phase is a certain portion of a planet's area that reflects sunlight as viewed from a given vantage point, as well as the period of time during which it occurs. The phase is determined by the phase angle, which is the angle between the planet, the Sun and the Earth.
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"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.
where a 0 and k 0 are constants, = is the imaginary unit, and t is time, correspond to a deferent centered on the origin of the complex plane and revolving with a radius a 0 and angular velocity k 0 = 2 π T , {\displaystyle k_{0}={\frac {2\pi }{T}}\,,}
Visual conjunction between the Moon and the planet Venus, the two brightest objects in the night sky. In astronomy, a conjunction occurs when two astronomical objects or spacecraft appear to be close to each other in the sky. This means they have either the same right ascension or the same ecliptic longitude, usually as observed from Earth. [1] [2]
[1] The brightness of an object is a function of the phase angle, which is generally smooth, except for the so-called opposition spike near 0°, which does not affect gas giants or bodies with pronounced atmospheres, and when the object becomes fainter as the angle approaches 180°. This relationship is referred to as the phase curve.
Neptune has 16 known moons; the largest, Triton, accounts for more than 99.5 percent of all the mass orbiting the planet. Triton is large enough to have achieved hydrostatic equilibrium, but, uniquely for a large moon, has a retrograde orbit, suggesting it was a dwarf planet that was captured.
At phase angles exceeding 90° (crescent phase) the brightness falls off especially sharply. The shape of the phase curve indicates a mean slope on the surface of Mercury of about 16°, [1] which is slightly smoother than that of the Moon. Approaching phase angle 0° (fully illuminated phase) the curve rises to a sharp peak.