Phase angle (astronomy)

Phase angle in astronomical observations is the angle between the light incident onto an observed object and the light reflected from the object. In the context of the astronomical observations this used to be the angle Sun-object-Earth.

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With the development of the space travel, as well as in hypothetical observations from other points in space, the notion phase angle became independent of Sun and Earth. Also, "Sun-object-Earth" is a simplified model, since the precise angle value would depend on the parallax between the two distant positions of the observer on the Earth surface, which, in the case of the observation of the Moon can be as much as 1°, or two full Moon diameters.

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 phase angle varies from 0° to 180°. The value of 0 corresponds to the position when the illuminator, the object and the observer are collinear, with the illuminator and the observer on the same side with respect to the object. The value of 180 is the position when the object is between the illuminator and the observer, known as the astronomical opposition.

For some planets, such as 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°.

The brightness of an object is function of the phase angle, which is generally smooth, only with the so-called opposition spike near 0° and with the object generally becoming brighter when the angle is approaching 0 and 180.

See also: illumination angle.