Phase angle

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Phase Angle

(glossary entry -- See also: phase and phases)


In astronomy and radiometry, phase angle is used to mean the angle between a light source and the observer as seen from an illuminated surface. For Earth-based observations of the Moon this is typically taken as the angle between the center of the Sun and the center of the Earth as seen from the center of the Moon. 

Additional Information

  • By convention, the lunar phase angle is given a sign. It starts at roughly -180° near New Moon and proceeds to near 0° at Full Moon (see phases). It then goes from near 0° to near +180° during the remainder of the cycle. The First Quarter (Moon half illuminated on the east) occurs near a phase angle of -90°, and the Last Quarter (Moon half illuminated on the west) near +90°.
  • The phase angle is listed as the "Sun-Target-Observer" or "STO" angle in the lunar ephemeris output from JPL Horizons. It is used to calculate the theoretical percent illumination of the Moon (in which the Moon is treated as an idealized constant radius sphere).
  • The phase angle is also important because there is a general tendency for the surface brightness of the Moon to increase as the magnitude of the phase angle decreases; and an extra enhancement (the opposition surge) when the phase angle is especially small (less than about 5°). See Retro-Reflection phenomena.
  • The phase angle is very precisely defined at any moment, but the values corresponding to points in the lunar cycle can be stated only approximately because the Moon can miss a line drawn from the Sun through the Earth by a considerable amount.
  • If the phase angle ever went exactly to zero, we would be at the middle of a perfect lunar eclipse. Approaching such a condition, an imaginary observer at the Earth’s center could see the Moon at a phase angle of as small as about 1.5° before any part of the Moon’s disk begins to be attenuated by the penumbral shadow of the Earth (which is about 4.7 lunar diameters in size). Due to the effects of parallax, an actual observer on the Earth’s surface watching the Moon enter the Earth’s penumbra at sunset, or exiting it at sunrise, can see the unattenuated Moon at a phase angle of as little as 0.53°, and can see the last/first parts of the lunar disk entering/leaving the penumbral at phase angles as little as 0.27°.
  • The conditions of the lunar eclipse are unusual. In most cycles, the Moon misses the Earth’s shadow by a wide mark, and (in such cases) the phase angle may never reach a value less than about 5°.
  • In photos of the Moon taken from short range (for example, from a spacecraft in orbit, or even more so, from a camera held near the surface) the phase angle varies over large amounts, and there is a corresponding variation in the apparent brightness of the lunar surface.
  • Although we assign a single value to the phase angle, the actual illumination at any particular point on the Moon consists of a mix of phase angles because the Sun is about 0.5° in diameter as viewed from the surface of the Moon. Hence even if some rays are being observed at a phase angle of 0°, the signal will be mixed with others at an angle of at least 0.25°.
  • In other branches of physics, phase and phase angle are sometimes used to express the time coordinate of a perfectly periodic phenomenon where the entire interval of repetition is arbitrarily assigned a range of 360 "degrees". Some amateurs have adapted a terminology of this sort to refer to points in the Moon's monthly cycle, dividing it into equal intervals of time or angle (measured in some way), but the Moon's orbit does not repeat in a strictly repetetive way, and this is not normal astronomical usage.

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