Phases a planet

Phase function for the Lambert sphere


Calculate phase function for a Lambert sphere.

The phase function of the Lambert sphere is given by:

\[\Phi(\alpha) = \frac{\sin(\alpha) + (\pi - \alpha)\cos(\alpha)}{\pi} \; .\]

Here, \(\alpha\) is the phase angle, which is defined as the angle between the star and the Earth as seen from the planet. Hence, at phase angle zero, the planet is found in opposition. Formally, the phase angle can be between 0 and 180 degrees. This function accounts for cases in which the given phase angle violates these limits by projecting it back into the valid range.

alphafloat or array

The phase angle(s) [deg] at which the phase function is to be calculated.

Phase functionfloat or array

The values of the phase function at the input phase angles.