Planetary Magnitudes

Despite several hours of searching, I could not find details of the algorithm for the ′Hapke′ model on the web. Instead, I assume a trapezoidal spike close to planetary opposition (or superior conjunction).

For the strength of the opposition surge, I use the "Geometric albedos" listed at:

http://en.wikipedia.org/wiki/Geometric_albedo

I use the the Bond albedo when the angular separation between the Sun and the Earth as seen from the planet is more than °, and the Geometric albedo when it is less than °. (Linear interpolation is used between these angles.)

Define "disk" as the fraction of the planet disk as seen from here. (0 to 1).

Magnitude = - log ( albedo * disk * square ( Planet_Radius ) /
square ( Earth_Planet_Distance ) / square ( Sun_Planet_Distance) ) / log ( 2.512 ) + ;
The last value of was calculated so that the formula gives the measured magnitude of -2.88 for the specific opposition of the planet Mars August 28, 2003 17:59 GMT.

In other words, all of the planetary magnitudes are calibrated using this one particular observation, and the surge characterization has been reduced to a linear interpolation.

(If anyone knows of a free version of the Hapke algorithm along with the planetary parameters, please send it to me.)