Hi Pierre,

There's a standard magnitude formula, using H (absolute magnitude, the
magnitude the asteroid would have if it were one AU from the sun as seen
from the sun itself) and G (the 'slope parameter', which roughly describes
the magnitude as a function of phase angle).

The absolute magnitude H essentially combines the diameter and albedo to
say "this is how much light the object reflects". It's what you actually
observe when you point a telescope at the object: you can't tell if it's
a really big object covered in black paint, or a small object covered in
mirrors. (You can put a lower limit on the object's diameter based on the
assumption that it reflects 100% of the incoming light. It might be
twice as big if the albedo is really 25%, or five times as big if the
albedo is actually 4%. Or a truly massive alien artifact cleverly disguised
as a small asteroid, covered in black paint.)

The IAU standard magnitude formula is :

mag = H + 5 log(r * delta) - 2.5 log((1-G)phi1 + G * phi2)

phi1 = exp[ -3.33( tan( beta / 2) ^ 0.63)]
phi2 = exp[ -1.87( tan( beta / 2) ^ 1.22)]

...in which logarithms are to base 10, r = the distance between the
asteroid and the sun, delta = distance of the asteroid from the observer,
and beta = phase angle.

If an asteroid has been observed for a while over a wide range of phase
angles, then the slope parameter G can usually be determined. But for most
objects, a default value of 0.15 is assumed. I don't know what that value
corresponds to in a physical sense.

-- Bill