magnitude of space debris

elisa.pinat

Dear all,
I'm new here and I'm sorry if my problem has already been discussed anywhere else.
I have some problems in determining the magnitude of space debris as a function of their dimension and distance.
I have to find the visual absolute magnitude of a 30 cm diameter debris, at 36000 km and with an albedo of 0.2.
As a reference, I have taken the vega V flux above the atmosfere, 8.8E5 phot/cm2/s.
If I start taking into account the photon flux from 470 to 700 nm, and I consider a Lambertian surface with a phase angle of 0 for simplicity, I can find the reflected flux of photons, phot/cm2/s. Nevertheless, this flux is independent from the dimension of the debris, but it depends only on the phase angle and the albedo of the debris. When I try to consider the dimension of the object, and multiply the photon flux with the surface of the debris, I find the number of the reflected photons, express in phot/s. How can I relate this number to the absolute magnitude?
Thank you a lot