SV: Calculating magnitudes - was [Re: Binoculars & Mag]

Björn Gimle (b_gimle@algonet.se)
Thu, 15 Oct 1998 20:36:37 +0200

: Philip Chien <kc4yer@amsat.org> wrote:
>
>Is there a reasonably accurate formula for calculating the predicted
>magnitude for a satellite?  I suspect that it would have to include the
>satellite's cross section area, albedo, percentage sunlit (usually =
either 1
>or 0), and distance from observer.  I would suspect that the same =
formula
>could be used to calculate the magnitude of the moon, planets, and any
>other objects which shine by reflected sunlight.
>
Skymap uses      mag =3D rm + 5*log(distance/1000 km) - =
2.5*log(1-cos(ph))

where rm is the reference magnitude at 1000 km half phase (ph=3D90 d)

Quicksat uses the rm at full phase (ph=3D180 d), which needs to be
reduced by about 0.7, (or 2.5*log((1-cos(ph)/2) for this formula.
There is also a substantial term for atmospheric extinction in Quicksat
for low elevations.

I have an old note that rm is 6.0 - 2.5*log(Area*albedo), but those
factors are rarely known for satellites, so empirical rm is preferred.

If full moon is -12.8, it needs rm =3D -24.9, which gives an albedo of =
0.25!
Half moon would be -12.0, and one day moon (ph=3D12 d) -7.8.
Something does not quite right there.

Bjoern