Setting: we have a fantasy world which is a planet with much of the same conditions that can be seen on Earth, but with the difference that it is orbited by a moon with a mean diameter of 3 500 km. The moon has an albedo of 0.12 and its distance from our planet is 20 000 km at perigee.
The moon/planet system orbits a star that has an apparent magnitude of -27, when observed from the moon/planet system. Assume that we have the same atmospheric conditions as on Earth, and - if other parameters have to be taken into account besides the atmosphere - assume those are equal to Earth's as well.
I would like to learn two things here:
- What would the apparent magnitude of the moon in question be to an observer looking up at the night sky from the planet it orbits, when the moon is at perigee and in its full phase?
- What does the equation that gives you the solution to this problem look like?