mars' orbit is ~1.5 that of the earth. Since its light is actually reflected sunlight the intensity reaching its surface is ~2.25 times smaller that the solar light on earth/moon.
Mars' diameter is about twice the moon: 6800 km vs 3500 km. therefor it's crosssection area is 4 times that of the moon.
If we neglect all reflective effects (practically assuming a flat coin shaped mars and moon) and assume similar reflective coefficient then mars emitts 4/2.25 = 1.8 times more light than the moon.
But the moon is closer to the earth: 384,400 km, while mars at the closest point is about half earth's orbit (astronomical unit) from earth: 149,600,000 / 2 km = 75,000,000 km.
Which means mars is at least 195 (~200) times farther than the moon, so the flux of light comming to earth from mars will be
1.8/200 = 0.009, that of the moon.
In practice, we spatially resolve the moon by eye so the moon's flux does not appear to be comming from a point source but spread over an area. This will lower the moon brightness by a few factors.
Still, this means that mars eye observed brightness is of order of a few times 1% of the moon. It will never outshine the full moon.
Bozon
