If total brightness of full moon is F, what will be its total brightness Q, when it is in quarter phase?

Answer 1

Actually, the full moon can be up to 10 time brighter then a quarter moon.

There are two reasons for this. One is that when the Moon is full, the Sun is shining straight down on it from our viewpoint. When the Sun is directly overhead here on Earth, there are no shadows, and when it’s low in the sky shadows are long. The same is true for the Moon. There are no shadows on the surface when the Moon is full. When it’s at first quarter there are lots of shadows, which darken the surface, making the Moon look less bright overall. When the Moon is full, those shadows aren’t there, and so it has more than twice as much lit surface from our view than when it’s at first quarter.

The other reason has to do with the Moon’s surface. Meteorite impacts, ultraviolet radiation from the Sun, and the violent temperature changes from day to night on the Moon have eroded the top centimeter or so of the lunar surface. The resulting powder is extremely fine, like well-ground flour. This powder has a peculiar property: it tends to reflect light directly back to the source. Most objects scatter light every which way, but this weird soil on the Moon focuses much of the light back toward the source. This effect is called back-scatter.

Answer 2

Since you asked for "total brightness Q," it will always be ' F ' !!

(You didn't ask "what brightness will we assign to it as seen from the Earth?")

The reason it will always be ' F ' is that one hemisphere of the Moon is lit at all times, but only at Full Moon do we see that. Barring minor changes due to Earth's atmosphere, differing albedos in the illuminated half of the Moon's surface, variations in its distance from the Sun due to both Earth's and the Moon's individual elliptical orbits, etc., the Moon will in first order always reflect the same amount of light from the Sun, no matter what phase it is in as far as we're concerned.

So, since you asked about "total brightness," theres your answer --- essentially always the same, with only minor variations.

Live long and prosper.

P.S. C'mon, guys, you've got to answer the question that's been ASKED, not the question that you WISH it were!

Answer 3

Hmm, is this a homework question? Is you're just asking, I'd say that, when the moon is at its quarter phase, i.e. a half-moon, it would be half as bright.

However, brightness is measured on a logarithmic scale, where an object 2.5 times brighter is one order of magnitude brighter. So, if a full moon has a magnitude of -11, a half moon would be about -10.

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Reading Walking Man's answer, his logic to suggest a full moon is actually ten times brighter than a half moon is pretty convincing. Heck, he's got me convinced. :) I figure, that would make the magnitude of a half-moon about -8.5.

Answer 4

The first answer is correct in its way, since half the moon is always illuminated by the sun (except during eclipses).

From Earth, however, a first or last quarter moon appears as a semicircle, half lit and half dark, so Q = F/2.