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Astrophotographer Adam (AJ) Smadi caught this image a few hours ago from Washington state. A thin crescent Moon, sunlight illuminating the rugged lunar surface. And 2,400 times farther away—and on the other side of the Sun—mighty Jupiter, and its moons Io (left) and Ganymede (right).

It's worth emphasising that the reason we see the full disk of Jupiter but a crescent Moon is because Jupiter is on the other side of the Sun. Indeed, we cannot see a crescent Jupiter from Earth; we'd have to be beyond it for that to work. A beautiful illustration of how the Solar System works.

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Your first sentence confused me, but your second sentence clarified, sort of. It doesn't matter which side of the sun Jupiter is on, it's always full. The only planets that go through phases as viewed from earth are Mercury and Venus. If you're on Mars, the earth has phases too.

I wonder if we're close enough to Mars to get a partial crescent when we're 90 degrees ahead or behind? I reckon we'd never see less than a half but I haven't got a clue how to check the math on that.

True. I overgeneralized a bit. Obviously the moon still has a phase even when it's farther from the sun than the earth. It depends on the relative distance and angle to the light source. Even Jupiter has a "phase" but it's probably 99.9999% illuminated.