Why do the moons crescent and gibbous phases appear curved?
Take a table tennis ball and use a black marker to draw a line following the seam between the two halves. Now colour one half in black. Now hold it up in front of you so the division between the black and white sides is vertical. Now rotate the ball slowly and watch the phases of the Moon appear on the ball! The Moon is like that table tennis ball. At any one time half of it is in sunlight and the other half in shadow (NOT the Earth’s shadow, as someone said here, but simply the side of the Moon that faces away from the Sun and is therefore not lit by it). The phases we see are due to the changing viewing angle we have as the Moon moves around us. We see different amounts of the lit and unlit sides as it orbits. The curve arises simply because the Moon is a sphere, just like your table tennis ball.
