W Wilson of Christchurch, asks :-
Is the date of the full moon the same all over the world, in the Northern Hemisphere does it move across the Southern Sky, and is there anywhere where it is overhead?
Saskia Besier, an astronomer at the University of Canterbury, responded.
Yes! As to where in the world it is directly "overhead" (I assume you mean that it is approaching midnight when it is perfectly full) when it is full then although the answer may also be "yes," a more appropriate reply would be that "it doesn't matter!"
The reason we see a full moon is that the Moon goes around the Earth as the Earth goes around the Sun. We see the surface of the Moon only when it is illuminated by the light from the Sun. As the Moon orbits around us, there is a time when it will be lying between us and the Sun. In this case, we can't see the part of the Moon that is being bathed in light: the side facing the Sun. We call this a New Moon.
As the Moon continues orbiting around the Earth we start to be able to see the crescent of the parts of the Moon that the Sun is shining on, till eventually the Earth lies between the Moon and the Sun. Now we can see the entire face of the Moon illuminated and we call this a Full Moon. The precise time of Full Moon is the time at which the Sun, Earth and Moon line up (with the Earth in the middle). This happens at the same time all over the world (to see what these times are check out http://aa.usno.navy.mil).
However, because the Moon is moving quite slowly there is a long time over which it appears full to us here on Earth and so "Full" Moon lasts the entire night, all over the world. In fact the night before and after a perfectly Full Moon, 97-99 per cent of the Moon's surface is illuminated by the Sun. Most people couldn't tell the difference between this and a perfectly full Moon. While there is an exact time of Full Moon, and only a few places in the world when this time will be when the Moon is at its highest point in the sky, during the course of that 24 hours everyone will see a Full Moon overhead.
Importantly, we don't have eclipses every month (which occur when the Earth and Moon line up precisely with the Sun). This is because the Moon's orbit is slightly tilted compared to our orbit around the Sun.
As to whether Northern hemisphere people see the Moon move in the South, the Moon behaves similarly to the Sun in this respect. Loosely speaking, the further North you are, the more South the Moon appears and the further South you go, the further North it appears. More interesting is that, viewed from the Northern Hemisphere the face of the Moon is upside down.