Dave Johnson, of Ashhurst, Manawatu, asks :-
The sun cuts an arc across the sky from sunrise to sunset that is high overhead in the summer and low in the winter. The moon's path is the exact opposite of this. High overhead in the winter, low in the summer. Is there some kind of mirror effect happening?
Alan Gilmore, an astronomer at the University of Canterbury's Mt John Observatory, responded.
You are on the right track with the mirror effect.
The sun and the moon orbit the earth in nearly the same plane. In other words, drawing the earth's orbit and the moon's orbit on a sheet of paper is close to reality for their orbit tilts.
Earth's axis is not vertical to the orbit plane. It is tilted 23 degrees from the vertical. That gives the seasons. In December Earth's south pole is tilted toward the sun. In June the south pole is tilted away from the sun. That causes the arc of the sun across the sky to be high in summer and low in winter.
A full moon happens when the moon is on the opposite side of the earth from the sun. So a full moon 'sees' the earth tilted the other way. The winter full moon is where the summer sun was. The summer full moon is where the winter sun was.
There are some details to add. The moon's orbit is actually tilted five degrees to the plane of the earth's orbit. Also the moon's orbit rotates over 19 years, a bit like a spinning top. So there are times when the full moon's north-south swing is five degrees greater each way than the sun's annual swing. Nine years later it is five degrees less than the sun's swing. (Five degrees is 10 moon diameters.)
Currently the moon's orbit is near a midway position. Its north-south swing is a bit less than the sun's. Summer and winter full moons are near where the sun would be at the opposite season. The moon was last at maximum swing around 2006. Back then the summer full moon was low in our north sky and the winter full moon seemed almost overhead at midnight.