Minor edits have been made to this post to make some important clarifications as suggested by commenter Tommy T below.
|Moonset this morning over the Boulder Flatirons. Sponsored by Bud Light.|
The moon's orbit is elliptical and thus not quite circular. Although the average distance to the moon is about 385,000 km, at perigee, when it is closest, it is about 365,000 km away, whereas at apogee, when it is farthest, it is about 405,000 km away.
There is no doubt that this causes a change in the apparent size of the moon. The solid angle subtended by the moon varies from about .56º at perigee to about .49º at apogee. This does make the size of the moon seem to vary. The moon subtends a larger solid angle and appears larger at perigee than it does at other points in it's orbital cycle.
However, there is another trick at play here and that is something called the Moon Illusion. When we observe moonrise, the moon often appears much larger than it does when it is near zenith (it's highest point in the sky). This is not because the moon is closer at moonrise than at zenith, but instead because the presence of nearby objects affects our brain's interpretation of the scene. The precise cause of this illusion is actually a subject of debate, but most of the photos I've seen of the Supermoon have this as an exaggerating factor.