I've been posting a lot of extreme close-ups of the Moon, but sometimes you can learn something by taking a step back.
For example, I imagine if I went out in the street and asked people what shape the Moon's orbit was, they'd say it was a circle (or, given recent poll results, they'd say it was Muslim). In fact, however, the Moon's orbit is decidedly elliptical. When it's closest to Earth -- the point called perigee -- it's roughly 360,000 kilometers (223,000 miles) away*, and when it's at its farthest point -- apogee -- it's at a distance of about 405,000 km (251,000 miles).
That's a difference of about 10% -- not enough to tell by eye, but certainly enough to see in a picture... like this one, by the Greek amateur astronomer Anthony Ayiomamitis:
[Click to emperigeenate.]
Amazing, isn't it? The Moon is noticeably different! He took those images at full Moon, but seven months apart, when the Moon was at perigee (last January) and apogee (just a few days ago as I write this). It's part of a project he does every year, and it's pretty cool. He was able to get these images within a few moments of the exact times of apogee and perigee.
You might wonder how the Moon can be at apogee when it's full one time, and perigee at another time it's full. That's a good question, and it's because the phase of the Moon doesn't depend on the shape of its orbit, it depends on the angle between the Sun, the Moon, and the Earth.
If the Sun is behind the Moon from our viewpoint, we see only the dark side, and the Moon is new. If the Sun is behind us, and shining straight down on the Moon, we see it as full. The crescent and gibbous phases happen in between those times. So while the Moon's phase depends on where it is in its orbit relative to the Sun and Earth, the orbit shape -- the fact that it's a bit of an ellipse and not a circle -- isn't all that important.
Not only that, the time it takes to go from full Moon to full Moon (called the synodic month) is not the same amount of time it takes to go from perigee, around the Earth, and back to perigee (called the anomalistic month). The first is about 29.5 days, the second about 27.6 days. That difference means that every time the Moon gets to perigee, it takes an extra 2.2 days or so for the phase to catch up.
Or, a better way to think about it is like this: say at some date the Moon is both full and at perigee. 29.5 days later, it's full again, but it's had an extra 2.2 days around the Earth. It's a little bit past perigee when it's full (or you could say it hit perigee before it was full again). Wait until the next full Moon and now it's 4.4 days past perigee (or, it was at perigee again 4.4 days before it was full a third time). Keep doing that; after about 6 cycles of its phases, that extra time will add up to about half of the anomalistic cycle.
In other words, full Moon will happen at apogee!
It's not an exact match, so you don't really get a perfect full Moon at perigee and another at apogee in one year. But as Anthony showed, you can get pretty close.
And if you're wondering why you've never noticed the 10% difference in Moon size, it's because when you look at it, you're not comparing it side-by-side with itself like in the picture. You don't have a good gauge of exactly how big it is from month to month, so you never notice. You need to photograph it, or observe it very carefully through a telescope.
I'll note that the Earth's orbit around the Sun is also an ellipse, so the Sun appears bigger and smaller throughout the year; the change isn't as big as for the Moon, but you can see for yourself because Anthony has images of that as well.
And if you're curious about on what dates the Moon reaches perigee and apogee, head over to Fourmilab's Perigee and Apogee calculator.
Amazing, isn't it, that something that seems this obvious can be hidden in plain view. It makes you wonder what else you're missing, doesn't it?