The Supermoon

This weekend there was a "Super" Moon.  Basically since the Moon's orbit around the Earth is elliptical (not perfectly circular) it will be closer and farther at different parts of its orbit.  On Saturday the Moon was full and it was also at perigee (its closest distance to the Earth) so it appeared slightly bigger.

But how much bigger was it actually?  The biggest difference would be between when the Moon is at apogee (farthest from Earth) and perigee.  According to Wikipedia the Moon has a mean diameter of 3474 km, distance at apogee: 405,410 km, distance at perigee: 362,570 km.  We can use the small angle approximation to say that tanθ ≈ θ and so θ ≈ s/d where d would be the distance to the Moon and s the diameter of the Moon.  θ is angular diameter in radians.

So at perigee: θ = 3474 / 362570 = 0.009582 radians

At apogee: θ = 3474 / 405410 = 0.008569 radians

This makes sense because the angular diameter should be bigger when the Moon is at perigee.  Their ratio is: 0.009582 / 0.008569 = 1.1182 so about 11.8 % bigger.  This is not insubstantial but it's actually very difficult to notice by eye.