Perfect Eclipse
Doug writes:
Can we calculate a probability for that coincidence?
Calculating the angle the Moon is seen to cover and the angle the Sun is seen to cover with simple trig, we find that they are very close, with a ratio of about 99% Moon:Sun.
If we take the data for the other 22 moons in the solar system, as seen from their planet's surface, we find a spread of data from 0.1029 moon:Sun viewable angle for Mars' tiny moon Deimos to 26.53 for Neptune's large moon Triton.
If we plot the 23 data points, there is no particular pattern that emerges, as we should expect. So we might reasonably assume a rectilinear distribution of $\frac{1}{26.53 - 0.1029} = 0.03784$ distribution height.
So we have to ask what range of moon:Sun visible ratios would give this amazing effect?
Our ratio is about 99%, so perhaps if we doubled the range, and allowed it to vary either side, we might assume this would be a reasonable range. This gives us bounds of 0.98 to 1.02, a range of 0.04. If we multiply this by our distribution height, we find that the probability of a moon:Sun ratio falling within this range is $0.03784 * 0.04 = 0.00151$.
This of course treats all areas of the distribution as equal, and does not account for the "specialness" of the range we are looking at. So we should probably consider this probability an upper limit.