Of course we know that the sun is several times larger than the moon and that the moon is much closer to the earth than the sun. But is it really a coincidence that these two celestial bodies appear to be the same size when viewed from Earth? (See full eclipses). What is the probability of this “perfect match”?
Answer
An intriguing question! How likely is this perfect match? Maybe our moon is the only one in the entire universe? Or are most moons like this?
Or an alternative question: Since a moon is to its planet as that planet is to its (their) sun, there is an intuitive possibility that a planet somewhere would appear as large from its moon as the sun from that same moon. But that’s another question 🙂
Incidentally, the match is not perfect at all. The Moon-Earth and Earth-Sun distances are not exactly constant. The average apparent ratio of luna (“our” moon) to the sun averages 97%, and varies between 90.5% and 104.5%.
I came across a photo of Titan (Saturn’s moon), in which she (he?) appears to be nearly the same size as the Sun, not taken from Saturn’s surface, but still…
A little geometry: When does a moon appear the same size as the sun when viewed from its planet? Answer, and for this you only need a little bit of trigonometry: when the ratio moon diameter / diameter sun is equal to the ratio planet-moon distance / distance planet-sun.
A little statistics. In the appendix you will find a table with the most large moons of our solar system. We left out the moons smaller than 100 km. In this table you will find, using the formula above, what the average apparent ratio is between each moon and the sun (penultimate column). [[In de laatste kolom staat de verhouding tussen de schijnbare grootte van elke maan en “onze maan” (luna), maar dat was niet de vraag.]]
How coincidental is the ratio 100% (or 97%)? Here we work intuitively. We list all the moons in order of their apparent lunar/sun ratio (see figure). Most of the moons appear to score between 100% and 1000%. With the outlier to the top Charon (from Pluto) with 26000%, and at the bottom a lot of micro-moons with less than 1%. Our moon (luna) is somewhere on the tail of the main pack. Not really exceptional. There could have been another moon within the 90%-110% range. And with some luck, something like a 1 in 20 chance, there could have been another one within the 97%-103% range.
In order to REALLY do statistics, they have to do this exercise again with a very large number of solar systems.
Answered by
Engineer Bart Dierickx
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