Posted on Apr 12, 2012 in Science & nature
Why do the sun and the moon both appear to be the same size? I know enough science to know they aren’t really the same size. But how does it work out that they look the same? Coincidence?
No, not really. But doesn’t it seem kind of convenient that the moon appears just large enough in the sky to cover the sun during a solar eclipse? How does that work? Isn’t the sun huge compared to the moon?
Here’s the deal: The moon has a diameter of about 3,476 km. The sun’s diameter is roughly 1,392,000 km. If you want to do the math yourself, you’re welcome to it, but that makes the sun roughly 400 times larger than the moon — 400.460 times, for you sticklers out there.
Here’s where things get fun. The sun is, on average, 149,597,870 km from Earth. The moon, on average, is about 384,400 km from Earth. Again, I’ll take care of the math here for you, so that makes the sun roughly 400 times as far from the Earth as the moon is — 389.172 times, using those mean distances.
Now, simple inference alone should be enough to tell you that makes both of those celestial bodies appear approximately the same size from Earth as a result, but if you really like math and science, then we can use a thing called angular diameter to show the apparent size of an object seen from a given position. So, using the formula:
…where 2.06 x 105 is the number of arc seconds in a radian, and make sure your distances are in the same units (i.e., km and km). This gives you an answer in arc seconds — simply divide by 60 to get an answer in arc minutes.
Now that your brain hurts, how about I just tell you that the angular diameter of the sun as seen from the Earth varies between 31.6 and 32.7 arc minutes, and the moon between 29.3 and 34.1 arc minutes.
So a lot of fancy math and words to tell you what I already told you in plain English.
Do keep in mind, the sun and moon are will rarely, if ever, appear the exact same size — due to the moon’s varying distance from the Earth and the Earth’s varying distance from the sun, their respective angular diameters won’t always sync up. But you have to admit, it’s close enough for government work.
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How fortunate to have this awesome combination of size and distance that allows us to have such spectacular things as solar eclipses both total and annular — an annular eclipse being that truly spectacular type where the moon appears just a bit smaller than the sun, leaving a brilliant ring. But… why?
According to astronomers, this phenomenon doesn’t occur anywhere else in our solar system. Does it occur in other solar systems? Maybe. We haven’t been there yet to take the measurements.
So the truth is, no one really knows what the odds are of this working out so wonderfully. Even a Vegas bookmaker would scratch his head at this one.
It’s worth mentioning, it hasn’t always been — and won’t always be — this way. The moon is moving away from the Earth by about 4 cm every year. This means that millions of years ago, there were no annular eclipses because the moon always appeared bigger than the sun. Also, this means that millions of years from now, there won’t be any total eclipses — they’ll all be annular — as the moon will always appear smaller than the sun.
Enjoy it while you can — your great grandchildren (times 100) will never know a total eclipse, except in pictures and stories.
Image above based on NASA educational drawing, showing the approximate relative size (not distance between) of the moon, the Earth and the sun. All three photos thanks to NASA and US taxpayers.
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