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What seems bigger: the moon, or the sun?
Viewed from the earth, the sun and the moon appear to have pretty much the same size. The apparent size (radius) is defined as arcsin(R/h) where R is the true radius of the celestial body, and h is the distance to the celestial body.
For the sun, R=695,000 km and h=150,000,000 km.
For the moon, R=1,700 km and h=300,000 km.
You would need to put 200 suns (or moons) next to each other, to create a ring of suns (or moons) stretching in the sky, from North to South, with no gap.
By contrast, you would need 300,000 times more of our closest star (outside the solar system) to create the same continuous ring of stars.
(by the way, the answer to the original question is: the moon and the sun look pretty much the same when you compute the apparent size with the arcsin formula)
For the sun, R=695,000 km and h=150,000,000 km.
For the moon, R=1,700 km and h=300,000 km.
You would need to put 200 suns (or moons) next to each other, to create a ring of suns (or moons) stretching in the sky, from North to South, with no gap.
By contrast, you would need 300,000 times more of our closest star (outside the solar system) to create the same continuous ring of stars.
(by the way, the answer to the original question is: the moon and the sun look pretty much the same when you compute the apparent size with the arcsin formula)
Replies to This Discussion
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Permalink Reply by Vincent Granville on -
It would be interesting to compute how many suns you would need to cover the entire sky, assuming the suns were cubes rather than spheres. Other than cubes, what other shapes would create a full coverage, with no empty space?
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Permalink Reply by Matt Coates on -
> the moon and the sun look pretty much the same when you compute the apparent size with the arcsin formula
...which is the reason we can experience a total eclipse with virtually perfect coverage of the sun by the moon (except when the moon is at its most distant from the Earth, resulting in an annular eclipse).
If you really want a challenge try to work out the probability of occurrence of this coincidence in apparent size for a planet with a single moon - conditional on there being intelligent life present on the planet to appreciate it!
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Permalink Reply by Andrzej Góralczyk on -
It seems not too easy for intelligent life, as we don't know what intelligence is :-). However, for the life based on proteins, let's assume:
- probability of the existence of planet with water and necessary substrates (lipids, hydrocarbons etc.) is nearly 1 (we know from the spectra of Universe "atmosphere");
- protein can exist and perform life function in certain temperature interval;
then
- the probability of the existence of proteins is about 1/3 - it follows from Bolzmann formula (distribution) and ergotic theorem.
Am I right?
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Permalink Reply by Matt Coates on
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Actually I was asking about the probability of the coincidence in apparent sun/moon size GIVEN THAT life could exist on the planet to observe it. This narrows the possibilities somewhat to just those planets of a certain size and distance from a sun (of a certain class) that would be capable of sustaining life.
Within these constraints, how likely is it that the sun and (for simplicity) a single moon would have approximately the same observed size.
Put another way, what proportion of planets capable of sustaining intelligent life could experience both total and annular eclipses, as ours does.
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Permalink Reply by Paris Granville on -
I think that the moon "seems'' bigger unless there is a lot of humidity in the air that acts as a magnifying. You would have to calculate air humidity as a factor of magnification.
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Permalink Reply by Patrick Cardiff on
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according to the lunar calendar http://kalender-365.de/lunar-calendar.php
our next full is October 4th
http://www.astromap.co.uk/full_moon_astrology_rites_rituals.htm
which will be a hunter moon. And you're right, sometimes depending on how close the moon is to the horizen in transit it can appear HUGE so I would not keep the apparent size of the moon fixed. I've seen summer moons that look like you could walk onto them from earth. Magical!
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Permalink Reply by Vincent Granville on
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Hi Patrick,
When the moon appears to be huge, it's usually due to atmospheric conditions (e.g. high humidity). The same conditions would make the sun appear equally huge: in other words, whenever a full eclipse moon/sun takes place, the moon and sun will occupy exactly the same apparent spot in the sky, regarless as to whether the moon looks normal or big.
I might be wrong, especially if space clouds between the moon and the earth magnify the moon's appearance, but not the sun. But I don't think space clouds exist in our solar system. Maybe other phenomena could cause a similar sun/moon distorsion though.
I'm sure you've also seen a huge sun at sunset, when the sun is about to vanish over the Pacific ocean, and the atmospheric conditions are right.
Vincent
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