For astronomers...I am interested in a plot of the apparent magnification effect of "horizon effect"?

Question

Can one ascertain a mathematical understanding of the optical illusion of how the moon and stars become larger closer to the horizon...

although...it is considered to be an optical illusion...one is able to see the constellations easier and closer to the horizon.

one would think that directly overhead...that the constellations seen should be the denominator
...not an earthly reference point...to "base magnification" by...

Answer 1

"i don't think so" is completely wrong here... There is a lensing effect in the atmosphere, but it actually makes things slightly smaller, and not larger. So, this has nothing to do with it.

Another interesting fact is that the moon is actually a little bit further away from you when it is on the horizon than when it is overhead. To see a diagram that shows why, look here: http://public.clunet.edu/~sjfahmie/moondist.gif

As for the moon appearing bigger because it is near trees or what have you on the horizon, that is not true either. This effect is observed in areas where there is nothing but a boring flat horizon with nothing on it.

The reason this happens is actually because the brain perceives the sky near a distant horizon to be further away than the sky that is above us. This is likely influenced by the appearance of clouds. We don't percieve the sky as a hemisphere in the sky, but more like a relatively flat layer above us. So, since the area on the horizon is further away, that part of the sky seems to be. Since the moon's apparant size is very close to the same on the horizon as it is when it is high in the sky, our brain thinks it must be larger in order to stay the same apparant size when it is (what it thinks is) much further away, so we perceive it so.

So, it is not an optical illusion. The apparant size of the moon is not bigger. It's merely a trick of the mind, a psychological thing.

Answer 2

There are two effects going on here.

For the first, when objects are very close to the horizon, the atmosphere acts like a lens and makes objects get bigger. The is why the sun looks slightly squashed when it is sitting on the horizon, with the bottom larger than the top. This effect can be measured and graphed as it relates to how light bends through dense air. I'm afraid I can't help with the exact formula, but it can certainly be calculated.

The second effect is psychological. Objects such as the Moon tend to look bigger when they are close to the horizon and in the same field of view of objects like trees and houses. The theory says because you can see things in the foreground, your brain knows the Moon must be really far away, and you tend to perceive it as larger. If the Moon is directly overhead, and you can't see any other objects in front of it, you tend to see it as smaller.

Since the second effect is all in your head, I'm not sure how you could plot it, except maybe a statistical sampling of perceived sizes from lots of people. Different people will see this differently. I personally do not see the Moon as larger closer to the horizon, but maybe that is just because I know it is not.

Of course when the Moon gets very low, it appears to get larger at the bottom the same way the Sun does.

I've never heard of either of these effects affecting sizes of stars or constellations. Stars (other than the Sun) are always just points of light, no matter how they are viewed. I would think constellations would be easier to see if they were up high in the clear.

Answer 3

This is purely a psychophysiological illusion, and has nothing to do with astronomy at all. It is a topic for psychology and physiology.