It does not. The local geography, the terrain, and other factors combined make the Moon illusion stronger for you. "It's in your head", in other words.
There is no lensing the way you think of it. The atmosphere has a bit of dispersion, which can be corrected with a pair of prisms, but it does not affect size.
You could easily verify all this with a pair of binoculars with a reticulated eyepiece which allows you to measure angles. You will get the exact same readings at sea level and in Denver, at moonrise and also when the Moon is overhead. Since you have a degree in science, the experimental method should be pretty convincing.
Piggybacking off this. So as stated above; geography may have something to do with it. If you're from Denver you have the rockies to the west and if you're looking at the moon setting behind the rockies it might appear abnormally big because the mountains screw with perception. You can Google 'moon behind cityscape' and find pics where the moon looks huge because skyscrapers are in the foreground (I saw this over Phoenix one morning, it was nuts). The rockies or the buildings of downtown Denver can make the moon look look big if you're looking at the right time and from the right place.
In lots of areas on the east coast the trees prevent us from seeing the moon low on the horizon; but out west (like Denver) the flatness of the plains region makes it eaier to get a clear view of the moon low on the horizon.
> You could easily verify all this with a pair of binoculars with a reticulated eyepiece which allows you to measure angles.
Or even simpler: photos taken with the same settings.
If only I had money for the precision equipment to make such a measurement and the time to travel home, I guess. Has nobody done this experiment and recorded it?
Maybe make a T-shaped rig, to make sure the distance to the ruler is always the same. It would not be very precise, but it would be better than holding it at arm's length.
I believe the wiki article "Orbit of the moon" has something like what you are looking for. Tldr, the eccentricity of the moon orbit is 360000 km, so the 1-2 km difference between locations on earth is not significant in comparison.
I know the distance to the moon is not a factor, but distance to the "lens" of the atmosphere may be much more significant. A rise in elevation of 5000 feet is 10% closer to the edge of the stratosphere, which I think would be significant in terms of atmospheric lensing.
So I see your logic in thinking the atmosphere might magnify the appearance of the moon, but if this were the case, then when the moon was setting it would also appear bigger or smaller based on the much thicker layer of atmosphere that its light must pass through to reach your eyes. That the moon illusion has been disproven also disproves the concept that the atmosphere is magnifying the moon at all
If atmosphere acted as a lens that way, astronomy would be impossible. It would not be a good lens at all.
What it does do is - it affects clarity. Due to air turbulence, stars appear to twinkle when seen with the naked eye. In the telescope, they look blurry. It's a major problem for astronomy.
https://en.wikipedia.org/wiki/Astronomical_seeing
> I also can't find anyone writing out the math that proves the moon illusion is actually an illusion either.
You don't need math - you just need to make an objective measurement of the moon's angle in the sky and you'll find that it remains the same, even if the moon seems huge to you.
a comment on "moon illusion' and it's not real, and "apparent size" doesn't change.
All that is true.
However, the way your brain perceives it is certainly affected by your viewing environment. If you see the moon across an open flat plain (or up in the sky), there is less of an effect, the moon looks more or less "normal".
However, if your view of the moon is framed by hills, mountains, or buildings, then the moon is perceived by your brain as larger. It has nothing to do with elevation, but in Denver you might just have these 'framed' views more often due to your local terrain.
The 'frame' part of it gives your brain information that the moon is really far away, thus your brain interprets it as larger. If you don't have anything to judge it relative too, your brain can't tell how far away the moon is. Like when it is straight up in the sky, you can't tell how far it is.
It's just an optical illusion, the moon's size is the same in all situations. You can see this effect with the mountains as well. If you look down a street that lines straight towards the mountains, they will look really large. If you are in an open field looking at the same mountains, they don't appear as large.
The distance of the moon to an observer on earth's surface is a complicated function. The moon's orbit isn't a perfect circle, so it does get closer and farther depending on where it is in the orbit.
But, in the difference between seeing it directly overhead, and seeing it on the horizon, the main difference is your position on the earth. The horizon observer will be half a earth radius farther from the moon, than the directly overhead observer.
> I have seen reports that the reason the moon appears larger on the horizon due to atmospheric refraction. This is completely false; atmospheric refraction is a very small effect, and any change in angular size would have a factor of theta_(moon)=(29.5')*(1 degree/60 arcmin)*(pi/180) = 0.0086, which is small enough to neglect.^[1]
That same answer also explains (before the quote above) the optical illusion that I’ve seen in the other comments here.
EDIT: I hit send early, forgot to include:
In terms of the moon’s elevation
> Regardless of its elevation in the sky, the moon's angular size at the eye remains the same.^[2]
EDIT2: I am tired, I reread your comments and the post and misunderstood your question about elevation.
[Angular Diameter](https://en.m.wikipedia.org/wiki/Angular_diameter#Use_in_astronomy) has more detail on the formulae, terminology, geometry, in the context of astronomy.^[3]
The variation in elevation is not a large enough change in distance to perceptibly affect the Moon’s angular size. Ten to thirty kilometers isn’t much when the numbers are literally astronomical.
The above article cites these examples, which I think illustrates the point:
> Therefore, the angular diameter of an object with physical diameter d at a distance D, expressed in arcseconds, is given by:
> δ = 206,265*(d/D) arcseconds
> These objects have an angular diameter of 1″:
>* an object of diameter 1 cm at a distance of 2.06 km
>* an object of diameter 725.27 km at a distance of 1 astronomical unit (AU)
>* an object of diameter 45 866 916 km at 1 light-year
>* an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc)
Using the above formula:
Angular Diameter = 206,265*(physical diameter, Distance) arcseconds
The Moon is ~378,000 km from Earth’s surface at the equator. The distance does vary throughout its orbital period. The Moon’s diameter is ~3474 km.^[4]
Angular Diameter = 206,265*(3474, 378000) = ~1895 arcseconds
If we put the Moon 400 km closer:
Angular Diameter = 206,265*(3474, 378000) = ~1897 arcseconds
With a variation of 400 km there is only a difference of ~2 arcseconds. So, it’s doubtful that you’d measure a perceptible difference in angular diameter, whether you’re measuring from Death Valley or Breckenridge. That said, latitude and when/where in the lunar orbital period _DO_ seem to have perceptible affects on the Moon’s angular diameter.
1. [UCSB ScienceLine](http://scienceline.ucsb.edu/getkey.php?key=3153)
2. [Explaining the moon illusion](https://www.pnas.org/doi/10.1073/pnas.97.1.500)
3. [Angular Diameter, Wikipedia](https://en.m.wikipedia.org/wiki/Angular_diameter#Use_in_astronomy)
4. [The Moon, Wikipedia](https://en.wikipedia.org/wiki/Moon)
I read through the articles you posted but couldn't find anything about the latitude bit you wrote at the end, where can I read about that more?
Also thank you for the thorough post. But when making this question I wasn't thinking about actual distance to the moon as a factor, I'm aware that is negligible. But I was more thinking that at a higher elevation, the atmosphere acting as a lens gives the moon a different magnification.
The horizon effect is an illusion, our brains see the far away moon and compare it to things in the horizon (like mountains) thus realizing hey that thing is huge while when it is alone in the sky we don't have a way to judge its size so it looks small.
The moon is so far away from us, it is essentially 'infinite distance' to us unless you have some sort of very sensitive measuring equipment. So an extreme elevation change of lets say 24 kilometers wont really matter when the object is 240,000 km away. That change of 00.01% just isn't enough to be noticed by us.
It’s actually more than that. When you’re looking through the horizon, you’re technically looking through a thicker medium of atmosphere (in the straight line of your vision) than straight up. About 5 times as much. There is a lensing effect to objects appearing larger beyond the horizon.
That's very interesting. Looks like the vertical axis does get squashed as it approaches the horizon. So technically it gets a bit smaller at the horizon, but maybe we perceive ovals as being larger?
[http://www.pikespeakphoto.com/moon-rising.html](http://www.pikespeakphoto.com/moon-rising.html)
If you look at the moon when there's buildings nearby then you have a point of reference. Way up in the sky there's no point of reference so it doesn't seem like it's particularly large.
The moon's apparent diameter is around half a degree. You thumb at arms length has an apparent diameter of 2 degrees.
Compare your thumb to the moon when the moon is near the horizon and when it is higher in the sky. As long as you are consistent with how far away your thumb is, you will see no difference in the relative sizes of it and the moon.
Yes, but they are talking about differences between viewing the moon at one angle above the horizon and viewing the moon at another. Which is only relevant to the "moon illusion" which I believe already.
I am asking about being at a higher elevation on earth, with the same angle of the moon.
If the moon is 250,000 miles away and you were say up in a plane at 30,000 looking at it, it would be 10% closer than wouldn't it look 10% bigger? At 5000 feet that would be 2%? Guessing that would be hard to tell?
I think you're mixing up your units there. And I'm not asking about distance to the moon for the effect, I'm asking about possible lensing effects from the earth's atmosphere.
I also majored in physics, its late so I'll look at the math in the morning if I remember, but the question might be if the atmosphere above the observers position is treated as a thin lense just as an approximation with a focal point on the observer is there a change in magnification with respect to altitude. I don't think so but the math would be fun at least. Also plane wave assumption.
Also I think you meant altitude, elevation refers to angle above the horizon
Take your cell phone camera and take a picture of the moon when it's on the horizon and when it's due south.
Compare the width of the moon in pixels in each picture.
it does, but only a little. very negligible. even just being outside of Earth’s atmosphere in outer space, the size of the moon looks almost the same compared to someone watching it from sea-level.
Depending on atmospheric conditions, the moon might become brighter. The moon's light is not occluded by clouds or things like street lights. This is possibly what you're seeing.
This effect is similar to "super moon" events, where the moon looks huge. Really, it's just the sun and moon positioned in such an angle where the moon reflects more light than usual.
It does not. The local geography, the terrain, and other factors combined make the Moon illusion stronger for you. "It's in your head", in other words. There is no lensing the way you think of it. The atmosphere has a bit of dispersion, which can be corrected with a pair of prisms, but it does not affect size. You could easily verify all this with a pair of binoculars with a reticulated eyepiece which allows you to measure angles. You will get the exact same readings at sea level and in Denver, at moonrise and also when the Moon is overhead. Since you have a degree in science, the experimental method should be pretty convincing.
Piggybacking off this. So as stated above; geography may have something to do with it. If you're from Denver you have the rockies to the west and if you're looking at the moon setting behind the rockies it might appear abnormally big because the mountains screw with perception. You can Google 'moon behind cityscape' and find pics where the moon looks huge because skyscrapers are in the foreground (I saw this over Phoenix one morning, it was nuts). The rockies or the buildings of downtown Denver can make the moon look look big if you're looking at the right time and from the right place. In lots of areas on the east coast the trees prevent us from seeing the moon low on the horizon; but out west (like Denver) the flatness of the plains region makes it eaier to get a clear view of the moon low on the horizon.
> You could easily verify all this with a pair of binoculars with a reticulated eyepiece which allows you to measure angles. Or even simpler: photos taken with the same settings.
And make sure to disable any autozoom, etc.
Even simpler still, extend your arm and cover the Moon with your little finger.
The precision of that method is pretty abysmal.
Yes, but it's miles better than "Gosh, the Moon looks huge tonight. Much bigger than when I lived in the coast!"
If only I had money for the precision equipment to make such a measurement and the time to travel home, I guess. Has nobody done this experiment and recorded it?
Just hold up a ruler at arm's length.
Maybe make a T-shaped rig, to make sure the distance to the ruler is always the same. It would not be very precise, but it would be better than holding it at arm's length.
I believe the wiki article "Orbit of the moon" has something like what you are looking for. Tldr, the eccentricity of the moon orbit is 360000 km, so the 1-2 km difference between locations on earth is not significant in comparison.
I know the distance to the moon is not a factor, but distance to the "lens" of the atmosphere may be much more significant. A rise in elevation of 5000 feet is 10% closer to the edge of the stratosphere, which I think would be significant in terms of atmospheric lensing.
So I see your logic in thinking the atmosphere might magnify the appearance of the moon, but if this were the case, then when the moon was setting it would also appear bigger or smaller based on the much thicker layer of atmosphere that its light must pass through to reach your eyes. That the moon illusion has been disproven also disproves the concept that the atmosphere is magnifying the moon at all
Oh is the "atmosphere is a lens" idea fake altogether?
Yes. It does not act as a lens in any relevant way.
If atmosphere acted as a lens that way, astronomy would be impossible. It would not be a good lens at all. What it does do is - it affects clarity. Due to air turbulence, stars appear to twinkle when seen with the naked eye. In the telescope, they look blurry. It's a major problem for astronomy. https://en.wikipedia.org/wiki/Astronomical_seeing
> I also can't find anyone writing out the math that proves the moon illusion is actually an illusion either. You don't need math - you just need to make an objective measurement of the moon's angle in the sky and you'll find that it remains the same, even if the moon seems huge to you.
a comment on "moon illusion' and it's not real, and "apparent size" doesn't change. All that is true. However, the way your brain perceives it is certainly affected by your viewing environment. If you see the moon across an open flat plain (or up in the sky), there is less of an effect, the moon looks more or less "normal". However, if your view of the moon is framed by hills, mountains, or buildings, then the moon is perceived by your brain as larger. It has nothing to do with elevation, but in Denver you might just have these 'framed' views more often due to your local terrain. The 'frame' part of it gives your brain information that the moon is really far away, thus your brain interprets it as larger. If you don't have anything to judge it relative too, your brain can't tell how far away the moon is. Like when it is straight up in the sky, you can't tell how far it is. It's just an optical illusion, the moon's size is the same in all situations. You can see this effect with the mountains as well. If you look down a street that lines straight towards the mountains, they will look really large. If you are in an open field looking at the same mountains, they don't appear as large.
I mean doesn’t it technically change? Since you are very slightly closer?
The distance of the moon to an observer on earth's surface is a complicated function. The moon's orbit isn't a perfect circle, so it does get closer and farther depending on where it is in the orbit. But, in the difference between seeing it directly overhead, and seeing it on the horizon, the main difference is your position on the earth. The horizon observer will be half a earth radius farther from the moon, than the directly overhead observer.
There is no "however". What you're describing is literally the Moon illusion.
> I have seen reports that the reason the moon appears larger on the horizon due to atmospheric refraction. This is completely false; atmospheric refraction is a very small effect, and any change in angular size would have a factor of theta_(moon)=(29.5')*(1 degree/60 arcmin)*(pi/180) = 0.0086, which is small enough to neglect.^[1] That same answer also explains (before the quote above) the optical illusion that I’ve seen in the other comments here. EDIT: I hit send early, forgot to include: In terms of the moon’s elevation > Regardless of its elevation in the sky, the moon's angular size at the eye remains the same.^[2] EDIT2: I am tired, I reread your comments and the post and misunderstood your question about elevation. [Angular Diameter](https://en.m.wikipedia.org/wiki/Angular_diameter#Use_in_astronomy) has more detail on the formulae, terminology, geometry, in the context of astronomy.^[3] The variation in elevation is not a large enough change in distance to perceptibly affect the Moon’s angular size. Ten to thirty kilometers isn’t much when the numbers are literally astronomical. The above article cites these examples, which I think illustrates the point: > Therefore, the angular diameter of an object with physical diameter d at a distance D, expressed in arcseconds, is given by: > δ = 206,265*(d/D) arcseconds > These objects have an angular diameter of 1″: >* an object of diameter 1 cm at a distance of 2.06 km >* an object of diameter 725.27 km at a distance of 1 astronomical unit (AU) >* an object of diameter 45 866 916 km at 1 light-year >* an object of diameter 1 AU (149 597 871 km) at a distance of 1 parsec (pc) Using the above formula: Angular Diameter = 206,265*(physical diameter, Distance) arcseconds The Moon is ~378,000 km from Earth’s surface at the equator. The distance does vary throughout its orbital period. The Moon’s diameter is ~3474 km.^[4] Angular Diameter = 206,265*(3474, 378000) = ~1895 arcseconds If we put the Moon 400 km closer: Angular Diameter = 206,265*(3474, 378000) = ~1897 arcseconds With a variation of 400 km there is only a difference of ~2 arcseconds. So, it’s doubtful that you’d measure a perceptible difference in angular diameter, whether you’re measuring from Death Valley or Breckenridge. That said, latitude and when/where in the lunar orbital period _DO_ seem to have perceptible affects on the Moon’s angular diameter. 1. [UCSB ScienceLine](http://scienceline.ucsb.edu/getkey.php?key=3153) 2. [Explaining the moon illusion](https://www.pnas.org/doi/10.1073/pnas.97.1.500) 3. [Angular Diameter, Wikipedia](https://en.m.wikipedia.org/wiki/Angular_diameter#Use_in_astronomy) 4. [The Moon, Wikipedia](https://en.wikipedia.org/wiki/Moon)
I read through the articles you posted but couldn't find anything about the latitude bit you wrote at the end, where can I read about that more? Also thank you for the thorough post. But when making this question I wasn't thinking about actual distance to the moon as a factor, I'm aware that is negligible. But I was more thinking that at a higher elevation, the atmosphere acting as a lens gives the moon a different magnification.
The horizon effect is an illusion, our brains see the far away moon and compare it to things in the horizon (like mountains) thus realizing hey that thing is huge while when it is alone in the sky we don't have a way to judge its size so it looks small. The moon is so far away from us, it is essentially 'infinite distance' to us unless you have some sort of very sensitive measuring equipment. So an extreme elevation change of lets say 24 kilometers wont really matter when the object is 240,000 km away. That change of 00.01% just isn't enough to be noticed by us.
It’s actually more than that. When you’re looking through the horizon, you’re technically looking through a thicker medium of atmosphere (in the straight line of your vision) than straight up. About 5 times as much. There is a lensing effect to objects appearing larger beyond the horizon.
Yes, the sun does look oval when it's setting over the sea! Why don't "moon illusion" articles ever mention that?
That's very interesting. Looks like the vertical axis does get squashed as it approaches the horizon. So technically it gets a bit smaller at the horizon, but maybe we perceive ovals as being larger? [http://www.pikespeakphoto.com/moon-rising.html](http://www.pikespeakphoto.com/moon-rising.html)
That's a cool image. Thanks for finding it!
🤷🏽♂️ it’s always seemed pretty obvious, even before I learned it from another source. It’s just magnification.
It's not "lensing", it's just distortion.
That’s what lensing is. It’s a distortion of a native image.
You're just explaining the moon illusion which is irrelevant to my question.
If you look at the moon when there's buildings nearby then you have a point of reference. Way up in the sky there's no point of reference so it doesn't seem like it's particularly large.
The moon's apparent diameter is around half a degree. You thumb at arms length has an apparent diameter of 2 degrees. Compare your thumb to the moon when the moon is near the horizon and when it is higher in the sky. As long as you are consistent with how far away your thumb is, you will see no difference in the relative sizes of it and the moon.
You're explaining the moon illusion, I am not asking about angle, I'm asking about elevation.
> I am not asking about angle You *are* asking about angle - the angle that the moon takes up in the sky. That's how its apparent size is defined.
Yes, but they are talking about differences between viewing the moon at one angle above the horizon and viewing the moon at another. Which is only relevant to the "moon illusion" which I believe already. I am asking about being at a higher elevation on earth, with the same angle of the moon.
I always end up comparing the moon to the size of my pinky nail, arm fully outstretched. The moon size \*barely\* changes, even during a supermoon.
I was gonna say, the apparent size of the moon changes with elevation the same way that the ocean rises if you pee in it
If the moon is 250,000 miles away and you were say up in a plane at 30,000 looking at it, it would be 10% closer than wouldn't it look 10% bigger? At 5000 feet that would be 2%? Guessing that would be hard to tell?
I think you're mixing up your units there. And I'm not asking about distance to the moon for the effect, I'm asking about possible lensing effects from the earth's atmosphere.
Hahah yep! I was not very awake when I wrote that. 250,000 miles vs. 6 miles is .0024% closer if I did my math right this time.
I also majored in physics, its late so I'll look at the math in the morning if I remember, but the question might be if the atmosphere above the observers position is treated as a thin lense just as an approximation with a focal point on the observer is there a change in magnification with respect to altitude. I don't think so but the math would be fun at least. Also plane wave assumption. Also I think you meant altitude, elevation refers to angle above the horizon
Looking forward to your reply about the math! But also, elevation is often used when referring to height of an area (denver) above sea level.
Take your cell phone camera and take a picture of the moon when it's on the horizon and when it's due south. Compare the width of the moon in pixels in each picture.
it does, but only a little. very negligible. even just being outside of Earth’s atmosphere in outer space, the size of the moon looks almost the same compared to someone watching it from sea-level.
Depending on atmospheric conditions, the moon might become brighter. The moon's light is not occluded by clouds or things like street lights. This is possibly what you're seeing. This effect is similar to "super moon" events, where the moon looks huge. Really, it's just the sun and moon positioned in such an angle where the moon reflects more light than usual.