From one moon to another

By Phil Plait | June 28, 2009 7:00 am

The Big Picture once again does the International Space Station. My favorite picture? No contest:

<a href="http://www.boston.com/bigpicture/2009/06/recent_scenes_from_the_iss.html#photo7" target="_blank"The Moon, from ISS

Oh how I love this picture.

Of course I love shots of the Moon, but this speaks volumes. Note the Earth just below the Moon; the ISS was seeing the Moon through the top of Earth’s atmosphere. As you may know, light bends when it passes from one medium to another, like from water to air, which is why a spoon in a glass looks bent. The same is true when light passes from a vacuum through air; it bends. In fact, the amount the light bends depends on the angle it intercepts the boundary; so that light coming in from one direction may get bent more than if it comes in from another.

So here comes the cool part: the Earth’s atmosphere follows the curve of the Earth, so you can picture it as a thick shell of air around us. Here’s a diagram:

ISS Moon line of sight diagram

The Earth’s surface is the lower arc, and the air above the upper arc. The Moon is to the left, the ISS to the right.

The red lines indicate the line-of-sight view to the Moon. When an astronaut looks at the bottom of the Moon, the angle of the air/space boundary is a bit different than it is when he or she looks at the top of the Moon. In my diagram that angle is close to being 45 degrees for the bottom line, but is more like 30 degrees for the top line. That means the light coming from the bottom of the Moon gets bent more than the top. As it happens, the light from the Moon gets bent upward as it passes through our air… so the bottom of the Moon looks like it’s getting pushed into the top.

This squashes the view of the Moon! All of the light is getting bent, but by different amounts; the upper part of the Moon is closer to being a circle but is still distorted significantly. Making it worse, the Moon was not quite full in this picture, so the "left" side looks off, too.

What a mess! But it’s an explainable mess, and one that’s not even all that hard to do. The math is really just a bit of trig and a bit of algebra. In detail it gets more complicated, because the Earth’s air gets thinner with altitude, and I didn’t account for that. And I bet there are a hundred other variables as well.

But making some quick assumptions explains the gross characteristics of this picture just fine. And to me, that adds to my amazement of such a shot. Knowing more about it doesn’t detract from its beauty and its wonder; it enhances them.

I really love that about science. It’s easy to be awed when you don’t know how something works, but when you get a glimpse into the machinery behind it, get an idea of how it really works, what you see becomes that much more beautiful.

Comments (41)

  1. Yes, that is an astounding and beautiful picture. I keep wondering, though: is there any particular reason why the picture is upside-down (or south-side-up)?

  2. gopher65

    That’s a beautiful picture. Every time I look at it I get this jarring feeling of wrongness because the moon is non-spherical.

  3. I’ve also found that knowing the explanation behind something makes me appreciate it even more than I otherwise would have.

  4. Stone Age Scientist

    And I bet there are a hundred other variables as well.

    Yes, if I’m not mistaken, earth’s gravity also plays into the equation. Last year, I read something about the light coming from a star getting bent by a black hole, which eclipsed the star. I think that same principle could also apply here.

    Thanks for sharing this. The pic is truly beautiful, and so is the science behind it.

  5. Stone Age Scientist

    Hmmm, it’s like looking at the moon through the surface of a pond.

  6. DrFlimmer

    @ Stone Age Scientist

    Yes, indeed! But the effect around the earth is FAR (and I mean VERY far) to weak to account for something detectable. You really need a strong gravitational field to have such a “lensing” effect – a field close to a black hole.

  7. TS

    Yes, that is an astounding and beautiful picture. I keep wondering, though: is there any particular reason why the picture is upside-down (or south-side-up)?

    ISS would have been orbiting the southern hemisphere when the picture was taken.
    Them wacky Australians turn everything upside down, including astronomy pictures.

  8. Absolute agreement that understanding the underlying mechanisms enhances the beauty. Thinking of a single photon’s path from the sun, motoring across 8-and-change light-minutes of vacuum (with minor perturbations from Mercury and Venus’ gravitational fields, possibly weaving a bit from atmospheric distortion if the ray grazed Venus), bouncing off the Lunar regolith. Then a quarter-million-mile ricochet weaving through Earth’s atmosphere getting joggled by simple refraction, complex refractions from heat and moisture related density variations, particulate matter, even the different compositions of atmospheric gases before splatting into a CCD element, joggling loose an electron and resulting in a pixel.

    Shocking, amazing, wonderful.

  9. Craig Sachs

    Hi,
    It must be nice to see the Moon set from space. Like floating in the ISS Copoula (if it makes it up there) and seeing thee huge solar panels and structure with the moon setting behind it.
    Thanks for pushing the good science.

    We like the mooon cuz it is close to us.
    Craig

  10. Nick Sharratt

    It is a great picture, and I agree the science behind it adds to it.

    However, to see the moon distorted in a very similar way, I just have to look at it without wearing glasses – for a different but scientifically related reason. One evening about 10 years ago I looked up and thought “hmm, I’m sure it would have been on the news if the moon had become egg shaped! Best get my eyes checked”. The astygmatism I was then diagnosed to have gives me a very similar view of the moon to this photo (not the upsidedown bit). Of course scientifically, the effect is related due to the astygmatism being due to similar lensing effects :)

  11. @ DrFlimmer, Stone Age Scientist
    Actually, you don’t need a black hole, the Sun’s gravitational field is enough to bend light measurably. During the total solar eclipse of 1919 the light from a star viewed near the Sun was bent enough to measure the difference, and this was the first tangible proof of Einstein’s theory of general relativity.

  12. Brian H

    @zandperl

    yes, though it was later demonstrated that that particular measurement was inconclusive, as the amount of shift was actually not larger than the uncertainties in the measurement from the technique. Of course, we have since performed the measurement many times with increasing precision and found exact agreement with Einstein’s theory. Just an interesting bit of science history, and a lesson to watch out for our own confirmation biases.

    (It’s also kind of annoying that crackpots will jump on the flaws in the original experiment, but never address all the times it has been repeated with tighter uncertainty and even better results. This seems to be a pattern with crackpots vs a number of different famous experiments which reinforced GR or QM)

  13. Parkylondon

    I don’t know if this is new, but they put hot links to Google Maps to show you where each image was taken. Nice touch.

  14. Mike Wagner

    @Craig Sachs
    We like the moon! But not as much as a spoon!

    I’d forgotten about that video. Now I can have both a sense of awe and be madly giggling at the same time.

    This must be what it’s like to be Gene Wilder.

  15. wow u sure like the moon

  16. The Other Ian

    Nit: the moonlight gets bent downward as it enters Earth’s atmosphere, not upward. If it were truly upward, the moon would appear stretched, not squashed.

  17. Sili

    Personally, I love the last little ‘film’ of the aurora.

  18. Hmmm, I’m not seeing the picture. I wonder if this is another IE8 incompatibility.

  19. Tim G

    While flying at over 35,000+ feet, I once saw a deep red full moon rise above the horizon. Another thing the atmosphere does is attenuate/scatter light differentially by wavelength.

    I agree with #16. Light from the bottom of the moon bends a bit more around the Earth so when the light from the top and bottom converge at the ISS, the angle is smaller.

  20. Torbjörn Larsson, OM

    I love the graded refraction index geometry of this, even if possibly overshadowed by the curvature.

    Nit on nit: Unless I’m mistaken, by that reasoning nothing would happen but a roughly parallel translation typical of light passing a window at an angle. The upwards refraction when entering the optically denser material (so refraction angle less than incidence angle) is roughly counteracted by the downwards refraction when leaving it (so refraction angle greater than incidence angle). It’s the curvature (and graded index) that makes the difference between paths.

  21. Clifton F

    Great picture, and I agree with you that knowing how something works makes it more awesome, not less.

    Your explanation doesn’t seem quite right to me though: The light with the steeper angle, ie the bottom ray, will be bent LESS than the top one; a ray at 90 deg to the surface would not be bent at all. I think what you might have done is forgotten that the values in Snells law are the angles from normal, rather than relative to the surface.

    If we consider a ray that just grazes the top of the atmosphere, then the angle (from normal) will be ~90 deg, giving the maximum refraction. However the refractive index at this point will be very low and so there will not be much deviation.

    If we treat the atmosphere as many concentric shells of increasing density, then the lower ray will pass through more shells of higher refractive index resulting in greater deviation and explaining the observed distortion. The resulting greater number of transitions, and their larger refractive index is the key to understanding the picture. Of course one has to make the number of shells tend to infinity to get the full answer, but I think this establishes the principle.

  22. Grizzly

    Wow. Number 11 hits home because on or about the day that was taken I was back country camping the next valley south of the fire. It was a controlled burn that I think was set as a defense against the mountain pine beetle.

    If you want a GREAT cross-country ski experience, (or nice hike / mountain bike), the valley to the north runs on the south side of Mt. Rundle… from Canmore to Banff. It’s amazing. It’s also amazing to see such a beautiful part of the world from on high.

  23. KC

    >Yes, if I’m not mistaken, earth’s gravity also plays into the equation….I think that same >principle could also apply here.

    No — the effect is much too small to contribute to the ‘flattening’ of the Moon’s image shown in this photo.

  24. Wow, and it was taken on my birthday as well. I guess I’m special (along with the other 16 million people who share it).

    Can you now stand the moon on end at the equinoxes?

    BTW, I would object to the description “a thick shell of air.” Relative to the size of the body it surrounds, the Earth’s atmosphere is far thinner than the skin of an apple.

    - Jack

  25. lawyerchik1

    Hi – just stopped in to see whether you had evaluated the TV mini-series “Impact.” I truly appreciated your takes on “Deep Impact” and “Armageddon”, and I was wondering what your take was on the theory of the moon’s crashing into the earth…. Thanks!

  26. MadScientist

    I wish there were more information posted on each photograph. The moon photo is obviously a limb view and the ISS is obviously above the bulk of the atmosphere to be able to get that relatively black sky (well, the truth is we know the altitude of the ISS). However, when you look at another limb view which includes part of the earth itself, we can see the atmosphere (scattering all that blue light) as a thin shell above the earth; the atmosphere doesn’t look so thin in this moon photo. So what equipment was used and what settings?

    @lawyerchik1: moon crashing into earth seems to be a popular story – but it’s not going to happen (despite the slow degeneration of the moon’s orbit). I think the BA discussed that issue in Bad Astronomy – I’m sure you’ll enjoy reading the book. Of course a very large comet can always come along and encourage the moon to make a landing. :) It’s got to be quite a comet though to be able to impart enough energy to reduce the moon’s motion enough that it falls to earth.

  27. StevoR

    Wow. :-D

    Thanks BA, I scrolled down through all of those & my favourite of them all was the very last one (35) showing the aurora australis and the stars and the Earth’s limb and atmosphere. Awesome. Truly. Awesome.

    @ 7 TS :
    Them wacky Australians turn everything upside down, including astronomy pictures.

    Actually no you’re the ones who are “upside down” and we’ve got everything the right way round! ;-)

    There is no up or down in space! North & South are arbitrary as is the convention that “north is up” not vice versa. ;-)

    (*Waiting eagerly for the next terrestrial magnetic field reversal.*)

  28. I can’t believe no one has said it yet, so, allow me:

    That’s no moon! It’s a Space Station!

    Thank you, thank you. It had to be said.

  29. Stone Age Scientist

    Hi DrFlimmer @ #6 & zandperl @ #11,

    Yes, indeed! But the effect around the earth is FAR (and I mean VERY far) to weak to account for something detectable. You really need a strong gravitational field to have such a “lensing” effect – a field close to a black hole.

    Thanks, DrFlimmer and zandperl. When I wrote my entry, I was actually thinking along those lines, too; and also that Earth’s gravitational force is too weak to cause significant time dilations.

  30. Acronym Jim

    @16

    Nit: the moonlight gets bent downward as it enters Earth’s atmosphere, not upward. If it were truly upward, the moon would appear stretched, not squashed.

    Double-nit: if one views the pic from a land-dweller’s perspective (head tilted to the left), the Great Grey Egg does “appear” stretched.

    Does a double-nit cancel out a single-nit?

  31. DrFlimmer

    @ #34 Stone Age Scientist

    Although you are right, the earth gravitational influence on things is strong enough that it causes a measurable effect of “time delay” on satallites. In fact, the GPS satallites must all correct for effects of SR and GR in order to give a correct position!
    Without GR GPS would lead you anywhere but not where you want to ;)

  32. MarkAH

    # 16

    See crop cirlces are real….
    what??

    circular crops?? never mind :P

  33. Mal

    Awesome series of photos, thanks for the heads up BA.

    I think you need to do a blog entry on the last one though, explaining the reason the stars can be seen. There is a similar picture of the aurora circulating the web that has starts visible in it (I think it was on APOD one day), and I saw a moon hoaxer website using it as an example where we should be able to see stars blah blah…

    From memory it was just due to longer exposure time, and you could tell because the clouds were fuzzy.

  34. Robert Carnegie

    Dr Plait’s personal physician, Conrad Murray – as recommended by Michael Jackson – has him on a special exercise and painkiller regime which should enable him to get through the arduous experience of criticising [Impact]. Plus taking over Michael’s series of concerts in London.

  35. Steve V

    I was wondering about number 14, the picture of the impact crater in Arizona. I was under the impression that all impact craters were circular, but this appears to be more of a square (squarcular?). Is this do to the angle of the ISS over the ground, time, misinformation that I have?

    thanks!

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