How could aliens tell how large the universe is without our Moon?
February 24, 2025 6:49 AM Subscribe
Without the luck of having a giant moon in the sky to measure against, how could observers on another planet be able to measure the universe?
I'm fascinated by the cosmic distance ladder that humans here on Earth have built over millennia to figure out the sizes of the Earth, Moon, and Sun, and the distances between them, the other planets, the stars in our galaxy, and the rest of the universe.
It's struck me that the first few rungs of that ladder seem to depend on the existence of a moon that's not only large enough to see and measure the transit of our planet's shadow across it, but the right size to cause solar eclipses. This seems like an unusual coincidence, and makes me wonder how hypothetical extraterrestrials living on a planet like Mars, without a large moon, would be able to figure out the distance from their world to their sun. Would they have to wait until telescopes and clocks to be able to get any real sense of the scale of the cosmos? Or would they still be able, with little more than sticks, notebooks, and geometry, be able to make some reasonable estimates of that scale? If the latter, then how exactly could it be done? What's the highest rung on that alternative cosmic ladder before it merges with the one that we humans built here on Earth?
I'm fascinated by the cosmic distance ladder that humans here on Earth have built over millennia to figure out the sizes of the Earth, Moon, and Sun, and the distances between them, the other planets, the stars in our galaxy, and the rest of the universe.
It's struck me that the first few rungs of that ladder seem to depend on the existence of a moon that's not only large enough to see and measure the transit of our planet's shadow across it, but the right size to cause solar eclipses. This seems like an unusual coincidence, and makes me wonder how hypothetical extraterrestrials living on a planet like Mars, without a large moon, would be able to figure out the distance from their world to their sun. Would they have to wait until telescopes and clocks to be able to get any real sense of the scale of the cosmos? Or would they still be able, with little more than sticks, notebooks, and geometry, be able to make some reasonable estimates of that scale? If the latter, then how exactly could it be done? What's the highest rung on that alternative cosmic ladder before it merges with the one that we humans built here on Earth?
You don't need a moon but you do need other planets in your solar system.
Once, you get a Kepler to tell you how the planets move around the Solar system, you just need a transit of one of those objects across the face of the Sun and different sites on your own planet to deduce distances.
This page from ESO provides a good explainer.
posted by vacapinta at 7:29 AM on February 24 [5 favorites]
Once, you get a Kepler to tell you how the planets move around the Solar system, you just need a transit of one of those objects across the face of the Sun and different sites on your own planet to deduce distances.
This page from ESO provides a good explainer.
posted by vacapinta at 7:29 AM on February 24 [5 favorites]
[socratic:] parallax
would they still be able, with little more than sticks, notebooks, and geometry, be able to make some reasonable estimates of that scale?
if you start with a notebook of astronomical size...
posted by HearHere at 7:39 AM on February 24 [1 favorite]
would they still be able, with little more than sticks, notebooks, and geometry, be able to make some reasonable estimates of that scale?
if you start with a notebook of astronomical size...
posted by HearHere at 7:39 AM on February 24 [1 favorite]
The ancient Greeks tried using the moon to measure the distance to the Sun but if you have access to telescopes and Venus you can do it using transits and skip the moon entirely.
These days we can measure the distance to Venus and Mars directly, by bouncing radar off them.
posted by BungaDunga at 7:45 AM on February 24 [1 favorite]
These days we can measure the distance to Venus and Mars directly, by bouncing radar off them.
posted by BungaDunga at 7:45 AM on February 24 [1 favorite]
[socratic:] parallax
I was going back and forth on whether you can reach this point in measuring without knowing shorter distances, but the only relevant number is the AU for that solar system, which is always 1 for your home planet. From the cosmic distance ladder link above, it appears figuring the distance between two planets (in that case Earth and Mars) by knowing the orbital periods and measuring at different times of year could also be calculated in AUs and not smaller units. So, a lot of distances could be figured out in units of "the diameter of my planet's orbit" and trigonometry.
posted by AzraelBrown at 8:49 AM on February 24 [2 favorites]
I was going back and forth on whether you can reach this point in measuring without knowing shorter distances, but the only relevant number is the AU for that solar system, which is always 1 for your home planet. From the cosmic distance ladder link above, it appears figuring the distance between two planets (in that case Earth and Mars) by knowing the orbital periods and measuring at different times of year could also be calculated in AUs and not smaller units. So, a lot of distances could be figured out in units of "the diameter of my planet's orbit" and trigonometry.
posted by AzraelBrown at 8:49 AM on February 24 [2 favorites]
You don't need a moon but you do need other planets in your solar system.
Once you get a Kepler to tell you how the planets move around the Solar system, you just need a transit of one of those objects across the face of the Sun and different sites on your own planet to deduce distances.
This is of course true, but note that you probably need telescopes to get measurements of sufficient accuracy using this method. The paths that Venus takes across the solar disk from widely separated points on the Sun's disk are only separated by about 41 arcseconds, and the resolution of the human eye is typically around 60 arcseconds. And the paths are separated by even less if your measurements are taken even closer to each other; Alexandria & Syene probably aren't far enough apart to make a naked-eye measurement plausible.
posted by Johnny Assay at 8:54 AM on February 24 [1 favorite]
Once you get a Kepler to tell you how the planets move around the Solar system, you just need a transit of one of those objects across the face of the Sun and different sites on your own planet to deduce distances.
This is of course true, but note that you probably need telescopes to get measurements of sufficient accuracy using this method. The paths that Venus takes across the solar disk from widely separated points on the Sun's disk are only separated by about 41 arcseconds, and the resolution of the human eye is typically around 60 arcseconds. And the paths are separated by even less if your measurements are taken even closer to each other; Alexandria & Syene probably aren't far enough apart to make a naked-eye measurement plausible.
posted by Johnny Assay at 8:54 AM on February 24 [1 favorite]
Response by poster: Johnny Assay, that's a good point. One could probably get around it with one of those room-sized camera obscuras, but is building such a room really any less technologically sophisticated than a couple of lenses in a tube?
According to Wikipedia, some suggest that pinhole images were used as far back as Neolithic times, but were definitely made in classical China and Greece in the 400s BCE. So in principle, they could fall within the parameters outlined in my question. I guess it's a question of how easy it is to make a camera obscura large enough and precise enough to discern the differences in the transit paths of a planet closer to one's star. So easy, a caveman could do it? Or would the precision required imply a whole civilization of such technological sophistication that they would probably also be capable of grinding lens precise enough to make a telescope?
posted by skoosh at 2:08 PM on March 6
According to Wikipedia, some suggest that pinhole images were used as far back as Neolithic times, but were definitely made in classical China and Greece in the 400s BCE. So in principle, they could fall within the parameters outlined in my question. I guess it's a question of how easy it is to make a camera obscura large enough and precise enough to discern the differences in the transit paths of a planet closer to one's star. So easy, a caveman could do it? Or would the precision required imply a whole civilization of such technological sophistication that they would probably also be capable of grinding lens precise enough to make a telescope?
posted by skoosh at 2:08 PM on March 6
That's an interesting question. A camera obscura of given dimensions has a fundamental limit on the resolutions of its images. For a "distant source" like the sun, ray optics says that the spot on the screen will be the size of the pinhole. But if the hole gets too small, diffraction effects take over, causing the light to spread out as it passes through the hole.
For a given distance from pinhole to screen, the optimum pinhole size d is roughly where these two effects are equaly; and it can be shown that this is roughly when d is the harmonic mean of the wavelength λ of the light and the screen distance s. A "point at infinity" will then create a spot on the screen that's about double the size of the pinhole, which corresponds to an angular resolution (it works out) of approximately √(λ/s). To get this angular resolution down to 40 arcseconds (our bare minimum to take this measurement), for visible light (λ ≈ 500 nm), you would need a pinhole-to-screen distance of roughly s ≈ 50 meters ≈ 170 feet, and a pinhole diameter of about 0.5 cm ≈ 1/4".
So the challenge would not be so much creating a sufficiently small pinhole as creating a dark, light-tight space of sufficient size. And if you needed an even higher angular resolution — which you would if your observation points were not at opposite ends of the earth — the optimal angular resolution scales inversely with the square root of the screen distance. A 10-arcsecond resolution requires a chamber that's half a mile (800 m) long, which probably requires just as much technology as figuring out how to grinding lenses.
(I also don't know whether the images created at such a great distance from the screen would be perceivable by the human eye, or whether they would be too dim. There's probably a way to figure this out, but optics isn't my field of expertise and I've nerd-sniped myself enough for one morning.)
posted by Johnny Assay at 7:00 AM on March 8 [1 favorite]
For a given distance from pinhole to screen, the optimum pinhole size d is roughly where these two effects are equaly; and it can be shown that this is roughly when d is the harmonic mean of the wavelength λ of the light and the screen distance s. A "point at infinity" will then create a spot on the screen that's about double the size of the pinhole, which corresponds to an angular resolution (it works out) of approximately √(λ/s). To get this angular resolution down to 40 arcseconds (our bare minimum to take this measurement), for visible light (λ ≈ 500 nm), you would need a pinhole-to-screen distance of roughly s ≈ 50 meters ≈ 170 feet, and a pinhole diameter of about 0.5 cm ≈ 1/4".
So the challenge would not be so much creating a sufficiently small pinhole as creating a dark, light-tight space of sufficient size. And if you needed an even higher angular resolution — which you would if your observation points were not at opposite ends of the earth — the optimal angular resolution scales inversely with the square root of the screen distance. A 10-arcsecond resolution requires a chamber that's half a mile (800 m) long, which probably requires just as much technology as figuring out how to grinding lenses.
(I also don't know whether the images created at such a great distance from the screen would be perceivable by the human eye, or whether they would be too dim. There's probably a way to figure this out, but optics isn't my field of expertise and I've nerd-sniped myself enough for one morning.)
posted by Johnny Assay at 7:00 AM on March 8 [1 favorite]
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