Is there a theoretical limit on how finely we could resolve details of a planet in another solar system? I was wondering if we might ever get a closeup of these guys some time in the future. (Let’s assume the telescope is not that much larger than the Hubble. No reflecting lenses the size of the solar system, thank you.)
Does light-based information degrade or disperse somehow such that it’s theoretically impossible to admire ET’s new solarium from 1000 light years away?
If you add the constraint that the size of the reflector is limited to Hubble-size, then yes, there’s a pretty hard limit on resolution due to diffraction.
As far as I understand it, that seems to be a limitation of current telescope technology, not the light itself?
I have no idea what it would look like, but I’m imagining some radically different distant imaging technology. So “telescope” in the title might be misleading – sorry! – if that means we must confine discussion to telescopes as we know them now.
The limit is imposed by light itself. The issue of diffraction is imposed by the diameter of the telescope (in this case the mirror diameter) and the wavelength of light. This results in the Raleigh limit of angular resolution.
ETA - this is why radio telescopes (and some optical telescopes) use multiple collectors separated by large distances. The further apart the collectors the higher the angular resolution.
The diffraction limit is a theoretical constraint on the maximum resolution achievable by an optical system of a given size, due to the nature of light.
Light coming from far away does not degrade or disperse in transit. But for any optical instrument of a fixed size, its resolution will be limited by interaction of light with the edges of the instrument (diffraction).
This is not a limit of current technology, it is a limit of all optics.
These links seem to imply that it is practically possible to construct a massive, super smooth optical telescope that could allow you to watch ET mow his lawn from a galaxy away.
Is that correct? (Given that such a telescope is beyond the means of current technology and would be massively expensive to construct)
What’s “practical”? We could draw up plans for one, sure. Maybe we could even design one that would survive tidal stress from other bodies in the Solar System. But while it’s theoretically possible, the engineering problems are centuries, maybe millennia, from from our current technology and know-how.
That could image a lawn in another galaxy? The plans would have to be for a telescope several orders of magnitude wider than the Milky Way Galaxy.
Even within our own galaxy, to image to a near neighborhood, would involve something wider than our solar system.
Unless you foresee god-like powers and FTL communication, the engineering challenges, much less the practicalities, aren’t just a few hundred or few thousands of years away from being solved.
That’s a big mirror.
I was imagining something like a planet-sized mirror, which seemed pretty crazy. A galaxy-plus sized mirror seems ludicrously beyond our means for thousands of years.
Thanks for the straight dope!
More generally, it’s a limit of any receiver of waves, be they electromagnetic, acoustic, leptons, etc.
There are formulas for lens resolution. As I recall from physics, it is highly dependent on the size of the eyepiece. The smaller the eyepiece, the higher the power, but the lower the resolution. As far I know, I believe The Hubble Space Telescope still has the best resolution for a telescope. This should give you some feel for the causes of limitation to resolution of an image.
However, it’s not crazy at all to make a telescope with a lens bigger than a planet. In theory, if you were to place a probe at the edge of the Solar System at just the right disance you could use the gravitational lensing of the sun as your lens; supposedly you could resolve a planet as far away as Andromeda that way.
First of all: sure, maybe it would be too damn big to be practical. People talk about Dyson Spheres, too, and we have no damn idea how to build them, but they’re not absolutely theoretically impossible. Besides, the OP asked not for a lawn in another galaxy, but a lawn in another stellar system. Twenty lightyears away? I don’t have any calculations in front of me, but that doesn’t seem nearly as nutty.
Second: A telescope array need not be solid. Consider the Very Large Array, a radiotelescope array which uses a group of smaller radiotelescopes. The effective resolution of the VLA is calculated by using the radius of the circle traced out by the outermost dishes on the array. By doing this, the observer sacrifices the total light-collecting ability of the array in exchange for a much greater ease of use and construction. A group of satellites (probably in orbit around the Sun, not the Earth) might be able to produce an image with an effective lens radius of thousands of miles, albeit with a rather low light-gathering ability.
To elaborate a bit–this is called interferometry. When talking about astronomy and light, it’s appropriately called astronomical optical interferometry.
There are already telescopes that use the technology every day, so it’s not a pie-in-the-sky thing. We don’t yet have planet-sized optical telescopes, but there’s no inherent reason we can’t have them.
To give you some hard numbers:
Resolution (in radians) is approximately wavelength / diameter, or:
R = λ / D
For our purposes λ is the wavelength of visible light, about 550 nm, or 5.5e-7 meters. For D let’s start with the diameter of earth, assuming orbiting satellites on opposite sides. This is about 1.28e7 meters.
So R = 4.31e-14 radians. We then multiply by the distance to our target (using the sin(x)=x approximation) of 1000 light-years, or 9.46e18 meters to get about 408 km resolution.
That’s not exactly someone’s backyard, but you’ll see the large-scale geography pretty well. A 32x32 icon-size image of earth is in the same ballpark.
If instead you put a pair of telescopes at Earth’s L4 and L5 Lagrangian points, you could potentially see down to 20 meters resolution. That’s starting to be pretty respectable, though I think the resolution increase is only in one dimension–for a 2D image you’d need more telescopes spread out along the orbit, and would only see well for planets more or less directly above or below the orbital plane.
To do interferometry, don’t you need to position the mirrors with wavelength precision?
More or less. For radio telescopes this is easy, since the wavelengths are so long. They can actually just record a timestamp with the data, store it, and then combine the data much later.
It’s harder for optical frequencies, and so the systems I’ve read about use long optical guides with adjustable mirrors, so that they can tweak how the images are combined.
They probably won’t be able to do that in space, but maybe some other system is possible. Fortunately, space makes a very stable platform, despite the large distances.