Spying on another star system

Question

I want to find out what's going on in another star system, but I don't want to go there. How feasible is it to just build a big telescope and take a look?

Scenario: Earth does not respond to communications any more, and nobody who enters the system leaves again. Is it physically possible to build a telescope, presumably a multi-part array type thing, at Alpha Centauri that could resolve human-scale objects (anywhere between "people themselves" and "aircraft carrier") and give me some idea of what is going on on-and-around Earth?

I assume the primary obstacle is something something signal diffusion meaning that a clear image of small objects doesn't actually survive the distance, or if this isn't the case, coordinating the movements of the telescope's component satellites over what is presumably a large orbital separation within the Alpha Centauri system.

Answer 1

Maybe. Probably not people. And not without some incredibly fine control and gobs of computing power. The hard limit is atmospheric conditions on Earth.

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According to the Rayleigh criterion, the resolution of a circular collector is a function of wavelength, diameter and distance.

resolution = 1.22 x wavelength x distance / diameter

To detect individual humans from above, let's say we want 50 cm resolution. Alpha Centauri is 4.3 light years away. The Earth's atmosphere is pretty transparent to visible light. How big does the mirror have to be?

diameter = 1.22 x wavelength x distance / resolution

diameter = 1.22 x ~500nm x 4.3 light years / 50 cm

Your telescope has to be 4 light minutes in diameter or half the diameter of the orbit of the Earth. Oh dear. That's ok, all is not lost!

Fortunately you don't have to make bigger and bigger mirrors to get the job done. Others have mentioned multiple array telescope concepts. It can get weirder.

SciShow recently did a piece on space telescope concepts to drastically improve resolution without having to build bigger and bigger mirrors. One is a giant umbrella which would take advantage of the diffraction of light waves around the edge of an object to focus the light.

The other is to carefully position glitter ... sorry... "smart dust" to form a giant mirror in space out of what are essentially tiny reflective pixels. The light pressure from lasers would be used to carefully nudge the particles into position and keep them there.

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Then you have the problem of focusing a planet going around the Sun at 30 km/s in a elliptical orbit. That means you don't just track it in a straight line, you have to track the curve of the orbit as well. Once you do that, you have to track a person on the surface rotating at 450m/s, again curved. The math isn't that hard, and since you're so far away you have to turn your telescope very little, but the minute and constantly changing motion of your telescope required is extremely difficult to resolve down to a few meters.

This is why we don't point the Hubble at the Earth. DSCOVR, the recently launched telescope we do intend to point at the Earth, will sit at the Sun-Earth L1 point 1.5 million km away and is only intended to do atmospheric readings.

Fortunately for our 4 light minute wide space telescope, this is all predictable! Each piece can focus their local element individually without having to communicate with the rest of the telescope. No internal FTL communication required.

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Atmospheric conditions are your ultimate limiting factor, the problem of atmospheric haze. Even on the clearest day, the atmosphere reflects and diffuses light making your image fuzzy no matter what you do. This is part of the reason we put telescopes in space. But it is mostly transparent to certain wavelengths. Visible light is one. Microwaves are much better, but humans and aircraft carriers don't emit microwaves. Also the longer your wavelength (microwaves are pretty long) the lower your resolution.

Scientists have been studying the problem of how to get good resolution through an atmosphere for a long time and have come up with some very, very clever ways to overcome the problem. The whole is covered under adaptive optics. But that's for looking out from inside the atmosphere. We want to look in.

Fortunately we don't have to run the numbers, we have had spy satellites which can do this since the 60s and 70s. They're good enough to see aircraft carriers and people through the atmosphere, a sufficiently large array at Alpha Centauri probably is, too. But I don't have the numbers.

The other place to look for information is in speculation about viewing exoplanets.

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You will be seeing 4.3 years into the past. You might think "great, then I can see whatever caused the Earth to stop communicating years ago", no. Information can only travel at the speed of light, so your information that there is a problem on the Earth would also be 4.3 years old. Even if at the moment you realized there's a problem on Earth you swung your super telescope to look, you'd still have missed the event. Best you can do is see the aftermath.

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What you can definitely do is gather data to theorize about what happened. For example, if you see a lot of atmospheric dust that could indicate meteor strike or nuclear war. Spectral analysis could tell you if there's a sudden increase in any elements in the atmosphere. Changes in albedo could tell you similar things. Color shifts could tell you if there was a massive plant die off (or if it goes the other way, Triffid attack). This is how we make guesses about exoplanets right now, just from a few smudged pixels.

With all that time and effort to get what will probably be a hazy image of what happened 4 years ago (plus time to make and focus the telescope), it might be best to just pack up the family car and take a road trip. Of course by then it will have been at least 8 years. But at least you can pick up souvenirs.

Answer 2

Use Multiple Satellite Imaging.

NASA has already planned a "Planet Finder." The basic idea is that the more telescopes you point at a place the finer image you get, enabling you to zoom in more....I suppose you could set up a system of thousands (maybe hundreds of thousands or millions, but I don't have time to do the math) and see the surface of a planet.

Rig them up in the outer reaches of the Alpha Centuri System and you can probably zoom in to a huge degree. The biggest problem I see is that you won't have a clear idea of what is actually happening as Alpha Centuri is 4.367 light years away. If you have the ability to reach alpha centuri in a timely manner then it would probably be easier to send a small team and have them send a signal back (assuming you have figured out how to instantaneously communicate with other star systems)

Answer 3

Realistically speaking, I see four major problems with your situation.

1. Alpha centauri is 4.3 lightyears form Earth. so you should see what happens 4 year earlier. Which can actually make for a pretty interesting concept.

2. The second big problem is that the telescope needs to stay fixed on earth (or worse, on a particular city). As you pointed out in your question. This feat seem almost impossible considering the distance, as a fraction of a degree would spell the difference between looking at Earth and looking at Pluto. But it is theoretically possible.

   Distin's idea of using many telescope might help on that regard. As the redundancy could be used to recalibrate the telescopes in real time, cover for errors and reconstruct a better image afterwards.

3. The last point concerns seeing through the atmosphere. The reason Hubble is located in space is that the atmosphere blurs image. This, along with point number 2, would probably make seeing a distinct city completely impractical. This would probably also prohibit the use of many telescopes like Dustin proposes. This site explains it quickly. This is not really a problem if you wish to see what's happening in space.

4. The telescope would need to be incredibly powerful to clearly see all the way to Earth. Which also implies it would be incredibly massive. Today's telescope do not allow us to see any kind of details of something smaller than a star. I'm afraid I can't give more precise guess at how big it would need to be. Dustin's idea makes this point a little better as the individual telescopes can be smaller.

More powerful telescopes need to be bigger and/or longer. Diagrams on this site shows a few ways how telescopes are made shorter. Yours could probably be the size of a small moon by itself. If you want to build such massive tool, the only realistic way would probably be a liquid mirror telescope.

Where the mirror is a rotating pool of reflective liquid. Those are used in the real world because a curved mirror of this size has higher risk of breaking under it's own weight. In your case, this is not as important as you would realistically be in space. But the size of the required mirror (and lenses) make those hard to craft in the first place. Either because they need to be crafted in space or because you need a massive amount of material to craft it.

In summary, building such a telescope might be possible and pretty interesting. Using it to see clearly enough in space would be theoretically possible but extremely complex and probably would not detect something smaller than a small moon. Going through the atmosphere is so complex that it seems simply impossible to me.

Answer 4

Here's another take on showing just how improbable it is to actually see a planet the size of Earth with any kind of clarity. I'll use existing telescope information to get an idea of the power of future tools. Then I'll look at the kind of magnification we need to see Earth.

The bottom line is that you'd need much better technology than what we have now (or custom epic-scale hardware) and you probably wouldn't realistically get the level of details you expect.

Bear in mind that I am in no way a telescope expert (these researches actually taught me a thing or two) and my knowledge of the finer details of telescope working is lacking.

What we can see now

I'll use Hubble as a point of comparison for image quality. The James Webb telescope is meant as the next space telescope, with launch due in 2018. According to the link, Webb is 17 times larger, has a collecting area 7 times larger. For a field of view 15 times larger and a "significantly better spatial resolution than is available with the infrared Spitzer Space Telescope". I know that we can't equate the field of view with resolution. But I'll assume it can translate relatively well if the telescope was made specifically for resolution.

From that, I'll assume that raw power of your telescopes to be around 50 times stronger than Hubble.

How to detect an exoplanet

Even without catching details, how can we just confirm that Earth still exists?

Turns out that most exoplanets are indirectly detected instead of actually being seen. There is, however, a list of directly imaged planets. The good news is that some are a lot farther than Alpha Centauri. The bad news is that the smallest is above Jupiter size.

Moreover, if you look at the pictures of those planets. All we can see are speck of light. This and this picture are among the clearest I've found. This view of Beta Pictoris b is annotated and can give you an idea of the scale we're dealing with.

If those images were magnified 100 times because of technological advancements, we could definitely "see" Jovian planets. But Earth-like planets would look like current images at best.

Possible but unrealistic

In the end, the magnification needed makes it theoretically possible to see what's happening in space. It would be possible if:

• What's happening is on the scale of Jupiter or a Dyson sphere. This object would be visible in the same way exoplanets or secondary stars are visible.
• What's happening emits a distinct form of radiation. Maybe a pattern is visible in non-visible light or it emits a special kind of radiation. This is basically how we detect neutron stars.
• Your society is much more advanced than we are.
• I underestimate how much of an effect a telescope swarm might have.

On top of that, if you decide you can see what's happening. Considering the distances involved, the smallest shake on the telescope would go off Earth. so that your final images would probably be the few good images that happened to showcase Earth. You couldn't really get a "film" if you had that in mind.

In the end, if I was your characters, I'd try to launch a series of probes in a hit'n'run : come in, take a clip of what's happening, get out. Repeat until you know what's happening or until the probes don't come back. This might require having an independent launching station/ship between Alpha and Earth.

The challenge of synchronizing a telescope swarm

I have added this section as I think it's the kind of information you want if you go ahead with this. But it's not the biggest problem. I don't really know what kind of performance you can get from a telescope swarm.

First of all, why would you want to synchronize telescopes? The main point would be to make them move as one and align them on the same object. Earth is a moving target after all.

As a starting point, the Webb telescope will be located at the Lagrangian point (L2), which is 1.5 million km from Earth but relatively close. There is a 5 second delay between Earth and L2, making synchronization impossible without FTL communication (which may or may not be acceptable for you).

This means that you can have a synchronized swarm of telescope in the same area of space, but it's simply impossible to have a swarm spanning the whole solar system. You could, however, collect separate data from multiple point of view in the solar system and reassemble them later.

Answer 5

Requirement:

"Build a telescope [...] at Alpha Centauri that could resolve [$1-100~\text{m}$] objects"

You are correct in assuming that "the primary obstacle is something something signal diffraction"

The way to think about diffraction is something like this. Imagine a wave of light headed towards you. If the wave hits one side of your telescope before the other, then you know that it must have come slightly to the side of where you are pointing. However, if the angle is so small that the difference in between when the wave hits each side of the telescope is less than the wavelength, then you can't tell that one hit before the other. You can only get around this by making your telescope larger to exaggerate the difference.

Although the precise number depends on the shape of the telescope, the minimum diameter required can be approximated by:

$$ D = \frac{\lambda d}{b} $$

Where $d$ is the distance to the target, and $b$ is the desired resolution. We can plug in some estimates for the quantities, assuming that the distance is from Earth to the Alpha Centauri binary, the resolution is typical for Earth-observing satellites, and a wavelength in the middle of the visible spectrum:

$$ \begin{align} D &= \frac{500~\text{nm}\times 4.3~\text{ly}}{15~\text{m}} \\ &= 1.4\cdot 10^6~\text{km} \\ &\approx 0.01~\text{AU} \end{align} $$

The required size scales inversely with the resolution. To get the same $0.5~\text{km}$ resolution as a next-generation geostationary imaging satellite the required size is only $42\,000~\text{km}$; but to acheive the $30~\text{cm}$ resolution of modern satellites the required size balloons up to $0.46~\text{AU}$.

Atmospheric turbulence (seeing in astronomical parlance) is not an issue here. As usual, Randall does a good job of explaining this.

So to detect human-size targets you would need a telescope the size of Venus's orbit constructed around one of the stars, and to detect an aircraft carrier you'd need a telescope just slightly larger than the Earth.

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A solid (a.k.a. monolithic) mirror this size would be impossible. Even a segmented mirror (like JWST will use) would require too much material to be practical.

However, in our wave analogy we only ever looked at the two edges of the telescope, not at anything in the middle. It turns out that the middle of the telescope doesn't actually contribute to the maximum resolution, so we can discard it. In fact, we can discard almost all of the mirror, since we don't need every point along the edge either.

This is the concept of a sparse aperture telescope, the leading theoretical design for massive spaceborne telescopes like the one you want to construct. This paper (coincidentally by one of my professors!) goes over the performance analysis of telescopes constructed of swarms of small mirrors.

As for the control of such a swarm, you have two options:

• If all of the mirrors know where they are, where the target is, and where the focal point is, they can all align themselves individually, without referencing the others. In this case, to target the mirror I would keep the optical axis of the system locked onto the Sun, and simply steer the detector to follow your target on Earth. Although the velocity of the Earth in its orbit is high (around $30~\text{km}/\text{s}$), 1) it will correspond to a much lower velocity in the focal plane of the telescope, and 2) the speed is pretty constant, so no matter how fast the sensor has to move it can simply coast along.

• Alternatively, you could take a cue from synthetic aperture radar and just record the incoming light pattern, and correct for any misalignment when you do your data processing. This way you only need a precise measurement system, much cheaper per unit than a precision maneuvering system. (Remember, precision in this context means nanometer accuracy.) Traditional SAR uses radio waves, which are slow enough that their instantaneous intensity can be recorded. Light has too high a frequency for this to work, so you'd probably instead use some sort of holographic method to record the phase of the incoming light relative to some reference beam. 'Steering' the array would be a data-processing operation; in effect, you'd be taking a petapixel image of the entire solar system.

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In terms of technology, such as system is not too far off. I interned under someone who was interested in these systems, and he helped put together this technology roadmap, which estimates large-scale swarm telescopes are only 20-50 years away. Such a telescope would certainly be cheaper, in terms of energy and materials, than travel to another star in human timescales (based on current understanding of physics). I would say go for it!

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One last thing to mention. You can get more data more cheaply by increasing your spectral resolution instead of your spatial resolution. That is, instead of only processing three spectral bands (red, green, and blue), you shoud record and process a couple dozen bands spread through the infrared, visible, and ultraviolet spectra. This would allow you to determine lots of interesting properties (like surface material and temperature) at every pixel in the image, and is useful for distinguishing similar-looking objects (like snow/ice/clouds/white roofs).

Answer 6

You might be able to do some interesting things with a swarm of satellites a few thousand AU out, using the local star as a gravitational lens. This is a long way out, but not as far as going all the way back to Sol. A mission called FOCAL has been proposed that would send a single telescope out to the Sun's gravitational focus. There's been various discussion about how good the image produced from such a mission would be, see for example Geoffrey A. Landis "Mission to the Gravitational Focus of the Sun: A Critical Analysis".

Unfortunately Alpha Centauri is a binary star which would likely complicate things. Maybe they could use Proxima as the lens instead.