Suppose that there is an alien spacecraft travelling towards the Sun. This spacecraft is similar in design, size and power output to Voyager 1 and Voyager 2 as they were immediately after launch from Earth, and is coasting in its orbit (no powered maneuvers taking place).

Also suppose that a budding scientist on present day Earth just so happens to point their instruments (optical telescope, radio telescope, or something else; ground-based or space-based) in exactly the right direction at exactly the right time.

If the spacecraft is communicating at all at this point, it seems unlikely to be transmitting in the direction of Earth.

How far from the Sun (or Earth) could the spacecraft be where we'd still have a chance of detecting it, assuming for a moment that all events line up perfectly for detection? Would we be able to determine that it is likely an extraterrestrial spacecraft, as opposed to some natural interstellar object?

This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    What is the status of its equipment? Voyager will be without power and with its radioisotope burned down by the time it gets to any other system, can we assume the same about this probe? FYI; Pu-238 has a half-life of 87 years, so in ~500 years you can assume that it isn't even generating heat any more. – kingledion Sep 13 at 19:40
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    Could you specify if the alien spacecraft is transmitting on wavelengths other than visible and IR? That will have a large roll in the detection range. – Green Sep 13 at 20:00
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    I wish I could put together a sensible, hard-science answer. I can tell you that the minimum NEO detection size right now is a shameful 140 m, more than capable of extreme impact damage. I suggest that Voyager's 12 foot dish size, relatively high albedo and the orientation or aspect of the craft would require a 'lucky spotting' without an energy signature of some kind. Please see this article arxiv.org/ftp/arxiv/papers/1506/1506.07085.pdf for some current standards of detection equipment and techniques. – Joe Sep 13 at 21:03
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    @Joe it appears that the question is asking about the "lucky spotting" scenario. – Alexander Sep 13 at 21:58
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    @Green I'm willing to settle for a power output similar to that of the Voyagers immediately after launch from Earth (so no RTG deterioration yet). As for transmitting, I'd imagine not, and even if it did, being alien in origin, it's unlikely that it would be transmitting in the direction of Earth. Remember, this is a Voyager-lookalike; the only major difference is that it's coming toward our solar system from afar, rather than being launched from within our solar system. – a CVn Sep 14 at 7:46

The angular resolution of an optical system is given by

$\phi_0 =1.22 $$\lambda \over D$, where D is the diameter of the optics.

The angular size of an object of size d at distance R is given by

$\alpha =arctan$$d \over 2R$$=$$d \over 2R$

Equalizing the two angles we get

$1.22 $$\lambda \over D$$=$$d \over 2R$

Solving in R we get that

$R=$$dD \over2\times 1.22 \times \lambda$

Assuming $\lambda = 500 nm$, and considering a mirror diameter of 10 meters (equal to the mirror of the GTC) and a size of 5 meters for the object, we get

$R = 40\times10^6 \ m$, or 40 thousand km. This distance is about the height of the geosynchronous orbit.

If we instead are using passive radioastronomy, we have the largest structure on Earth to have a diameter of 500 meter (Chinese FAST) operating at a wavelength of 0.10 meters.

This would give a minimum detection distance of about 11000 meters. But I guess in this case we would first see the optical trail of the satellite burning in the atmosphere.

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    You seem to assume here that optical detection is the best we can do. ColonelPanic's answer indicates that such might not be the case; can you show in some way that optical detection would be the best approach for long-range detection? – a CVn Sep 14 at 13:52
  • @MichaelKjörling, 0.10 m wavelength is not in the optical range. It's more in the radar range. – L.Dutch Sep 14 at 19:28
  • True, but 500 nm is definitely in the optical range, and your discussion about detection distance for the 500 nm wavelength, 10 m mirror case certainly seems to me like optical detection. It's also the case you provided which gave the (much) greater detection distance. – a CVn Sep 14 at 19:57
  • @MichaelKjörling I compared the limitation due to angular resolution both using optical detection (500 nm) and radar detection (0.1 meter). I didn't assume one was the best. It just came out of the calculation. – L.Dutch Sep 14 at 20:22
  • EM detection has no real bounds in frequency, it can be whatever we want it to be, which is the basis of my answer. With current space tracking technology we can reach hundreds of thousands of km easily. The reason this is limited is because there is little need to look much farther for most reasons. Higher frequency systems certainly do exist and could easily extend detection ranges out to the edge of the solar system (if we ignore that the chances of looking in the right place/time are basically nil, as the OP allows). – ColonelPanic Sep 17 at 9:26

Optics are a bad choice, so maybe thing about the radars used in tracking space debris, which have incredible resolution. Of course, that will be reduced the farther out you are looking. Detection of a 2cm object at 1000km is not out of the question, so detecting something 12' large (if you just want to see it, not gain any surface information) would roughly be 180,000 km. By using an active transmission component, it can double the detection range.

So around 400,000 km isn't out of the question with current equipment (optimized for a different purpose). It wouldn't be out of the question to use more power, more or larger receivers, different frequencies etc. to increase this range by a considerable amount. You eliminate the largest factor by allowing the 'lucky spotting' scenario. With this in mind, I see very little reason why detecting something at the edge of the solar system with a purpose built system is out of the question.

As for knowing if it is alien or not, I doubt this is all too feasible without receiving transmission from it. You would know its path, speed, and approximate size. Other than that, you'd have to wait for optics and the object to be much closer.

  • For scale, 400,000 km is only out to the Moon. – Futoque Sep 14 at 15:50
  • Right, that was just a comment on how far we could possibly look using technology designed for completely different purposes. With currently existing technology we could easily envision building a system with considerably farther reach. Doubling power in electromagnetics in free-space usually isn't a huge deal. We usually talk about amplifiers, even low-noise, in the range of several orders of magnitude, not measly doubling or even a single x10. A solar system of 4billion km in radius is in that ballpark. – ColonelPanic Sep 17 at 9:31

IR detection

Source: Ledeboer, 2018.

Instead of using reflected optical wave light from the sun, lets try to detect something that the probe itself is emitting. Any radio emissions are very unlikely to be targeted at Earth, so the most likely emission that we would capture would be black body radiation from the probe itself.

Voyager's propellant lines are filled with hydrazine, which must be kept at a minimum of 1.6 C (275 K). These lines are external to the spacecraft, so they set the limits for how cold the spacecraft can get while being 'operational.' The current model in the paper above suggests that Voyager's hull temperatures are in the range 15-20 C. Lets round this to 300 K. The emissions curve at 300 K looks roughly like this:

enter image description here

One possible alternate calculation of detection is to simply use the optical resolution equation that L.Dutch used, except substituting in a wavelength of 10,000 nm for 500 nm. This makes the detection range 800,000 km: greater than the distance to the moon.

I tried to calculate difference between Voyager's IR emissions and background IR, but couldn't get enough data; not on background spectra, Voyager's surface area or in many other areas.

I did note that cosmic IR background peaks in the 100-1000 $\mu$m range, significantly higher than the peak for Voyager. This suggest that we might be able to get good resolution at the lower wavelengths where Voyager's IR emissions will be maximized.

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