How long would it take us to detect a Deimos-like object moving towards Sol from Alpha Centauri

Question

In a backstory for a potential videogame I'll likely never realize I've got the situation that a Deimos-like object... let's drop the facade here, the object is indeed Deimos, one of Mars' satellites, complete with:

• a large spacestation attached to it that originally was orbiting Mars on its own
• about 60-80 personnel aboard (engineers, scientists, military personnel; what you expect a team of astronauts from all major space agencies to be composed of)
• permanent living spaces, storage and laboratories dug into Deimos to shield against radiation
• telecom equipment that relied on relay satellites in orbit around the sun to communicate with earth; as well as long range sensor equipment
• half a dozen short range Mars-to-Orbit shuttles
• at least one or two Mars-to-Moon Transferships
• and loads over loads of fuel generated using the material available on Mars' surface and Deimos itself

Thanks to an alien artifact found on Deimos, the whole thing was instantaneously warped into orbit around a planet of similar mass as Mars, but in the Alpha Centauri system (presumably orbiting the whole thing at quite some distance). It kept its current speed and did not rotate or anything, it simply has been picked up at one point and set down at the other point so to say. It is also assumed that the personnel aboard the station does, if at all, only manage to reproduce the effect and land in the same orbit they're already at (they do not manage to set any new coordinates).

The year all of this happens is about 2050, humanity has established a permanent base on the earthward-side of the Moon complete with a beanstalk dangling into Eart-Luna-L1 for easy transport of material off Luna.

Technologywise we haven't made any big leaps other than presumably quadrupled current processing powers of computers and more or less improved ion-drives to a point where the transittime between Luna and Mars takes about 18 months on average. Chemical propulsion and rockets are still a thing and used to get stuff off Mars and Earth.

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Question: Assuming it takes the team aboard Deimos a Month or so to puzzle out where they are and where Sol is; they immediately make about converting the shuttles and docked ships into an array of thrusters and head off towards Sol.

How long does it take anyone at Sol to make out the object moving towards us?

Assume them to try everything imaginable in their position, e.g.:

• trying to increase the albedo of their space object
• try positioning themselves between one of the stars of Alpha Centauri and Sol (so they created a 'shadow')
• reworking their comms and sensoring equipment into equipment more suited for absurdly-long-range-comms

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Addendum: Facts assembled from what I (assume to) know:

• EM-Waves take about 4.4 light years (that's distance, cut the 'light' for time) from Alpha Centauri to Sol; same the other way around
• even using directed beams the signal would most likely be dispersed and interrupted by space-factors along the way, making it difficult even detecting a simple morse S.O.S. (... _ _ _ ...)
• the albedo of Deimos itself is approx 0.068; I have no idea if covering the surface of Deimos with solar panels will increase or decrease this number

Answer 1

Assuming the people on board Deimos are doing everything they can to be seen, about 5 years.

Alpha Centauri is around 4.37 light years away. So that is the absolute minimum time for whatever is being observed to reach Sol from there.

The scientists aboard Deimos would immediately set about building the most powerful transmitter they can. Lets say it takes them a month or so to recover from the transport event and work out where they are. They then have a month or two to prepare a transmitter and start broadcasting a tight beam directional radio message.

Considering we were beaming messages to nearby stars back in the 90's (for example see Cosmic Call) scientists with near-future/future tech should have no difficulty making themselves heard.

The directed radio messages will be far more effective than any sort of increasing the brightness of Deimos. Quite apart from anything else there is very little light to reflect in interstellar space!

Answer 2

If they seriously try to communicate (by signals), it's probably their best chance to be noticed. Better than anything else anyway.
And they really have no reason to move towards Sol. They're probably better off staying put - they get more energy, and finding them would be easier.

(Incidentally, the other answer was not posted until several hours after I started writing this one. But I decided to reference it anyway.)

From an Earth-based perspective, they're right next to Alpha Centauri. As they move towards Sol, they are still within a few AU of the line between Sol and Alpha Centauri, and any telescope that could possibly be picking them out would be getting much stronger images of α-Cen itself.
The shadow would be tiny; modern Earth telescopes still view stars of that size as dots, so the only noticeable difference would be in brightness. Deimos is 20-odd kilometers across, the Alpha Centauri stars about a million each (they're fairly similar size), so the difference will be a fraction of less than 1 in a billion - completely unnoticeable. (And even if it was, your typical stellar activity is on much larger scales. You'd have to be able to see kilometer-level details to tell a shadow from a sunspot.) This, of course, should also be obvious for the Deimos station crew, so they won't attempt that in the first place anyway.
Albedo manipulation might be more effective in that it doesn't require them to be right next to the star from an Earth perspective, but it, well, requires them to be right next to the star in space-based terms. And still not very useful anyway (Deimos is tiny, so even with perfect albedo will only have 1/1000 of the light of a Moon-sized and Moon-albedoed planet - probably unnoticeable in all the glare). If anything, they should be getting away from the direct Sol/α-Cen vector, at least up to a few AU away, or nobody'll notice them from the star glare. But, the α-Cen system being binary, they won't be directly at the line for any long time anyway (unless they try to).

Would they actually want to move towards Sol, though, or just stay put? In any case, their best chance is probably waiting until Earth develops good enough technology to get to them reasonably quickly. Their ability to be noticed isn't much different whether they're still in the α-Cen system or going away from it - they're still within a few AU/arcseconds (α-Cen to us is 1.34 parsecs, so one arcsecond corresponds to almost exactly 1.5 AU) of the visible location of the stars, unless they're not moving directly to Sol (and there's no reason why they would move anywhere else).
Under current or immediate near-future "chemical rocket" tech, it would be very hard to accelerate beyond 100 km/s or so; a speed that will take 13000 years to reach α-Cen (half that if both sides are moving towards each other, though then they'd have problems slowing down to meet). The Deimos expedition will not survive 13000 years (or even half as long) - unless they stay put and take energy from local "Mars" (then it becomes a question of whether they have enough population for genetic diversity; "team of astronauts from all major space agencies" means healthy people from diverse backgrounds, which is about the best case - though it might be biased too much towards males - and 60-80 people is just above the minimum viable population assuming decent genetic checking, so if they really really try, and figure out they will have to stay for centuries in any case, they might actually have just enough to survive).

They probably could try to make a very precise mirror that tries to take a big quantity of light from the star and reflect it back to Earth. However, they likely don't have the technology to make it precise enough (or to make it follow the star well enough), and the resulting signal would be orders of magnitude less than even that from their planet.
Or, yes, they could just make a directed radio transmitter. Stars don't transmit in radio bands (especially lower-frequency radio bands, like 100 MHz) very much, unless they're radio sources (which, as far as I know, Alpha Centauri is not), so a radio transmission from Alpha Centauri should be immediately detected as of artificial origin.
So eventually the Deimosians cobble together a decent radio transmitter and send a signal at 452.129 MHz (or anything else they think of, probably within whatever the radioastronomy band is at their time). If the transmitter is powerful enough (I suck at the math, but it shouldn't be too much), they are heard on Earth 4.4-4.5 years later, which is, like the other answer said, probably within 5 years of when they got teleported originally.

From that point on, Earth knows where they are (as long as they don't attempt something stupid like moving towards Sol at Voyager speed... which the question seems to presuppose), and will probably send a rescue team, eventually. Given the limits of chemical rockets, a very long eventually.
With enough food stockpiled, and enough energy to make new food (and enough energy to get needed materials from the new planet's surface, presumably with some sort of remote-controlled robots), survival shouldn't be a problem, at least for the first few decades; with a decent breeding program, survival shouldn't be a problem for the next few centuries either.
At this point this becomes a (very slow, by regular human standards) race of whether Earth/Sol based humans can develop fast ship technology (something better than regular chemical rockets) and get to Alpha Centauri in reasonable time (13000 years is probably not reasonable time, so we need better propulsion).
But if they get there quickly enough (or if the Deimos side get lucky with genetics), they're going to come to an existing well-established colony. A starting population of 80 healthy people (plus remote-controlled - or even autonomous - robots for much of the material extraction stuff; this isn't mentioned directly in the OP, but pretty much certain given the tech level) with centuries/millenia of preparation time and nothing else to do except survive and expand can result in a surprisingly large colony.
Perhaps - depending on how livable this other!Mars is, and how many millenia had actually passed - even a planet-wide colony.

(Sorry for such a wall of text, incidentally.)

EDIT: I noticed the "ion drives" part in the OP. This makes my "100 km/s" figure kinda obsolete, but it was a ludicrous overestimate anyway. Make it 500 km/s, and 2600 years; this is still long enough that something faster will probably come up earlier, but even if it won't - there's a bit more chance that there is still a surviving colony. I didn't really believe in it surviving for 13000 years, anyway.

EDIT2: changed the star name shorthand to (more) correct form "α-Cen" (it used to be ACen). Thanks @JDługosz!

Answer 3

We'll never detect them, because they'll never actually get out of orbit around the planet in the Alpha Centauri system. Deimos out-masses their docked shuttles to such an extent that they'll barely have moved it before they run out of fuel.