Suppose there was an exact replica of our solar system 4.4 ly away (people included). What would we be able to detect and with what telescope(s)? Which planets? Could we detect radio transmissions and/or any atmospheres?
I assume detection would be optimal if we were co-planar with the other star's ecliptic, so what would we see in the best- and worst-case (90°-view?) scenarios?
Post Script: a few months later I asked something like this during a von Karman lecture by Neil Turner.
This is a broad question and too broad for me to answer comprehensively. It should be broken down into Doppler methods, transits and direct imaging; and that's before we get to questions of detecting Kuiper belts, radio emission etc.
Direct Imaging
Exoplanets might also be detected by direct imaging. At the distance of Alpha Cen, a separation of 1 au corresponds to an angular separation of about 0.7 arcseconds. This is easily within the angular resolution of big astronomical telescopes, but the problem is the contrast between the very bright star and the very faint planet. This means that even though the point spread function (what a point source looks like when imaged), might be very sharp, with a full-width at half maximum of <0.1 arcsec, there is still enough light at 0.7 arcseconds to mask a nearby exoplanet.
To get around these problems, astronomers use coronagraphs (that block some of the light from the central star) and clever adaptive optics imaging techniques to make the images as sharp as possible. The observations are conducted in the infrared to maximise the relative brightness of the planet with respect to the star (in particular, the exoplanets may emit some thermal infrared if they are giant planets or reasonably close to their star).
State of the art observations of Alpha Cen A are presented by Wagner et al. (2021). These would be able to detect Jupiter from 4.4 light years, but probably not Saturn or the ice giants. However, as pointed out by userLTK, Jupiter would not be stable in the Alpha Cen AB system and any planets would be restricted to <3.8 au orbits. Nevertheless, an astronomer near Alpha Cen A would detect Jupiter with our current technology by direct imaging.
As for closer in planets, Wagner et al. say that their current observations are able to place a limit that they would be able to detect Neptune-sized objects within the habitable zone of Alpha Cen A. Unfortunately, none of the Solar System objects meet this description so the inner Solar System planets would not be (currently) detectable. However, the prospects for the future look good. Quanz et al. (2015) suggests that the direct imaging system on the ELT (METIS), exploiting its higher angular resolution, should be capable of imaging the thermal emission from Earth-sized exoplanets at 1 au around Alpha Cen A.
Doppler Technique
The reflex radial velocity semi-amplitude of a star for the case of a planet of mass $m_2$ orbiting a star of mass $m_1$, in an elliptical orbit with eccentricity $e$, and orbital period $P$ and with an orbital axis inclined at $i$ to the line of sight from Earth is: $$ \left( \frac{2\pi G}{P}\right)^{1/3}\frac{m_2 \sin i}{m_1^{2/3}} (1-e^2)^{-1/2}. $$ A (very) detailed derivation is given by Clubb (2008).
So I built myself a little spreadsheet and assumed that all the planets were seen optimally at $i=90^{\circ}$ (they could not all be seen optimally, but the smallest inclination would be about $i=83^{\circ}$ for Mercury, so it doesn't make too much difference) I'll also assume the mass of Alpha Cen A is about $M \simeq 1.1M_{\odot}$.
The results are
| Planet | RV semi-amplitude (m/s) |
|---|---|
| Mercury | $8.3\times 10^{-3}$ |
| Venus | $8.1\times 10^{-2}$ |
| Earth | $8.4\times 10^{-2}$ |
| Mars | $7.5\times 10^{-3}$ |
| Jupiter | $11.7$ |
| Saturn | $2.6$ |
| Uranus | $0.28$ |
| Neptune | $0.26$ |
The limits of what are possible are well illustrated by a planet around Alpha Cen B, claimed to be in a 3 day orbit and with a mass similar to the Earth (Dumusque et al. 2012, and see exoplanets.org). The radial velocity semi-amplitude detected here was $0.51\pm 0.04$ m/s, and some spectrographs, notably the HARPS instruments, are routinely delivering sub 1 m/s precision. Thus Jupiter and Saturn would be detectable (but recall, would not have stable orbits), Uranus and Neptune are right on the edge of detectability (remember you can average over many RV observations), but the terrestrial planets would not be found (Earth detections would require precisions below 10 cm/s). Remember also that the weaker signals would have to be dug out from the larger signals due to the Jupiter- and Saturn-like planets.
However, there is a second limitation: to find a planet using the Doppler method you need to observe for at least a significant fraction of the orbital period. Given that current m/s precisions have been available for only $\sim 5$ years, it is unlikely that Saturn would yet have been detected.
A picture that illustrates the situation can be obtained from the exoplanets.org website, to which I have added lines that approximate where RV semi-amplitudes would be for 10 m/s and 1 m/s precision (assuming the Alpha Cen A mass and circular orbits). I've marked on the Earth, Jupiter and Saturn. Note that few objects have been discovered below the 1 m/s line. Also note the lack of planets between the 1 and 10m/s lines with periods longer than a couple of years - the recent increase in sensitivity has yet to feed through to lower mass, longer period exoplanet discoveries.
In conclusion: only Jupiter would have been so far found by the Doppler technique.
Transit techniques
I'll also add a few comments about the transit technique. Transit detection will only work if the exoplanets orbit such that they cross in front of the star. So high inclinations are mandatory. Someone who is better at spherical trigonometry should use the published data for the Solar System to work out how many (and which) planets transit in some highly optimal orientation. Given that the planets have orbital inclinations with a scatter of a few degrees, then some straightforward trigonometry and a comparison with the solar radius, tells you that these orbits will generally not all transit for any particular viewing angle. Indeed a number of the Kepler-discovered multiple transit systems are much "flatter" than the solar system.
The Kepler satellite is/was capable of detecting very small transiting planets thanks to its very high photometric precision (the dip in flux is proportional to the square root of the exoplanet radius). The picture below, presented by the NASA Kepler team (slightly out of date now), shows that planetary candidates have been discovered that are down to the size of Mars. However these tend to be in short period orbits because a transit signal needs to be seen a number of times, and Kepler studies this patch of sky for about 2.5 years (when this plot was produced).
So from this point of view, possibly Venus would have been seen, but none of the other planets could be confirmed.
However, there is a wrinkle. Alpha Cen A is way too bright for these kinds of studies and way brighter than the Kepler stars. You would have to build a special instrument or telescope to look for transits around very bright stars. Some of this work has been done by ground-based surveys (mainly finding hot Jupiters). A new satellite called TESS (Transiting Exoplanet Survey Satellite, launched in April 2018) is a two year mission, focused on finding small planets (Earth-sized and bigger) around bright stars. However, most of its targets (including Alpha Cen) are only observed for a 1-2 months, so only the inner parts of their planetary systems will be probed.
First, I think Rob Jeffries answer is brilliant. I'll just add a minor points that might be worth mentioning.
What would we be able to detect and with what telescope(s)?
Alpha Centauri A is a binary star with Alpha Centauri B and they are close enough in size to have no stable L4 or L5, so anything that orbits either one of them would need to be either very close (Mercury distance perhaps Venus) or very far and very cold, much greater than Pluto distance, orbiting both stars like Proxima Centauri does. *** EDIT *** Professor Rob says up to 3.8 AU could be stable. That's much further than I'd have guessed, but he quotes a source, that's probably right.
If you put a Jupiter in it's solar orbit around A or B, the 3 body effect would almost certainly create a wildly unstable orbit for the planet that likely wouldn't last long, so, one answer to this question is that our solar-system type of orbit around A or B is impossible.
Could we detect radio transmissions and/or any atmospheres?
For now, our detection of atmosphere is very limited and only to large planets very close to their stars, but, the article says they're working on that with bigger telescopes on the way, so maybe in a few years we'll get something on that for habitable zone planets.
exoplanet atmosphere detection
On radio-waves and worth mentioning, visible light, I couldn't find a good article, but if an alien planet shoots a message towards us in a tight beam - then, I'm sure we could detect that, provided they shoot a big enough beam, But could we detect another earth with our current output? I don't think we're close to that kind of detection technology.
(and if I got any of that wrong, I welcome correction).
(I asked something like this during a von Karman lecture by Neil Turner)
Did he answer you? Did he say anything good?
Neal Turner's answer from the "The Birth of Planets" von Karman Lecture
How would we detect planets around a far-flung, identical copy of our solar system? Would our planets need to be detected using the transit method?
On the whole, yes. Jupiter you could probably detect by the radial velocity method if you're willing to wait one orbit or maybe two to be sure, so 12 years for Jupiter to go around the sun.
The other planets would be really tough. If they transited you could detect them with technology similar to ours. You'd have to be lucky because our solar system is not compact like [others discovered by Kepler]; it's quite spread out. If you have a planet very close to its star, you have a decent chance, if it has a random orientation, that it'll be along your line of sight. If it's very far away there's many more possibilities for its orientation and there's a much smaller probability if things are random that you'll get it along your line of sight exactly.
So for someone to see our Jupiter from a nearby star is much less likely than for us to see a hot Jupiter. There's only a small number of aliens looking at our solar system and seeing it through transits right now.
