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How strong would a telescope (and what kind of telescope) on Proxima Centauri b have to magnify to discern any planets around Sol, and which planets would be easiest to spot? One might think the farther the better which would make Neptune observable most easily, but on the other hand farther-away planets are less illuminated, maybe too dark. This makes Jupiter an easier observable candidate, but it is 1/6 the distance of Neptune from the Sun which would make it harder to discern. I think no solid planet would be observable directly.

I also wonder which planets have the correct size and distance to Sun to be recognized by the transit method from Proxima b, rather than by direct imaging.

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Here is a brief explanation of the various techniques that can be used to detect exoplanets. The scatter plot suggests that for a planet to be detected by direct imaging, it has to have (roughly speaking) an orbit as large as Jupiter's, and a mass as great as Jupiter's. So Jupiter looks like the best candidate.

As for your second question, the declination of the Alpha Centauri system is about -60°, and the earth's axial tilt is only 23°. So the Alpha Centauri system lies below the plane of the ecliptic by at least 37°, and none of the planets (which are all approximately in the plane of the ecliptic) can transit the sun from the viewpoint of Proxima Centauri b.

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  • $\begingroup$ Oh, I'm completely wrong, never mind! I always work in ecliptic coordinates because I'm playing with planets mostly. $\endgroup$
    – uhoh
    Commented Jul 18, 2021 at 13:20
  • $\begingroup$ Thank you. But you mean "none of the 8 recognized planets", and where you define Mercury's orbital tilt depends on how liberal you mean "approximately". What about Eris at 44° inclination? Is it too small to be recognized against the background of the Sun? A dwarf planet was found around another star, after all. $\endgroup$
    – John
    Commented Jul 18, 2021 at 14:10
  • $\begingroup$ @John, your question specifically says planets. Four times. This doesn't include dwarf planets! But yes, they would be too small to see. As for Mercury, its orbital inclination is about 7°, which is comfortably less than 37°. $\endgroup$
    – TonyK
    Commented Jul 18, 2021 at 14:14
  • $\begingroup$ @TonyK I say planets, therefore I mean all planets, including dwarf planets (and Mercury is a dwarf planet that is an IAU-recognized planet). You only mean the eight IAU-recognized planets but the arbitrary "clearing the neighbourhood" requirement is an invention by the IAU. The Sun is a yellow dwarf star, don't you consider it a star therefore? As for the dwarf planet Mercury, you said the planets lie approximately in the plane of the ecliptic, but Mercury's orbit is quite tilted. $\endgroup$
    – John
    Commented Jul 18, 2021 at 14:34

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