Can any telescope be capable to see some one walking on Mars? How much time dilation would there be? What is the theoretical best resolution?
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2$\begingroup$ No. But maybe if xe has a mobile phone? $\endgroup$– gerritCommented Sep 6, 2018 at 8:26
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1$\begingroup$ @gerrit excellent! 1, 2, 3, 4, 5 Now I just have to figure out the difference between xe and ze. i.sstatic.net/ygrsu.jpg $\endgroup$– uhohCommented Sep 12, 2018 at 5:58
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From here, discussing images of Mars taken by Hubble while near to its closest approach to Earth:
The telescope snapped these pictures between April 27 and May 6, 1999, when Mars was 87 million kilometres from Earth. From this distance the telescope could see Martian features as small as 19 kilometres wide.
Theoretically
Our resolution is limited by the diffraction limit:
$$ \theta = \frac{1.22 \times\lambda}{d}$$
Where $\lambda$ is the light's wavelength, $d$ is our aperture size and $\theta$ is the angular resolution.
We can express $\theta$ in with an object's distance $s$ and radius $r$ and use a small angle approximation:
$$\theta= arctan(r/s) \approx \frac{r}{s}$$
If we want to resolve a ~1m human from 87 million km, we would need a telescope aperture some ~50km in diameter.
Note: techniques like interferometry can 'bypass' the diffraction limit to some extent, but imaging small objects at very large distance is inherently very hard.
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$\begingroup$ Thanks and +1 I know the Hubble has its limitation but is it possible in theory to see someone walking on Mars from Earth? $\endgroup$– MuzeCommented Sep 5, 2018 at 20:09
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11$\begingroup$ @Muze To see the the lunar rover on the Moon with a telescope would require a telescope that is 75 meters in diameter. For reference, the largest telescope is 39 meters in diameter. Mars is a lot farther away than the moon. $\endgroup$– called2voyage ♦Commented Sep 5, 2018 at 20:45
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4$\begingroup$ Jack - thanks for doing the math on resolving. 50 km would be a terrifying telescope. $\endgroup$– called2voyage ♦Commented Sep 5, 2018 at 20:47
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$\begingroup$ Really nice answer how would it look with the interferometry? $\endgroup$– MuzeCommented Sep 5, 2018 at 20:57
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2$\begingroup$ @leftaroundabout Interferometry does bypass diffraction limit by (as you said) creating a giant aperture. But it cannot go beyond the seeing disk (atmospherical seeing) set by earth's atmosphere which is at best $0.4$ arcseconds. $\endgroup$ Commented Sep 6, 2018 at 14:46
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It's not exactly "from earth", but the Mars Reconnaissance Orbiter has an instrument that should be able to just barely detect the presence of a person on the surface. They would be about a single pixel wide, so you should be able to detect their moving around but not much else. https://mars.nasa.gov/mro/mission/instruments/hirise/
Coverage would be intermittent due to the orbiter not being overhead at all times.
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$\begingroup$ Welcome to Space Exploration Stack Exchange! There are generally two types of responses to posted questions: answers, that directly address the question posed; and comments, that provide or ask for additional information or clarification, point out problems with the question (such as assumptions) that can be fixed, etc. Your response here would be more appropriate as a comment, since the question specifically refers to observation from the Earth-to-Mars distance. $\endgroup$ Commented Sep 6, 2018 at 5:51
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1$\begingroup$ @TomSpilker This should not be a comment. It doesn't meet the criteria for a comment (which you laid out). $\endgroup$ Commented Sep 7, 2018 at 11:54
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$\begingroup$ @LightnessRacesinOrbit One other criterion for a comment—one for a situation not appropriate for new participants, so I omitted it—is for participants with sufficient reputation to advise new participants of the protocols regarding questions, answers, and comments. If you peruse the records (which would take some time!), you'll see this happening fairly frequently. MagicOctopusUm is particularly deft at this, delivering very useful advice to new participants in a friendly (exemplary of the Code of Conduct) and welcoming manner. $\endgroup$ Commented Sep 7, 2018 at 17:54
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$\begingroup$ @MagicOctopusUm I just invoked your moniker in an example I used in a comment. I hope you don't mind! $\endgroup$ Commented Sep 7, 2018 at 17:57
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$\begingroup$ @TomSpilker If you look at my profile you'll see I'm quite familiar with Stack Exchange, thanks. $\endgroup$ Commented Sep 10, 2018 at 10:25