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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?

Muze
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2 Answers2

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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.

Muze
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Jack
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  • Thanks and +1 I know the Hubble has its limitation but is it possible in theory to see someone walking on Mars from Earth? – Muze Sep 05 '18 at 20:09
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    @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. – called2voyage Sep 05 '18 at 20:45
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    Jack - thanks for doing the math on resolving. 50 km would be a terrifying telescope. – called2voyage Sep 05 '18 at 20:47
  • Really nice answer how would it look with the interferometry? – Muze Sep 05 '18 at 20:57
  • Interferometry can't really bypass the diffraction limit at all, it just creates a giant aperture out of multiple radio telescopes. – leftaroundabout Sep 05 '18 at 22:24
  • @Muze FYI (because I did the math) even just to see a man on the moon would take a 187 m telescope (violet light only; 350 m for the full visible spectrum). Not quite as absurd as Mars, but still 18 (34 for full-spectrum) times the size of the largest visible light telescope on earth. – Kevin Sep 05 '18 at 23:21
  • @leftaroundabout Depends on the definition of "aperture" I assume - it certainly doesn't create a 50km "hole through which light travels" – user253751 Sep 06 '18 at 01:12
  • @Jack Wouldnt the resolved image be just be one pixel? Also, what's the exposure time that's needed, assuming such a telescope is built? – Coloured Panda Sep 06 '18 at 08:31
  • Yes, that’s why it’s a limit - the relevant physics is airy disks. Exposure time depends on many different factors, not least the brightness of the subject. Photography SE probably covers it well. – Jack Sep 06 '18 at 08:38
  • You should also note that (i) The telescope of $50$ kilometers would have to be built in space the seeing disk of the atmosphere limit's resolution in the visual band and that (ii) it cannot be overcome using interferometry as it is not yet widely implemented for the visual band. – Agile_Eagle Sep 06 '18 at 14:44
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    @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. – Agile_Eagle Sep 06 '18 at 14:46
  • @called2voyage Which largest telescope are you referring to? The largest optical telescopes I know of have 10 meter (~33 feet) segmented primary mirrors, like the Keck telescopes. There are plans to build a 30 meter telescope (https://www.tmt.org/), but actual construction of that is well into the future. – Tom Spilker Sep 09 '18 at 23:41
  • @TomSpilker Yes, I meant the one under construction. I glossed over the fact construction hasn't even started yet, but that does demonstrate how monumental such a telescope is. – called2voyage Sep 09 '18 at 23:45
  • @Kaspars Your question about exposure time is very appropriate for an interferometer. A well-designed interferometer gives the resolution of a single mirror the size of the maximum spacing between elements, but not the photon-collecting aperture! Assuming a 1 square meter human (a big person!) with albedo 0.25 (but add a bit of opposition effect) on Mars at an average opposition distance (~0.52 AU), photons reflected from the person arrive at Earth at the rate of ~1 per square meter per 100 sec. The 50 km telescope would pick up 20 million photons per second... – Tom Spilker Sep 09 '18 at 23:53
  • @Kaspars ... from that human, enough for a fairly short integration time. But with 3 10-m telescopes in interferometer configuration (like the VLA radio interferometer) the combined collecting area is only a 10 millionth that of the filled-aperture 50-km telescope, so they average less than 1 photon per second each from the person. SNR becomes a problem. – Tom Spilker Sep 10 '18 at 00:04
  • @called2voyage I talked with Ed Stone (Voyager Project Scientist, board member for the TMT Project) a couple weeks ago and he said they're still working up the money to start the project. With donations they've already received they're doing R&D tasks that will allow them to finish the detailed design of the TMT, but they are far from starting the actual construction. – Tom Spilker Sep 10 '18 at 00:10
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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.

Chris Nava
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  • 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. – Tom Spilker Sep 06 '18 at 05:51
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    @TomSpilker This should not be a comment. It doesn't meet the criteria for a comment (which you laid out). – Lightness Races in Orbit Sep 07 '18 at 11:54
  • @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. – Tom Spilker Sep 07 '18 at 17:54
  • @MagicOctopusUm I just invoked your moniker in an example I used in a comment. I hope you don't mind! – Tom Spilker Sep 07 '18 at 17:57
  • @TomSpilker If you look at my profile you'll see I'm quite familiar with Stack Exchange, thanks. – Lightness Races in Orbit Sep 10 '18 at 10:25