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I'm researching a scene for a sci-fi novel in which the near-future protagonists observe earth through a station-mounted telescope in Mars orbit. My goal is to understand how much detail they reasonably could discern.

The Hubble telescope is probably a reasonable comparison for my purposes. I found images Hubble took of Mars during a close approach, but I don't know if those represent the best resolution possible or simply the resolution that was selected or available at the time, or indeed, if the whole planet was imaged at a higher resolution than the photo published in popular media outlets.

Can a Hubble-like telescope observe significantly greater detail than displayed in the article below? If so, what might reasonably be resolved? Large cities? Individual buildings?

From Vox.com's Hubble can see galaxies impossibly far away. Here’s what happens when it looks at Mars and Saturn.

Mars, ASA, ESA, and STScI

above: Cropped from Source NASA, ESA, and STScI

Mars, NASA/Hubble

above: Cropped from Source NASA/Hubble

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    $\begingroup$ First, you need to understand that magnification is not what you want to ask about, but angular resolution. $\endgroup$ – AtmosphericPrisonEscape May 5 at 20:58
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    $\begingroup$ I've brought the images into the question because over time links break (popular websites move or archive old articles) and then the question becomes invalid. This way future readers will still be able to see what images are being talked about. Also, they are really beautiful! $\endgroup$ – uhoh May 6 at 0:36
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    $\begingroup$ The resolution of the public images seems about right to me. I'm sure more detail could be extracted via heavy processing, but that also tends to create artifacts. $\endgroup$ – Florin Andrei May 6 at 1:07
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    $\begingroup$ @Tim In general images from NASA are freely available for public use, but I don't know the exact license. The policy itself is probably a lot older than cc by-sa and may be established by US law somehow as part of the funding mandate. This is certainly look-up-able on the internet. spacetelescope.org/copyright If there's more to discuss, maybe it's a good topic for a meta question. $\endgroup$ – uhoh May 6 at 12:45
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    $\begingroup$ In the event you need to describe the scale of these telescope in human reference terms, a handy graphic from Wikipedia. $\endgroup$ – bishop May 6 at 13:31
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Forget about magnification. People who know telescopes don't think in terms of magnification. What matters is the angular resolution, or the resolving power: the angular size of the smallest details that you could see in an instrument.

Rule of thumb: the resolving power of a telescope with a diameter of 10 cm is 1 arcsecond when using visible light. The numbers are inversely proportional. A 20 cm telescope resolves details 0.5 arcsec in size. A 1 meter telescope resolves 0.1 arcsec.

Hubble has an aperture (diameter) of 2.4 m, so its resolving power is 0.04 arcsec.

The minimum distance between Earth and Mars is about 55 million km and it only happens very rarely. The maximum distance is 400 mil km. The "average" distance is 225 mil km (but actual distance varies all the time).

Let's apply the tangent of 0.04 arcsec at 55 mil km:

https://www.wolframalpha.com/input/?i=tan(0.04+arcseconds)+*+55000000

It's 10 km. It would only be able to see the major geographic features.

To see buildings (down to the scale of 10 m), it would need a 1000x increase in resolution. That means an aperture of 2.4 km. None of the classic telescope designs can provide that. It would have to be some kind of interferometric design - a large, flat field where several mirrors are placed several km apart and are coupled optically to function as a single huge mirror (well, sort of - this is more of an intuitive explanation).

It would be similar to the Navy Precision Optical Interferometer near Flagstaff, Arizona.

NPOI

Some of the wide, flat parts of Valles Marineris might provide a good location for the interferometer. Acidalia Planitia would provide even more space for building huge interferometers, and should be a good place to build structures in general - flat to beyond horizon; it's the place where much of the book/movie The Martian set their story. But any big, reasonably flat field would work.

All of the above assumes the distance of closest approach between Earth and Mars. In practice, the distance is greater than that, so aperture must increase. You're contemplating an interferometer with a base of dozens of km if you want to distinguish structures such as buildings.

Conceivably, the interferometer could be built in orbit, but you must ensure that the distance between mirrors is maintained with extraordinary precision. On the planetary surface, the ground provides the required rigidity. In space you'd have to... I dunno, use space magic.

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    $\begingroup$ Thanks, that's a wonderfully detailed answer. The plot doesn't in any way depend on seeing small features so I'll go with the ability to resolve major geographic features. I strive to get the science right in my novels and greatly appreciate your help! $\endgroup$ – Eric J. May 6 at 0:52
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    $\begingroup$ @EricJ. - alright, then the orbital telescope would work. Good luck with your project! $\endgroup$ – Florin Andrei May 6 at 1:09
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    $\begingroup$ @PM2Ring. Indeed, I do reference Olympus Mons in the story. In this scene, an orbital station (around Mars) lost contact with earth in the weeks after an alien invasion. The role of the telescope in this scene is to highlight their desperation for news from home. It doesn't actually tell them anything, but I want to accurately describe what they see. It works fine for story purposes that they can see major geographic features only. Thanks for the thought! $\endgroup$ – Eric J. May 6 at 5:26
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    $\begingroup$ @ChrisStratton It's not that the telescope must be in orbit, but that the humans find themselves there. The Martian atmosphere is so thin that it shouldn't have much impact on observational astronomy from what I know. I suppose they could build a large telescope on the surface (e.g. on Olympus Mons as suggested above) given enough time, but the story will take them in a different direction. $\endgroup$ – Eric J. May 6 at 5:29
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    $\begingroup$ Rather than try to look at image detail like buildings, your characters would probably look at things like night-side lighting patterns (normal, absent, sudden flares with worrisome spectra), possibly disrupted weather patterns, radio chatter (normal, absent, never before seen modulations) and so on. It's almost the SETI problem, but now with three choices - familiar, nothing, unfamiliar $\endgroup$ – Chris Stratton May 6 at 6:01
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The Hubble space telescope has a 2.4m mirror and is pretty much diffraction limited, so at near-UV wavelengths of say 240nm it has an angular resolution of about $10^{-7}$ radians. Mars' closest distance to Earth is about 54.6 million km, so the theoretical minimal resolution is between 5 ad 6 km. So large cities might be visible if they have lots of contrast. Since at closest approach an observer on Mars is looking straight at the night side of the Earth, a well lit city might be easy to spot, on the other hand, they are also looking more or less straight at the Sun, which might give some problems. Still there will be times when the distance is only 70 or 80 million km and the angle from the Sun is more manageable, so a resolution of 10km in the UV, 20 in visible light is credible.

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    $\begingroup$ What's not clear to me is whether the minimum Earth-Mars distance coincides with the transit of Earth over the solar disc, seen from Mars. Since the orbits are not exactly coplanar, the coincidence is not guaranteed - at least that's my intuition. I could be wrong. $\endgroup$ – Florin Andrei May 5 at 23:28
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    $\begingroup$ @Florin Good point. Closest approach does occur when Mars is at opposition, but that may not be a transit. I bet Meuss could tell us... $\endgroup$ – PM 2Ring May 6 at 5:03
  • $\begingroup$ @FlorinAndrei The orbital planes of the planets are quite a bit inclined relative to each other (several degrees) - they are quite far from being co-planar. Given the tiny angular size of the sun (0.5° from Earth POV) and the vast distances involved, transits are actually pretty rare. Earth transits, seen from Mars, happen only a few times per century! $\endgroup$ – Oscar Bravo May 6 at 8:06

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