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I've mentioned in earlier posts that it will be much cheaper to build immense space-based observatory instruments than to even come close to launching an interstellar expedition.

There are several figures of merit including total light gathering area and separation of light gathering points.

Imagine nanotechnology that "grows" a module from material in the asteroid belt, and then dispatches it out beyond the dust of the inner solar system. The technology can record the visible and infrared light waveforms in sufficient resolution to combine them from different modules and synthesize an image from a mirror the size of the separation. (This kind of recording delayed synthesis has long been a thing for radio frequency observation.)

How small of details on exoplanets could be seen? Is there a diminishing return when making the distributed modules ever bigger, or can resolution go up indefinitely?

Does the light gathering capacity matter as well? What is the right order of magnitude to match the magnification? Off hand, I expect the target to be lit as bright as daylight, just very tiny; does the total light gathered change with the apparent target size?

Today, a star-shield is needed to prevent a planet from being washed out from the nearby star. Would a narrow enough field of view make that simply unnecessary, or is there some optical effects related to absolute separation of the targets?


summary

  1. How small of details on exoplanets could be seen? math: separation between modules, individual module size, and resolving power; resolving power to esoplanet distance and ground feature size.
  2. Is there a diminishing return when making the distributed modules ever bigger, or can resolution go up indefinitely?
  3. What is the relationship between light gathering capability, brightness of the image, and size of the imaged object?
  4. Use with star shield?
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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

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    $\begingroup$ We use large objects like galaxy clusters to view distant objects in more detail. Those lenses could use some polishing though. $\endgroup$ – Kys Jul 1 '16 at 15:21
  • $\begingroup$ What should this "dust of the inner solar system" be? $\endgroup$ – Karl Sep 4 '16 at 15:03
  • $\begingroup$ @karl en.wikipedia.org/wiki/Zodiacal_light I recall that dust affects infrared visibility inside the orbit or Jupiter approximately. $\endgroup$ – JDługosz Sep 4 '16 at 15:52
  • $\begingroup$ Nobody interested in the bounty here? $\endgroup$ – JDługosz Sep 8 '16 at 14:23
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    $\begingroup$ There are actually many possible answers (using gravitational lensing as part of your array would make a huge difference, for example), but the biggest practical mirror I have any figures for is one the size of the Moon's's orbit, which could resolve objects 10's of kilometers in size from 454 parsecs: nextbigfuture.com/2016/02/… $\endgroup$ – Thucydides Sep 11 '16 at 21:37
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There's a couple of different questions in there, and I'm going to take a stab at some of them.

First, you seem to be generally familiar with aperture synthesis, as you imply it in one of your questions. That basically means if you have a bunch of comparatively small data sources (telescopes) you can merge them into one image as if you had on telescope the diameter of the distance between any two of them.

This gives you a much better angular resolution than you might expect. Unfortunately, you seem to be correct about the diminishing returns aspect. Take a look at this, which graphs total diameter of a telescope against its angular resolution for given wavelengths of light. It's on a log scale, and only goes up to 10,000 km. On an astronomic scale, that's roughly the size of the earth.

This introduces quite a problem. Humans already do something like this by taking advantage of the Earth's annual trip around the sun. By taking measurements six months apart (from anywhere on Earth), you get an effective dish size of around 300 million kilometers. And as it turns out, with a dish that large the closest star is still only 0.772 arc-seconds across. Fortunately, that seems to be within a reasonable range (that is, appears on) at least one axis of the chart I linked earlier.

My conclusion is either I'm really misunderstanding something here1, or you should be able to get a reasonable picture (in some wavelength of light) by creating a satellite cloud between Earth and Mars. If you have to build it bigger, that should actually help.

As a side note, when I started researching this question, I expected to need a telescope the size of the solar system or larger, implying the limit to the size of the telescope is actually how long you can keep the satellite powered (shout out to the Voyagers!) before they stop giving you data back. I was pleasantly disappointed on that.

1Some math would really help here for verification.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

  • $\begingroup$ Between Earth and Mars has the drawback of being in the dust-filled inner solar system. Going farther out gives a clearer view which is specifically benificial for IR but also avoids peturbing the photons allowing more delicate measurements. And it naturally gives you a diameter of over a billion miles. $\endgroup$ – JDługosz Jun 30 '16 at 6:09
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    $\begingroup$ You seem to be confusing Parallax measurements with Interferometers. Currently we do Parallax measurements across the solar system. Interferometers have much higher resolution but currently for optical measurements require the beams to be physically recombined. The largest Optical Interferometer (Navy Precision Optical Interferometer) is ~250 meters across and has an imaging resolution of ~3 mas (milli arc seconds). Once we can recombine beams on the solar system scale... well it will be amazing. $\endgroup$ – AstroDan Jun 30 '16 at 16:31
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    $\begingroup$ For interferometry to work, one needs to be able to receive signals from multiple stations at the same time, and to recombine them with a time-precision that is less than the period of the light waves you're receiving. In practice, this means either physically recombining the signals or looking at lower-frequency waves (so that you can record the peaks and troughs of the signal.) The Event Horizon Telescope will use the latter approach in the microwave band, and is designed to get an image of the Milky Way's central black hole. $\endgroup$ – Michael Seifert Jun 30 '16 at 20:00
  • $\begingroup$ @MichaelSeifert -- very-long baseline interferometry (VLBI) involves recording individual observations at each telescope (with, critically, very accurate atomic-clock timestamps), then later sending the data (e.g., on tapes) to a central facility for processing and analysis. So you don't actually need to "receive signals from multiple stations simultaneously". $\endgroup$ – Peter Erwin Sep 4 '16 at 15:15
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It warms the cockles of my heart to find someone else who realised space-based observatories are much, much cheaper than interstellar expeditions. They would gather the same or possibly more information than our first generation of interstellar probes. Perhaps, hypertechnological telescopes are one solution to the Fermi paradox. Aliens aren't visiting us or are wandering up and down the galaxy because their telescopes do all that work for them.

Aperture synthesis is definitely one way to go. Both optical and radio telescopes can ramp up the size to truly heroic sizes. However, there is an alternative astronomical observatory that will yield a cornucopia of information about so much of the galaxy. Basically it exploits the gravitational lens formed by the Sun and this is located outside of the solar system. The proposed FOCAL mission doesn't need new technology. Although it is way beyond the space technology because the extremely long mission time. The Sun's gravitational lens is roughly 550 AU away. That's a cool 82,500,000,00 distant. More information can be found at the following links.

http://www.centauri-dreams.org/?p=785

https://en.wikipedia.org/wiki/FOCAL_(spacecraft)

http://www.newyorker.com/tech/elements/the-seventy-billion-mile-telescope

The FOCAL mission can involve both optical and radio telescopes. Radio telescopes are capable of gathering information which is orders of magnitude more information than in any photograph. It's possible to imagine a future ring of FOCAL observatories strung around the solar system studying the galaxy in fine detail. They would still be cheaper than sending just one relativistic starship.

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This question asks for hard science. All answers to this question should be backed up by equations, empirical evidence, scientific papers, other citations, etc. Answers that do not satisfy this requirement might be removed. See the tag description for more information.

  • $\begingroup$ The problem with that is your station for observing one target, and you have a looong way to move it to look at anything else. $\endgroup$ – JDługosz Jun 30 '16 at 13:19
  • $\begingroup$ Doesn't solve the version of the fermi paradox where exponential population growth uses up a solar systems resources and a small spaceship is sent to the next one. Repeat and the galaxy could be full of humans given generational ships carrying 10's of people, 1 sent to each star system from a nearby one. $\endgroup$ – Donald Hobson Jun 30 '16 at 14:29
  • $\begingroup$ @JDlugosz Interesting point. One, FOCAL-type observatories could be orbiting the Sun & tracing out an arc of observed regions. Two, this is why I suggested a ring of FOCAL's. Three, a looong way yes, but not compared to an interstellar voyage. Nothing's perfect. $\endgroup$ – a4android Jul 1 '16 at 6:20
  • $\begingroup$ @DonaldHobson. Certainly. It also doesn't answer a dozen plus other versions of the Fermi paradox including FTL travel. It's only one more plausible suggestion for safe-at-hand aliens. I expect exponential growth civilisations to go extinct in their home systems. They won't be able to spare the resources for starflight. Generation ships with 10's of people aren't biologically viable; 100's to 1000's are needed, then it's feasible. The resource cost remains very high. I'm pro-space, but I know it won't be easy. $\endgroup$ – a4android Jul 1 '16 at 6:32
  • $\begingroup$ @a4android my own worldbuilding idea bypasses this feasibility problem and the central plot involves stimulating them to make the leap ASAP, driving technological development. $\endgroup$ – JDługosz Sep 4 '16 at 10:41

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