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Since the National Reconnaissance Office offered NASA a left-over Hubble sized mirror that might be used for the WFIRST space telescope, I wonder if the NRO has satellites in operation that could do similar astronomy? Would the instruments that are likely used by existing spy satellites for Earth observation (optical and radio) be useful for astronomy?

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    $\begingroup$ Here is the reverse question considered by XKCD. $\endgroup$ – Arthur Feb 19 '18 at 13:52
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Surprisingly, yes, in at least a few limited cases. There are aspects of astronomy that could be done by pointing a spy satellite at solar-system objects besides the Earth.

As any photographer will tell you, the brightness of an extended, resolved object like a person, or the disk of a planet, does not decrease with distance between you and the object, and so the surface of the Moon, or of Mars will look roughly as bright to the spy satellite as the surface of the Earth right below.

If you are 10x farther away, the amount of light from each point on the surface is 100x lower, but the total area of the object's disk contributing to each square arcsecond of solid angle (or each pixel) will be 100x larger.

So as long as the attitude control of the spacecraft is commensurate with the optical resolving power of the telescope for Earth imaging, it could potentially be used for high resolution monitoring of the surface of the Moon, or of Mars.

Of course Mars at opposition is still fairly small, but this great answer shows a Hubble image of Mars' surface features, and it will be a factor of 2 dimmer because of the 50% larger distance from the Sun, and the average albedo of the Moon is only about 0.1 compared to Earth's 0.3 (see here and here) so it will also be somewhat dimmer, but not an order of magnitude.

Since the spy satellite's telescopes image sensor will certainly have a pixel density commensurate with the ultimate optical resolution, there shouldn't be any fundamental limit here either.

As an aside:

As discussed in a different question and its answers, an orbital telescope's resolution looking down through the atmosphere to the Earth's surface does not reach the seeing limit until an aperture of a few meters (unlike looking up through the atmosphere, where an aperture of 15 to 20 centimeters is usually at the seeing limit without adaptive optics) so the sensor will indeed be already matched to the diffraction limit of the larger aperture.

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    $\begingroup$ What about focal length? $\endgroup$ – Basic Feb 19 '18 at 14:42
  • $\begingroup$ To be clear, I'm assuming you are talking about apparent brightness here, not luminosity? $\endgroup$ – TylerH Feb 19 '18 at 15:22
  • $\begingroup$ @TylerH Terms that refer to an unresolved star-like object would not apply here, as I'm talking about an extended, resolved object, in this case the image of a planet's (or the Moon's) disk. The units would be Watts per unit area (telescope aperture) per unit solid angle, after integrating over a suitable wavelength range, which seems so far to be best matched by the term Radiance, but neither of the terms you've mentioned. $\endgroup$ – uhoh Feb 19 '18 at 23:25
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    $\begingroup$ Hmmm.... layman here, but... when talking about visible light photography, isn't there a world of difference between the primary goal of a spy sat (resolution) and an astronomy sat (mirror size, to get as much light as possible from dim objects)? $\endgroup$ – DevSolar Feb 20 '18 at 10:18
  • $\begingroup$ @DevSolar both resolution and light gathering increase with increasing aperture. In the case of spy satellites, remember that they are moving about 7 kilometers per second relative to the ground, and would like to take as many un-blurred images as possible, so a very short exposure time afforded by the large aperture is also important, not just the resolution of one, perfectly timed image. The full discussion is outside of a few comments thought. There are many kinds of observations in all of astronomy, and not all of them need to push for the dimmest objects. However, throughput still matters $\endgroup$ – uhoh Feb 20 '18 at 10:36
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Spy satellites are used to look at a really bright object: daytime Earth. This needs short exposure times, detector noise is no problem, and you want a B/W or full-color image.

Astronomical telescopes are used to look at very dim objects (magnitude 20 stars), so they need far more sensitive detectors, and longer exposure times with accurate tracking. They also need to do spectroscopy.

So if you take a spy satellite in orbit now and point it the other way, you wouldn't get very good results.

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    $\begingroup$ You could, however, help science with Earth Observation. $\endgroup$ – gerrit Feb 18 '18 at 11:13
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    $\begingroup$ Spy satellites don't only do B&W and full-color. You also want other wavelengths which can be used for false color images. There are a million applications for other wavelengths. $\endgroup$ – Dietrich Epp Feb 18 '18 at 18:36
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    $\begingroup$ Satellites are also used to observe Earth at night. They do not only operate during the daytime. Related: NASA's black marble (nasa.gov/mission_pages/NPP/news/earth-at-night.html) $\endgroup$ – Darren Feb 19 '18 at 15:11
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Yes! Gamma-ray bursts from deep space were actually first discovered by the VELA spy satellites looking for hidden nuclear tests. The original 1973 paper Observations of Gamma-Ray Bursts of Cosmic Origin (also here, Klebesadel, Strong and Olson, 1973, ApJ 182:L85-L88). The paper indicates:

The observations were made by detectors on the four Vela spacecraft, Vela SA, SB, 6A, and 6B, which are arranged almost equally spaced in a circular orbit with a geocentric radius of ~1.2 X 10^5 km.

The large orbits mean that the time of arrival varies by a faction of a second due to the speed of light (~3 X 10^5 km/s) which allowed the authors to verify for at least some of the events that the source was not in the direction of the Earth or the Sun.

Arrival-time differences have been derived approximately in all cases, and fairly accurate (±0.05 s) for a number of cases. For a two-spacecraft coincidence the transit delay defines a circle on the celestial sphere on which the source position must lie. For three spacecraft we can define intersecting circles, whose points of intersection represent the source position and its mirror image in the orbital plane of the spacecraft, a presently unresolved ambiguity. Nevertheless, it has been possible by this technique to rule out the sun as a source. Also, in none of the 16 cases was there found any close correlation with any recorded indications of solar activity.

One event has been observed which almost certainly was associated with a solar outburst. It differs distinctly from the 16 bursts reported here, and will be described in detail at a later date.

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    $\begingroup$ That's a good point (and a good catch). Since the OP mentions radio as well as optical, answers should not be limited to just optical (as the others are at the moment). $\endgroup$ – uhoh Feb 18 '18 at 23:09

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