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?
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.
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.
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.