Let me amend the S/N calculation I gave for seeing-limited vs. diffraction-limited telescopes above (it was late). For a seeing-limited telescope of diameter D, the signal from a point source goes as D^2, and the sky background flux in an aperture also goes as D^2, Poisson noise is sqrt(N), and so the S/N improves as D^1. For a diffraction-limited telescope, the signal from a point source goes as D^2, the image diameter goes as 1/D and so the aperture area goes as 1/D^2 and the sky background flux in the aperture is constant, so the S/N improves as D^2.

For deep imaging from space, if everything else is equal, large telescopes tend to win over small because of the improvement from diffraction-limited imaging. Comparing ground-based telescopes of diameter D with equal atmospheric seeing, the signal collected in a given exposure time goes as D^2, while the cost of construction goes as some power of D (2.5 or so). But for space-based telescopes, the diameter of a diffraction limited image goes as 1/D. This means that the solid angle occupied by a point source goes as 1/D^2. The smaller size of a point source means there is less sky flux under it. For deep observations longward of about 500 nm (depending on the detector, etc), observations are limited by Poisson noise in the background from the zodiacal light, so for diffraction limited imaging the S/N can go as D^3 rather than D^2. (But you need to spend a lot on a big detector to get a decent field of view because the pixels are smaller. Detectors often drive the size and cost of instruments for telescopes, more than the optics do.)

Of course, everything else is not equal, the cost of putting large things in space doesn’t necessarily go as D^2.5 (it’s probably steeper) and smaller projects can come to fruition faster, take advantage of advances in detector technology, are better suited to mapping large areas of sky, and so on. So there is a place for both small and large satellite observatory projects.

Lawrence B. Crowell

has any thought been given to having several smaller telescopes working in concert, a brace of Hubblets if you like?

I’ve actually looked into putting together a proposal for something like this, and the problem is that you can’t really get a pointing system as good as Hubble’s on a low-cost satellite bus. You’d still get good UV sensitivity, so the UV folks have been considering small satellites in the latest round of SMEX proposals. But, you can’t get the same level of spatial resolution, which is the science I’m most interested in at the moment.