As I note in this blog post, it is possible to infer that the Universe is expanding, even if you have only velocities and no distances. The idea is that you would marginalize out all distances and the Hubble Constant, and do a likelihood test (or equivalent, like, say, cross-validation). The two hypotheses would be a gas of galaxies with finite velocity dispersion but a well-defined mean rest-frame velocity through which we are moving (at unknown speed) vs an expanding gas, again with the finite velocity dispersion and through which we are moving. I think the test is very easy to set up and the problem is very easy to solve, and would demonstrate that it only takes a handful of velocities (but very good sky coverage!) to demonstrate expansion.
2016-01-04
use exoplanetary transits to infer the Kepler PSF
Like many astronomical missions and data sets, the NASA Kepler satellite imaging is crowded; there is no part of the imaging that contains reliably isolated stars. For this reason, it is hard to infer (from the data) the point-spread function of the instrument simply; any PSF inference requires modeling the images as a crowded image of many overlapping stars (of unknown brightnesses and positions). However, when a star is subject to a planetary or stellar transit, the change in the scene during the transit should be modeled well as a PSF-shaped deficit. So we should be able to infer the PSF from these deficits. The transits are rare, so they rarely overlap. They are also very faint (low-amplitude) events, but (a) the eclipsing-binary stellar transits are not so faint (and very common), and (b) Kepler has good signal-to-noise even on planetary transits.