Stokes vs ram pressure

Macroscopically, air resistance is ram pressure (proportional to cross-sectional area times velocity squared). Microscopically, drag is Stokes-like (proportional to radius times velocity). Where does the cross-over happen? I didn't have the guts to put that on problem set one of my course for pre-health students, but it will be in around problem set eight. It could be on problem set one, because the transition can be obtained purely by dimensional analysis.

In transport processes, there are often qualitatively different effects working at small scales than at large. Another good example is diffusion vs convection.

Apollo 11

Pete Mao (Caltech) sent me a note for Newton's birthday, pointing out that all sensible transfer orbits to and from the Moon ought to have half-periods (transfer times) of about 5 days. And yet, as he also pointed out, Apollo 11 came back in 2.5 days. What gives? Did NASA waste fuel to improve the filmic value of the mission, or does the enormous tidal effect of the Sun change the sensible set of transfer orbits for some reason I don't understand?

(His note on this subject also had a nice discussion about what a 5-year-old wants when he or she asks a scientific question, and why just answering it is the wrong response.)

astronomical detectors

Another problem-set problem, inspired by an email today:

Imagine measuring the brightness of two stars, one of which is a 100,000 K blackbody, and one of which is a 3,000 K blackbody. You are interested in the flux ratio in the V band. In one experiment, you perform this pair of measurements with a (flatfielded, calibrated, etc) CCD with a standard V-band filter on it. In another, you perform this pair of measurements with a bolometer with the same filter on it. Do you expect the flux ratio you measure to be the same in the two cases, and, if not, what is the expected difference? Imagine that both detectors are very high in quantum efficiency over the wavelength range of interest, and that you are capable of making accurate, calibrated, sky-subtracted measurements in both cases.

perspective

Future problem-set problem: These two images were taken from the same three-space camera position, with the same digital camera. What, physically, was changed about the camera, and why did it have the effect that it did?