One place we can observe geodetic precession is in binary pulsars. A pulsar is a neutronstar that emits a narrow beam of light misaligned with its spin axis, so it's

like a flashlightspinning around on the floor if you look at it from a distance it seems to be flashing orpulsing as the light beam rotates through your line of sight. Hence the name "pulsar." Goahead and read the Wikipedia article on pulsars if you like; it's one of the good ones and hasa nice animation. Due to the beamed nature of the radiation, you can see the pulses changeas the spin axis precesses. They have been observed to apparently switch off in some casesas the beam precesses so much it no longer intersects the line of sight to Earth. Suppose you are lucky enough to observe an eclipsing binary pulsar that is, the neutron star passes in front of and behind its companion, which implies that the orbital angular momentum is perpendicular to the line of sight. Then supposing the orbit is circular you can measure the time-dependent Doppler shift and get the full orbital velocity V. And of course you get the orbital period P. Suppose further that the companion mass M is much more than that of the neutron star. Assuming the weak gravity approximation in Hartle's Equation (14.19), how many orbital periods does it take for the neutron star's spin to precess all the way around?