Compass aboard the International Space Station If an astronaut brought a compass aboard the ISS and watched it for the duration of an orbit, what would it do?
 A: A compass reacts to the strongest magnetic field. A compass would point to the magnetic north of the Earth unless you bring a magnet sufficiently close. As you get further away from Earth, its magnetic field weakens. However, the ISS is still sufficiently close to make the compass point towards the Earth's magnetic north, given that its plane is not orthogonal to the magnetic field. The further you get away from Earth, the weaker the field becomes. At some point, the compass will respond to the sun's magnetic field. If you go even further away, all fields become so weak that your compass probably won't respond to anything. Note that there is also a quality different in compasses. Stronger compasses will respond to weaker magnetic fields, and are thus more likely to point to anything in space.
A: Since the question is not very precise I will consider only one case:
Compass needle parallel to earth surface
The orbits of the ISS look like this:

It barely reaches the 50°latitude. Assuming that in 300-400 km above the sea level at this altitude the earth magnetic field lines still have a strong horizontal component, the compass needle should presumably align to the magnetic poles during the whole orbit. 
Using the picture assume that you are in the ISS at the yellow point holding the compass at a fixed location. (I could not find any information about rotation or spin so we just consider a linear movement.) 
When you reach London the compass will be pointing to the north. Define this as the zero deflection. When the ISS is moving over Europe and the Middle East the compass needle will be deflected to the left. The deflection will reach the maximum value of ca. $52°$ (since this is the inclination of the ISS orbit) at the equator above the indian ocean. From there on the needle will be going to the zero deflection and reach it somewhere south of Australia. Then it will start deflecting to the right and reach the max deflection of $52°$ again at the equator in the pacific. So there will be one oscillation of the needle between $-52°$ and $52°$ during one orbit (actually a little bit more than one oscillation since the orbit does not end where it started). 
Of course one has to consider that the magnetic and geographic poles are not equally located. But the small differences should not cause too much derivation from the $52°$.
