Win some money by designing an algorithm to optimise the orientations of the various ISS solar panels during orbit. It's not an easy problem because there are numerous constraints.
Full details here:
http://www.topcoder.com/iss/
http://www.topcoder.com/iss/challenge-details/
More detailed problem description here:
http://community.topcoder.com/longcontest/?module=ViewProblemStatement&compid=27068&rd=15520 (http://community.topcoder.com/longcontest/?module=ViewProblemStatement&compid=27068&rd=15520)
I'm very tempted to give it a go ...
At least now I understand why the ISS solar panels are at such weird angles in some of my images.