Recharging Philae Lander
Philae Lander sits in a shadow on comet 67P and its battery is drained. How difficult would it be to aim a laser (or mirrored sunlight) from Earth that would track the motion of Philae and top up its battery?
Of course at the moment we do not know where on the comet Philae is, but it is surely just a question of time before it is located by the imaging systems on the mother Rosetta craft.
Don't shoot me for this question. It might be more doable than another 10-year Rosetta-like mission...
One other option is to wait and see. As the comet moves through space, on its journey around the Sun, the sunlight conditions might improve. It will have the equivalent of seasons, and this could play to Philae's advantage by altering the angle, timing and intensity of the sunlight hitting the solar panels.
PS The brave little probe eventually did wake up, on 14. June 2015!