The short answer is: rocket science!! Of course…but how really?
First, let’s congratulate and recognize the ESA (European Space Agency) who sent the Rosetta spacecraft with the Philae lander onto Comet 67P/C-G. A truly awesome and historic accomplishment!!! Hurray for another epic, cosmic score for rocket science!
It takes an entire multi-disciplinary team to make this possible. But 3 of the most crucial jobs fall to those who handle orbital mechanics, propulsion, and GNC (Guidance, Navigation, and Control). GNC is actually 3 disciplines in itself but they are often grouped together because they are so tightly coupled and integrated in their system and function.
Orbital mechanics is the study of how objects move through three-dimensional space in outer space. In this case, there wasn’t much orbiting happening per se. It was more of a single approach path and formation flight between the spacecraft and the comet. But if you love to think about the three-dimensional paths and trajectories of objects, and want to analyze or predict that on a planetary or cosmic scale, orbital mechanics could be a dream job for you. Pay attention to physics class and Newton’s laws of motion!
Propulsion is another key discipline and technology because it isn’t any use in knowing how to cozy-up to a comet unless you have the energy (thrust) to get there.
Then, it isn’t enough to have the available power and flight path either. You have to be able to control this energy, measure the current state so you can respond and adjust accordingly, and communicate back to people on Earth for situations that need it.
You can’t ignore or discount all of the other disciplines that are needed too, like structures, energy management, thermal management, quality control, testing, etc etc.
Do you still wonder about particular jobs or disciplines that are needed to land a spacecraft on a comet? Or how they actually did it? Write a comment here and I’ll try to answer, or guide you somewhere else for better options.