Todayâ€™s landing of a spacecraft on a comet is truly a stupendous engineering feat. ESA Rosetta spent 5 years, including three flybys of Earth and one of Mars in order to slingshot in order to land a 3-ton machine on a 4-km round rock moving at 135,000 km/hour. (meaning that the comet moves ten times itâ€™s entire length every second)
Given the past few weeks of difficulty and failure in the always difficult engineering discipline of using high energy chemistry and physics to propel objects at (literally) astronomical speeds - the Rosetta success is particularly welcome. No one working in the field of aerospace ever thinks their tasks are easy or error-free; their missions are audacious and must be accepting of these grand failures to acheive even grander achievements.
Become a rocket scientist
If you want to try your hand at building, launching, and flying across the solar system - I highly recommend checking out Kerbal Space Program. It includes a decently accurate physics models so you can experiment with the trade-offs of spacecraft size to rocket size to fuels. Earth is a large gravity well and requires large amounts of combustible materials to reach orbit where subsequent maneuvers become relatively easier.
Now is where your geometry lessons come in. Rotational dynamics can be mind-bending at first, and you start becoming obsessed with energy management.
Kerbal has a vibrant community who have created hundreds of mods for additional spacecraft parts, celestial bodies, AI pilots, and atmospheric dynamics. Many of these are on Github and you could learn to build your own. If you really get into it, I recommend reading Fundamentals of Astrodynamics or Fundamentals of Space Dynamics.