TRANSFERS

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Transfers — once you're in orbit, you're halfway to anywhere.

Robert Heinlein wrote that. He was right. Reaching low Earth orbit costs about 9.4 km/s of ∆v — the hardest part of any trip. Going from there to Mars adds only ~3.6 km/s. Once you're free of the planet's atmosphere and in a proper orbit, the rest of the solar system is mostly geometry.

The seven sections in this tab cover the geometry. The Hohmann transfer is the cheapest possible trip between two orbits — two burns, eight months of coasting. Lambert's problem generalises Hohmann to arbitrary departure and arrival dates. Gravity assists let you steal speed from a planet (essentially) for free, which is how Voyager 2 reached Neptune. Free-return trajectories are the safety net that brought Apollo 13 home. Patched conics is the working approximation that lets us compute all of this in a browser.

If you only read one section: Hohmann transfer. Everything else builds on it.