Field noteWhy the maneuver matters more than the engine
A spacecraft does almost nothing the way intuition says it should. To rendezvous with a target ahead of you, you slow down. To slow down, you sometimes burn forward. The intuitive move — point at the target and accelerate — sends you into a higher, slower orbit, and the gap grows. The right move is counterintuitive, often non-local, and always cheaper than the wrong one.
That's why every flight plan goes through review long before any propellant moves. A Hohmann transfer to geostationary orbit is roughly two engine burns and several hours of coasting — but weeks of math, simulation, and red-team review.
NumbersWhat it actually costs to get up there
Reaching low Earth orbit requires about 9.4 km/s of delta-v — most of which is spent fighting gravity and atmosphere on the way up. From LEO to geostationary is another ~3.9 km/s. From LEO to a lunar transfer is a relatively cheap ~3.2 km/s. Every kilometre per second is bought with mass, and every kilogram of mass requires more propellant to lift it.