Rockets · trajectories · the road to the Moon
From the rocket equation to a full Earth–Moon trajectory you can scrub through, with every burn, velocity and timeline annotated. Built around the two programs that defined lunar flight: Apollo and Artemis.
How rockets work
A rocket moves by throwing propellant backwards. Every result below follows from that single idea, formalised by Konstantin Tsiolkovsky in 1903.
The logarithm is the tyranny of the rocket equation: doubling your mass ratio adds only a fixed Δv, so reaching orbit (~9.4 km/s to LEO) demands either ferocious exhaust velocity or throwing away empty tanks — i.e. staging.
Tune an engine and a rocket, see the Δv.
Getting to orbit and beyond
Orbit is not about height; it is about sideways speed. Go fast enough horizontally and you fall past the planet. The vis-viva equation ties speed, distance and orbit size together.
Two special cases drop out immediately:
To change orbits efficiently you burn at the right point — the Hohmann transfer, the cheapest two-burn route between circular orbits.
From a 300 km parking orbit to a target altitude.
The main event
Scrub through a full lunar mission. Watch the spacecraft climb out of Earth's gravity well, coast for days, and arrive at the Moon — with every phase, burn and number exposed. Switch programs to compare how Apollo and Artemis fly.
Trajectory geometry is schematic (not a numerical integration); milestones, burns and durations are representative real-mission values. Velocities/distances shown update continuously as you scrub.
Program I
Six crewed landings, built on the largest rocket ever flown to operational service: the Saturn V. Apollo 11 carried Armstrong, Aldrin and Collins to the Sea of Tranquility, landing on 20 July 1969 at mission-elapsed time 102:45:40.
110.6 m tall · ~2,970 t at liftoff · ~34.5 MN sea-level thrust.
After surface operations the ascent stage of the Lunar Module (Eagle) lifted off, rendezvoused with the Command Module (Columbia), and a trans-Earth injection burn started the three-day coast home, ending in splashdown on 24 July 1969.
Program II
NASA's Artemis program aims for a sustainable lunar presence, targeting the south pole and building the Gateway station. It flies the Space Launch System (SLS) and the Orion spacecraft with its European Service Module.
~98 m tall · ~2,600 t at liftoff · ~39.1 MN liftoff thrust (~8.8 million lbf).
Uncrewed. Orion flew to a distant retrograde orbit, then home — a 25.5-day, ~2.0-million-km shakedown that ended with splashdown on 11 Dec 2022.
First crewed flight: a free-return lunar flyby with four astronauts (Wiseman, Glover, Koch, Hansen). ~10 days; no lunar orbit.
The crewed landing — near the lunar south pole, using a SpaceX Starship Human Landing System. Crew transfers from Orion to the lander in a near-rectilinear halo orbit (NRHO).
Artemis II and III dates and architecture have shifted over time. For the current schedule and crew, check up-to-date NASA sources (enable web search).
| Dimension | Apollo (11) | Artemis (I–III) |
|---|---|---|
| Launch vehicle | Saturn V | SLS Block 1 |
| Liftoff thrust | ~34.5 MN | ~39.1 MN |
| Crew capsule | Apollo CM · 3 crew | Orion + ESM · 4 crew |
| Lunar orbit | Low lunar orbit (~110 km) | DRO (I) / NRHO (Gateway) |
| Lander | Lunar Module | Starship HLS (III) |
| Return profile | Direct entry, ~11 km/s | Skip entry, ~11 km/s |
| Goal | Reach the Moon first | Sustainable presence, south pole |
Beyond the Moon
The same equations send probes across the Solar System and beyond. Click any mission for its key numbers and the physics trick that made it possible.
Quick reference