Toggle a free-return path against a hybrid (non-free-return) path, then scrub the phase slider to watch a craft swing behind the Moon and either aim back at Earth or miss with a high perigee.
Early Apollo free-return designs targeted about 110 km (~60 nmi) lunar altitude at pericynthion. Apollo 13's restored free-return pass sat near 250 km (~135 nmi), and at that closest lunar approach the crew reached 400,171 km from Earth - the farthest humans have traveled from Earth.
Drag to orbit and scroll or pinch to zoom. Switch paths, press Play or Pause, or drag the phase slider from Earth departure through lunar flyby to Earth return or miss.
Apollo Free-Return Trajectory 3D Explorer
This browser explorer shows how an Apollo-style free-return path uses the Moon's gravity to loop a spacecraft home without a lunar-orbit insertion burn - and how a hybrid path, like Apollo 13 after MCC-2, can miss Earth's atmosphere corridor unless another burn restores free-return.
Apollo 8, 10, and 11 flew free-return translunar trajectories so that, if the service propulsion system failed before lunar orbit, lunar gravity alone would still return the crew toward Earth. Later landing missions switched to hybrid trajectories that reached sites farther from the lunar equator, but those hybrids needed a burn to get home if the landing was aborted.
After the oxygen-tank explosion on Apollo 13, the spacecraft was on a hybrid path with an Earth perigee near 2,500 nmi - too high for atmosphere capture. The crew used the lunar module's descent engine for a 34.23-second burn at GET 61:29:43 to restore a free-return geometry, then flew past the Moon and home.
- Toggle between a free-return teaching path and a hybrid (non-free-return) path
- Scrub phase from Earth departure through lunar flyby to Earth return or high-perigee miss
- Read published NASA figures for pericynthion altitudes, furthest Earth distance, and the DPS-1 restore burn
- Drag to orbit the camera, scroll or pinch to zoom
- Runs fully in the browser with the vendored three.js engine - no account, no upload
History and STEM teachers use the toggle to show why free-return was a crew-safety design, not a scenic detour. Readers who already know Hohmann transfers use this page for the lunar-flyby return geometry that Hohmann alone does not teach.
| Figure | Published value |
|---|---|
| Early Apollo free-return pericynthion | ~110 km (~60 nmi) lunar altitude |
| Apollo 13 restored free-return pericynthion | ~250 km (~135 nmi) |
| Apollo 13 furthest from Earth (at PC) | 400,171 km |
| Pre-restore hybrid Earth perigee | ~2,500 nmi (no atmosphere capture) |
| DPS-1 free-return restore burn | 34.23 s at GET 61:29:43 |
For a two-burn circular-orbit transfer between planets or altitudes, see the Hohmann Transfer 3D Explorer instead - that page teaches delta-v and transfer ellipses, not lunar free-return geometry.
Everything renders on your device with WebGL. The 3D engine loads once (about 0.7 MB) and is cached; no scene data is sent to a server.
This is an educational approximation, not a patched-conic reconstruction of Apollo burns - on-screen sizes and the Earth-Moon distance are compressed for readability, while the table holds the real published figures.
Frequently Asked Questions
What is a free-return trajectory?
A free-return path aims a spacecraft so the Moon's gravity bends it behind the Moon and back toward Earth without needing a lunar-orbit insertion burn for the return geometry. Early Apollo missions used this as a crew-safety design.
How is this different from a Hohmann transfer?
A Hohmann transfer is a two-burn ellipse between circular orbits. Free-return is a lunar flyby geometry that returns the craft to Earth. Use the Hohmann Transfer 3D Explorer for delta-v transfers; use this page for the Moon-assisted return path.
What went wrong with Apollo 13's path before the restore burn?
After MCC-2, Apollo 13 was on a hybrid path. Once the oxygen tank exploded, that path would have left Earth perigee near 2,500 nmi - too high for atmosphere capture - until the lunar module descent engine restored free-return.
How far from Earth were the Apollo 13 astronauts at closest lunar approach?
At pericynthion they reached 400,171 km from Earth, the record for furthest humans from Earth, because the Moon was near apogee and the free-return flyby passed farther from the Moon than a standard lunar-orbit pass.
Are the on-screen distances to scale?
No. Earth, Moon, and the path are compressed so the flyby and return corridor stay readable on one screen. The facts table lists the real published altitudes and Earth distance.
Does this page integrate Apollo burns with a physics engine?
No. It is an educational path explorer using published NASA figures. It does not integrate gravity, thrusters, or a patched-conic solver.