MOON FLYBY SIMULATOR

This path is called the free-return trajectory — one of the most elegant tricks in all of spaceflight! The spacecraft traces a figure-8 path, with the Moon sitting inside one loop and Earth sitting inside the other.

The spacecraft doesn't orbit the Moon. Instead, it approaches on a long outbound arc, gets bent by the Moon's gravity like a ball curving around a corner, swings behind the Moon, and naturally arcs all the way back to Earth.

Try the flyby distance slider — change how close the spacecraft passes the Moon. Too close and the curve gets very tight. Too far and the Moon's gravity barely bends the path. The sweet spot sends the spacecraft exactly back home!

The free-return trajectory is a figure-8 shaped path — technically a translunar orbit — that satisfies the restricted three-body problem for the Earth-Moon system. At exactly the right energy and approach angle, the combined gravitational forces of both bodies create a closed path that returns to Earth's atmosphere without any additional propulsion.

The elegance of the design: this trajectory has zero fuel cost for return. If all propulsion fails after the trans-lunar injection burn, gravity alone closes the figure-8 path back to Earth. The flyby distance must fall within a narrow window — adjust the slider and observe how approach distance changes the loop geometry and return arc. Too close, and the deflection angle overshoots Earth. Too far, and the Moon's gravity is insufficient to close the figure-8.