Orbital Mechanics

Here's the key insight: an orbiting spacecraft is falling toward Earth - it's just moving sideways fast enough that it keeps missing.

Throw a ball, and it arcs down and hits the ground. Throw it faster, and it goes further before landing. Throw it fast enough (about 28,000 km/h at low Earth orbit altitude), and by the time it falls, the curved Earth has fallen away beneath it by exactly the same amount.

That's an orbit. Perpetual falling, perpetual missing. No engine required to maintain it - just the right balance of speed and altitude.

This is why the counterintuitions make sense. Speed up in a circular orbit, and you rise higher - you're now going too fast to fall at this altitude. Slow down, and you fall closer. The relationship between speed and altitude is fixed by physics.

Orbits come in different shapes, all ellipses (or circles, which are just special ellipses).

A spacecraft in low Earth orbit circles at about 400 km altitude, completing one orbit every 90 minutes. The Moon orbits much higher - about 384,000 km away - taking 27 days per orbit.

To travel between these orbits, a spacecraft needs to change its shape - stretch out from a circle to an ellipse that touches both altitudes, then circularise at the destination.

The interactive below shows a lunar mission profile. Notice how the transfer orbit connects low Earth orbit to the Moon's orbit.

In 1925, German engineer Walter Hohmann discovered the most fuel-efficient way to move between two circular orbits. It uses exactly two engine burns.

First burn: At the starting orbit, fire your engine to speed up. This stretches your circular orbit into an ellipse whose far point touches the destination orbit.

Coast: You're now on a transfer ellipse. No engine needed - you're falling outward, slowing down as you climb against gravity.

Second burn: When you reach the high point (apoapsis), fire again to circularise. Otherwise you'd fall back down the ellipse.

Watch the transfer below. Notice how velocity drops as altitude increases - trading speed for height.

Here's something strange: a rocket engine produces more useful energy when the spacecraft is already moving fast.

The engine produces the same thrust regardless of speed. But kinetic energy depends on velocity squared. Adding 1 km/s to a spacecraft moving at 10 km/s adds much more energy than adding 1 km/s to one moving at 1 km/s.

This is why Hohmann transfers work so well. Both burns happen at the fastest points in the orbit - periapsis (closest to Earth) and apoapsis (at the destination). Burning at these points extracts maximum value from every kilogram of fuel.

Try adjusting the orbital parameters below to see how the required velocity change (delta-v) varies with the orbit ratio.

Real lunar missions add complexity. The Moon is moving, so timing matters - you need to arrive when the Moon is actually there. The spacecraft needs to enter lunar orbit, not just fly past.

Apollo used a direct transfer: launch, trans-lunar injection burn, coast for three days, enter lunar orbit. Simple and fast.

Artemis uses a more complex trajectory involving a near-rectilinear halo orbit (NRHO). It takes longer but requires less fuel and provides better geometry for lunar surface access. Different constraints, different optimal solution.

Explore the mission phases below to see how the full trajectory breaks down.