Rocketta

Meet Rocketta, a rocket who goes forward by throwing her own mass backward.

A rocket in space has nothing to push against. Instead it pushes on its exhaust, and the exhaust pushes back. Momentum conservation, applied as the rocket burns fuel bit by bit, gives Konstantin Tsiolkovsky's rocket equation, published in 1903: the change in velocity equals the exhaust speed times the natural log of the starting mass over the final mass.

The logarithm is harsh. Burning until the mass falls by a factor of e, about 2.72, adds exactly one exhaust speed. Adding a second exhaust speed needs a mass ratio of e², about 7.4. Reaching low Earth orbit takes roughly 9 to 10 km/s of total Δv, including losses, while chemical exhaust speeds are around 3 to 4.5 km/s. So most of a launch rocket's mass must be fuel.

That is why rockets drop empty stages: less dead mass means more Δv from the fuel left.

The equation ignores gravity and air drag during the burn. Ion engines achieve much higher exhaust speeds, but with very low thrust.