THE GRAVITATIONAL SLINGSHOT — a dart

THE GRAVITATIONAL SLINGSHOT steal a planet's speed

A free ride across the solar system: fly behind a moving planet, and in the Sun’s frame you leave with up to twice the planet’s velocity added — an elastic bounce off a mass so huge it barely notices. The planet loses an unmeasurable sliver of orbital speed; you gain kilometers per second. Voyager reached the outer planets on Jupiter’s slingshot; it is momentum, borrowed.

THE TECHNIQUE v_out = v_in + 2U (head-on flyby)

The demo runs a head-on elastic flyby: incoming 10 km/s off a planet moving 13 km/s: live demo

HISTORY & CREDIT Minovitch · 1961

“A slingshot creates energy.” — energy is conserved; the spacecraft borrows kinetic energy from the planet’s orbit, which slows by an immeasurable amount. cited

the bounce · an elastic collision with a moving wall — in its frame you keep your speed, in the Sun’s you gain 2U.
the ledger · the planet loses exactly what you gain (m·Δv conserved).
1961 · Michael Minovitch worked out gravity assist; Voyager rode Jupiter’s.

Momentum, borrowed and repaid by a rounding error. physics

RECOMMEND FOR I-13 the steal, on the compiler

On i-13, a head-on flyby (10 km/s off a 13 km/s planet) leaves at 36, a gain of 2U:

$ i13 run gw_slingshot.i13 RUN OK · 20 step(s) v_in = 10 u_planet = 13 v_out = 36 -- v_in + 2*U gained = 26 max_gain_is_2u = 1

Recommend as a NULL — conservation (B39). The maximal gain 2U is momentum/energy conservation in the elastic limit; the ledger balances exactly (touching the seated conserve-remainder axis, not extending it). NULL — steal a planet’s speed.