In astronautical mechanics the gravitational slingshot maneuver which NASA calls a gravity assist exploits the gravitational attraction of a planet to alter the speed and trajectory of an interplanetary spacecraft A spacecraft can thereby be accelerated by a near planetary flyby to enable considerable savings of fuel in missions to the outer planets such as Jupiter and Saturn At first sight this might seem like a cosmic somethingfornothing scam But the physics depends straightforwardly on conservation of momentum and energy and the huge planettospacecraft mass ratio which leaves the planetary orbit essentially undisturbed This Demonstration considers a hypothetical slingshot maneuver around the planet Jupiter orange sphere with radius ≈ 143000 km which moves at an average speed of 131 kmsec in its orbit around the Sun A spacecraft with initial speed which has a negligible mass and size compared to the planet follows a hyperbolic path in Jupiters frame of reference In the Suns frame of reference however the hyperbolic path is tilted and moves with velocity which provides a terrific boost to the spacecraft after it crosses the orbit of the planet The graphic shown is highly schematic with both space and time scales significantly distorted Refer to the references for more accurate formulas when you plan your next space mission