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How Do Spacecraft Use Planetary Gravity To Navigate Space?:

How Do Spacecraft Use Planetary Gravity To Navigate Space? ‘The Slingshot Effect’ By Ollie Ashton

Why Use The Slingshot Effect?:

Why Use The Slingshot Effect? The effect of the planetary gravity can accelerate a spacecraft during a flyby. ‘Slingshotting’ can therefore save fuel. The spacecraft continues in original orbit gaining only speed. Weeeeeeeeeee! How can this be possible?

Slingshot Effect: Principals:

Slingshot Effect: Principals Momentum must be conserved in the spacecraft-planet interaction. The momentum of the planet is much greater than that of the spacecraft. Total kinetic energy must be conserved. The effect can be modelled as a collision in the simplest case. You’d better be right about this! u U

Slingshot Effect: Collision Model:

Slingshot Effect: Collision Model Spacecraft with mass m & speed u. Planet with mass M & speed U. Both travel towards each other. Craft approaches (and must also recede) at u+U relative to planet. Woooooohooooo! u+2U U Spacecraft recedes with speed u+2U.

Slingshot Effect: Momentum:

Slingshot Effect: Momentum In terms of momentum: M*U1 - m*u1 = M*U2 + m*u2 Assume U1 = U2 = U u2 = ([1 - m/M] u1 + 2U) / (1 + m/M) As m is negligible compared to M we get: u2 = u1 + 2U Which was our original estimate.

Slingshot Effect: Outcome:

Slingshot Effect: Outcome If u1=U the spacecraft will triple it’s speed! The spacecraft’s extra momentum comes from the planet. The planet will actually slow down by a very small amount. About a few atom widths behind it’s original orbit had the flyby not occurred. The planet is effectively untouched!

Summary & Random Facts:

Summary & Random Facts The escape velocity of Earth is 11km/s, but spacecraft usually travel between 5-10km/s once out of Earth’s strong gravitational range. Jupiter’s mean orbital speed is 13km/s, which would give a craft 26km/s more speed. The fastest spacecraft on record are the NASA-German Helios solar probes which reached speeds of 70km/s in 1976 using this method. Ah Crap.