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.