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In my mind, I picture a gravity assist sling shot boost like a ball on the end of string being swung until the centrifugal force grows strong and then is released. Where gravity is the string, the planet is the swinger, and ship is the ball.

If your ship is under acceleration when performing a gravity assist, would there be centrifugal force applied? Or asked another way, what would be the perceived gravitational increase to the occupants/cargo of ship using gravity slingshot while under thrust?

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No, there would not be any perceptible acceleration of the occupant. This is because the occupant is accelerated as much as the craft. With a ball on a string, the force is communicated through the point of attachment of the string on the ball. With gravity the force is communicated directly to all the mass.

(If one were using something like a neutron star to provide a gravitational assist, it would be possible to experience gravity different than the center of gravity of the [rigid] ship due to the force of gravity varying by square of the distance. This tidal force is a major plot point in Larry Niven's short story "Neutron Star". [If the ship was very large and still rigid, a less dense star could provide sufficient tidal force to be noticeable.])

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  • $\begingroup$ So the thrilling force you experience during the gravity assist around the moon in Mission Space at Epcot is scientifically inaccurate? $\endgroup$ – Hugh Jan 8 '18 at 17:26

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