How does the slingshot effect or gravity work to assist a change in orbit of a spacecraft?

Answer 1

Gravity AssistIt's called Gravity Assist. Overcoming gravity is all about velocity. Escaping Earth's gravity requires approximately 25,000 mph. Escaping the Solar System needs more than 45,000mph. We dont have a large enough rocket to achieve that speed so spacecraft can use a planets gravity to increase its velocity and then the planet can "slingshot" it onto a new trjectory toward the next target. The gravity of a large object can "pull" something to a higher velocity and then, rather than crash into the object, the craft can just miss the planet or moon and, for a moment, go into orbit. The centripital force of the orbit will increase the craft's velocity and "shoot" it off on a new trajectory.

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Nope, that's wrong. An orbit is (by definition) symmetrical. There is no change of energy in an orbit (that is, no change to the sum of kinetic energy and potential energy). Any kinetic energy gained by a spacecraft on approach to a planet, by trading gravitational potential, must be lost on leaving it, as the kinetic energy is converted back into potential.

You can only make sense of a gravity assist by also considering the planet's orbit around the sun. By arranging a suitable slingshot configuration you can steal the orbital energy of the planet around the sun and give it to the spacecraft. The planet ends up in a lower (less energetic) orbit, while the spacecraft ends up in a higher orbit relative to the sun. It has nothing to do with the centripetal force of the spacecraft's orbit or hyperbolic trajectory around the *planet*.