Would a spaceship that used a planets gravity as a slingshot save on fuel by doing that?
Our robotic spacecraft use this technique all of the time to save on fuel. This is called a gravity assist. One of the most notable examples is the Voyager mission, which used each gas giant’s gravity to boost it to the next planet in a rarely-available trajectory called “the grand tour.” The 4 gas planets were roughly lined up so that each could be used to slingshot up to the next one, and eventually out of the solar system. Cassini used a very long gravity assist where it flew by Venus for a gravity assist not once, but twice, then the Earth, then Jupiter in order to reach Saturn. New Horizons used Jupiter’s gravity to cut the travel time to Pluto down from 15 years to about 11. One mission, I forget the name at the moment, even used Jupiter’s gravity to boost it into a polar orbit around the Sun, which would have been an impossible orbit using our rocket technology – no rocket has ever been built that is large enough to directly launch onto a polar orbit around the Sun. The drawback
