How much fuel does a planetary slingshot save? Pick your destination.
A gravity assist sounds like free energy. It isn't. You are borrowing speed from a planet. The planet slows down a tiny bit. The spacecraft speeds up a lot. Because the planet is huge and the spacecraft is tiny, you never notice the planet's slowdown. But you notice yours. Voyager 1 used Jupiter to slingshot out of the solar system. Without Jupiter, it could never have left. It did not have enough fuel.
The trick works because the planet is moving. If you fly behind a planet in its orbit, the planet's gravity pulls you along. You gain speed. If you fly in front, you slow down. The Parker Solar Probe did this seven times with Venus. It was stealing speed, not adding it, because it needed to slow down to fall into the Sun. You read that right: to hit the Sun, you have to slow down. To leave, you speed up.
Cassini went to Saturn and used Venus twice, Earth once, and Jupiter once. Four gravity assists over seven years. A direct launch would have needed a rocket too big to build. Instead, it borrowed speed from four planets. This is how we reach the outer solar system: not with bigger rockets, but with clever orbits.
The Voyager grand tour only happens every 175 years. The outer planets line up just right. Voyager 2 took it. It flew by Jupiter, Saturn, Uranus, Neptune. Each flyby slingshotted it to the next. Without that alignment, Uranus and Neptune would have taken 30 years each. It did it in 12. We are still getting data back from it.
No. The spacecraft gains kinetic energy, but the planet loses exactly the same amount. Since Jupiter is 318 Earth masses, the speed change is unmeasurably small. You are borrowing, not creating.
No. Each assist requires a flyby geometry that only opens up rarely. You cannot loop Jupiter forever. The planets move. The alignment window closes. Voyager's grand tour happens once every 175 years.
Because falling into the Sun requires canceling Earth's 30 km/s orbital speed. Firing rockets to do that takes too much fuel. Flying in front of Venus steals speed for free. Seven Venus flybys. Seven free brakes.
In theory yes, but the math gets dangerous. Get too close and the tidal forces tear you apart. Stay too far and you get nothing. No one has tried. Probably for the best.