... we could stop Jupiter?

This may sounds strange but during New Horizons mission, which goal is to reach Pluto with a spacecraft, we actually slowed down the Jupiter.

Vehicle passing planet used it's rotation speed to increase it's own momentum without spending additional fuel. Gaining around 4,000 m/s for New Horizons shuttle costed gas giant around 10^-21 m/s of it's velocity. A slight, almost irrelevant change, took effect by bringing Jupiter closer to the sun expanding it's sun year by small statistical error.

If we would like to slow it even more we would definitely need more than just one small probe. New Horizons mission costed The U.S. Government over 700 000 000 $ in period of 2001-2016. In the same time governments all around the world spent around 191 519 360 000 000 $. That means if all that money would be taken from army, social, education, health etc. and putted into building probes similar to the one launched by New Horizons we could produce around 274000 vehicles.

Of course on Earth there's not enough materials for such project, but let's skip that fact. If we would manage to launch this amount of shuttles and lead them next to Jupiter's atmosphere, still the loose in it's speed would be irrelevant. Just few nanoseconds.

Actually we could throw all our planet into direction of Jupiter (Yes, I know how it's sounds) and we would slow down Jupiter, less than one hundred kilometres per hour. It's simply too big and too fast.

But what would happen if Jupiter would actually significantly slow down or even stop? Simplest explanation. Nobody knows. Of course we can just make wild theories. First of all whole gravitation in solar system would be disrupted. Rotation of other planets in system would change it's velocity or even change direction. The Jupiter would vanish because without power gained from it's momentum it couldn't keep it current state. Even if Earth would last through change of gravity, it would be destroyed quickly because, so far Jupiter was our protection while it was beaming larger asteroids toward itself saving Earth, which wouldn't stand similar impact.

But of course chance of this happening is less than difference in Jupiter speed after New Horizons mission.