[nick238]

I don't know what you mean by "gravity assist around the Sun":

1. Using the perihelion in an orbit "around the sun" as a gravity assist?: spacecraft usually care about their speed relative to the sun (characteristic energy, C3), and a (free) gravity assist around the sun won't do much. Dropping close to the sun to perform a powered bi-elliptic transfer could be a thing if you wanted to travel extreme distances (e.g. put a telescope at 500 AU to use the solar gravitational lens)

2. Using other bodies that are "around the sun" to get a gravity assist?: spacecraft do this all the time.

Also "get around the solar system faster":

1. Decrease the orbital period (lower orbits orbit faster): This is exactly what Messenger and Parker Solar Probe is doing flying by Venus/Mercury. They're 'bouncing' off of the planets, trading orbital energy and raising the planets' orbit around the sun while dropping their own.

2. Get to places faster: This is what outer planets probes (Voyagers 1/2, Cassini, New Horizons) do. If Jupiter wasn't there, these missions might not be possible.

[JumpCrisscross]

> If Jupiter wasn't there, these missions might not be possible

If Jupiter weren’t there and moving relative to the destinations. The gravity isn’t the critical piece, it’s the relative motion.

Just having a massive object does nothing because gravity isn’t doing any work, it’s just coupling you to a moving object.

[nick238]

Oh, sorry, I didn't specify which Jupiter I was referring to, the real, moving Jupiter that orbits the sun vs. the stationary, straw-man Jupiter that jumps out at you in bad faith retorts.

[JumpCrisscross]

> I didn't specify which Jupiter I was referring to, the real, moving Jupiter that orbits the sun

This is why I said you can't gravity assist around the Sun to travel around the Solar System. The Sun is moving around the galaxy at a terrific speed. But so is the Solar System. Dropping into and out of the Sun's gravity well does nothing other than change your trajectory.

[ahazred8ta]

If you fire rockets at closest approach to get more delta-V, that's an Oberth Maneuver - https://en.wikipedia.org/wiki/Oberth_effect

And as you say, an unpowered planetary flyby is a gravity assist.