Probably a bunch. I'm not a rocket scientist, but Google tells me Jupiter's orbital velocity is about 13,000 m/s, with Earth's velocity being about 30,000 m/s.

Probably a bunch. I'm not a rocket scientist, but Google tells me Jupiter's orbital velocity is about 13,000 m/s, with Earth's velocity being about 30,000 m/s. If my KSP-taught understanding of orbital mechanics is correct, you'd first have escape earth's gravity(~13,000m/s), then reverse your orbital velocity(about 60,000m/s, also matching the orbital plane of the asteroid in the process), and then do a standard hohmann transfer to the asteroid orbit(looks like about another 5,000m/s) just to get to the asteroid, but then you have to cancel the closing speed. I don't know enough to know how to calculate the approach velocity but looks like it might be a bunch. Chart showing d/v required to reach various objects in our solar system: https://i.imgur.com/WGOy3qT.png https://i.imgur.com/WGOy3qT.png