Lise Eleanor wrote:

I'm a screenwriter and I have a question:

If a big enough asteroid hit Jupiter and a piece of Jupiter broke off, could
it become a rogue asteroid and head for Earth? (I've heard that Jupiter's
many moons were once actually part of Jupiter that broke off.)

Jupiter is gas planet. In the unlikely event an asteroid strike produces
something out of Jupiter, this something will be a puff of gas.

If not, what type of situation can be proposed that would produce a
threatening rogue asteroid?

Take a look he

http://seds.lpl.arizona.edu/seds/cha...t/science.html

Look under "Origins".

Regards,

- Alex