Consider a Photon from Sun and travels with a velocity $c$. Now think we are that photon. For us, it looks like Sun is moving away from us with a velocity $c$. So, why don't we get attracted back towards Sun, because the mass of Sun would be infinite for us since it moves away from us with a velocity $c$.


Question: Can I use a package manager of one distribution on another?
Answer: It is possible, although it will take quite a bit of work to get operational, and it won't be supported by either distro's teams generally. I only know it's possible because I've watched as a co-worker of mine did it one time merely to say he could/had.

As for the logistics of it, I think the init system differences is going to be one of the biggest hangup. The init system in gentoo is going to be completely different from the init system in fedora. As such, you'll have to either hack portage so that it will work with fedora's init system, or hack fedora to work with gentoo's. The other hangup you'll run into is that portage doesn't like dealing with software and packages that haven't been installed by portage to begin with.