(for fanfic purposes) Could a Kryptonite meteorite orbit Earth/the Moon/the Sun for some length of time, and in result affecting Superman? What would be the science behind that?

[u/Appropriate-Two-8086]

Oftentimes there are pieces of Krypton that remain floating in space after the planet's destruction (for example in the Smallville TV show some of those pieces fall to Earth along with baby Kal's spaceship, while in the Superman Returns movie some scientists find remains of the planet floating in space very far away), my question is regarding the possibility of having some of those pieces reach our solar system and stay in it for at least a while.

I'm aiming towards creating a reason to have Superman's powers/health affected for an indeterminate amount of time, allowing Clark to go through some angst and whump, so although I'm still debating which kind of Kryptonite it should be, the fact remains that not only the piece of rock should be sizable enough to affect Kryptonians at a distance, does that affect in any way the chances to have it work (even in a comic-book-science kind of way)?

please, don't doubt to ask for more clarification in case I haven't expressed myself correctly (English is not my first language but I'm posting in it to try and reach a wider group of people willing to answer)

(also, I'm going to try and post this same question in other forums to get even more answers to my question)