Is there any in-universe and in-canon explanation of how Captain Jack found the Doctor's hand after it got cut off by the Sycorax leader, and how he knew it was the Doctor's?

I mean, did he just happen to take a walk underneath the Sycorax spaceship, and he saw the hand falling, and he thought, oh look, a hand, and hey, it looks remarkably like the Doctor's, even though it's from a different regeneration, so let's keep it, just in case?

Or is there a better story to it?