Planets, by definition, have cleared their orbits around their respective star. So a planet killer threatening earth cannot share the earths orbit, or earth wou

Planets, by definition, have cleared their orbits around their respective star. So a planet killer threatening earth cannot share the earths orbit, or earth wouldn't be a planet. So a circular orbit shared with the earth is ruled out. But if it had a circular orbit that did not intersect the earths orbit, then there would be no chance of it hitting earth, so not really a planet killer either. The possible orbits that remain must be elliptical. Now if a planet killer passed us every year then we probably would have hit them by now (or provided a gravity slingshot to alter its orbit!), so it follows that it must have a large orbital period :p