# How much more massive would Pluto have to be to clear its neighborhood?

How much more massive would Pluto have to be to clear its neighborhood?

• Can you add a bit more detail and context to your question? – Rob Jeffries Jul 26 '15 at 22:54
• Pluto and Neptune kind of cross orbits, so this is a tough one. How big would it have to be to clear Neptune out of it's orbit, or, do we overlook that and let them both have clear orbits cause they're in resonance. – userLTK Jul 27 '15 at 1:56

In order to have cleared its orbit over a period of billions of years, an object needs a "Stern-Levison parameter" $\Lambda$ which is $> 1$; Pluto has $\Lambda \approx 3$-$4 \times 10^{-3}$. Since $\Lambda$ depends on the square of the object's mass (see the Wikipedia page, or Equation 4 of Stern & Levison), Pluto would need to be about fifteen to twenty times its current mass in order to cross the threshold.
As we know, Pluto is within the Kuiper belt, and it only makes up about $0.077\%$ times the mass of all of the object within its orbit. Now, in comparison, Earth has objects in its orbit, but it is $1.7$ million times the mass of all of the objects.