Chapter 11, Problem 74P

Neptune has a mass of $1.0\times {10}^{26}\text{kg}$ and is $4.5\times {10}^9\text{km}$ from the Sun with an orbital period of 165 years. Planetesimals in the outer primordial solar system 4.5 billion years ago coalesced into Neptune over hundreds of millions of years. If the primordial disk that evolved into our present day solar system had a radius of ${10}^{11}\text{km}$ and if the matter that made up these planetesimals that later became Neptune was spread out evenly on the edges of it, what was the orbital period of the outer edges of the primordial disk?