The answer depends on your situation, and if you need the money from your Sterling home to buy in Petersburg.
Is your Sterling home listed? For how long? Why hasn't it sold? Could it be price? Think about the worst case scenario. What if your house is not worth what you think it is? What if you get considerably less for it than you expect? Will you still be buying the same house in Petersburg at the same price? If the answer to that is NO, then you need to get your Sterling home solidly under contract before you enter into a sales agreement for the Petersburg property.
My office is in Leesburg, and I work throughout the Loudoun/Dulles area. If you would like to talk with me about the Sterling property in detail, please email or call. Vchrisner@kw.com and 703-669-3142