You are a promising theoretical physicist who does not believe that gravity is a distinct fundamental force but is instead related to the other forces by an all-encompassing relativistic, quantum-mechanical theory. In particular, you do not believe that the universal gravitational constant G is really one of nature's elite set of fundamental constants. You believe that G can be derived from more-basic constants: the fundamental constant of quantum mechanics, Planck's constant h; the fundamental speed limiting the propagation of any force, the speed of light c; and one other—a fundamental length l, important to the one unified force. Using simply dimensional analysis, find a formula for G, then an order-of-magnitude value for the fundamental length.
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