We use r ˙ ˙ and θ θ ˙ ˙ to denote the standard derivatives of how this distance and angle change over time. We take the derivative of a vector to see how it changes over time by subtracting its location at time t from that at time t + δ δ t and dividing by δ δ t . The result is also a vector. Because our basis vector r ^ ^ moves as the object orbits, we start by differentiating it. From time t to t + δ δ t , the vector r ^ ^ keeps its beginning at the origin and rotates from angle θ θ to θ θ + θ θ ˙ ˙ δ δ t which moves its head a distance θ θ ˙ ˙ δ δ t in the perpendicular direction θ θ ^ ^ giving a derivative of θ θ ˙ ˙ θ θ ^ ^ .