From the heliocentric point of view consider the vector to the planet r = r r ^ ^ where r is the distance to the planet and r ^ ^ is a unit vector pointing towards the planet. d r ^ ^ d t = r ^ ^ ˙ ˙ = θ θ ˙ ˙ θ θ ^ ^ , d θ θ ^ ^ d t = θ θ ^ ^ ˙ ˙ = − − θ θ ˙ ˙ r ^ ^