<P> As the planets have small masses compared to that of the Sun, the orbits conform approximately to Kepler's laws . Newton's model improves upon Kepler's model, and fits actual observations more accurately (see two - body problem). </P> <P> Below comes the detailed calculation of the acceleration of a planet moving according to Kepler's first and second laws . </P> <P> From the heliocentric point of view consider the vector to the planet r = r r ^ (\ displaystyle \ mathbf (r) = r (\ hat (\ mathbf (r)))) where r (\ displaystyle r) is the distance to the planet and r ^ (\ displaystyle (\ hat (\ mathbf (r)))) is a unit vector pointing towards the planet . </P> <Dl> <Dd> d r ^ d t = r ^ _̇ = θ _̇ θ ^, d θ ^ d t = θ ^ _̇ = − θ _̇ r ^ (\ displaystyle (\ frac (d (\ hat (\ mathbf (r)))) (dt)) = (\ dot (\ hat (\ mathbf (r)))) = (\ dot (\ theta)) (\ hat (\ boldsymbol (\ theta))), \ qquad (\ frac (d (\ hat (\ boldsymbol (\ theta)))) (dt)) = (\ dot (\ hat (\ boldsymbol (\ theta)))) = - (\ dot (\ theta)) (\ hat (\ mathbf (r)))) </Dd> </Dl>

State and explain the kepler's law of planetary motion