Planets have roughly circular orbits around the sun. Using the table below of the orbital radii and periods of the inner planets, how does the centripetal acceleration of the planets depend upon their orbital radii? That is, find the exponent \(n\) in \(a=\operatorname{con} \times r^{n}\). (Note that 1 A. U. \(=1\) astronomical unit, the mean sun-earth distance.)

Planet Mean orbital radius (A. U.) Period (Years) Mercury 0.387 0.241 Venus 0.723 0.615 Earth 1.000 1.000 Mars 1.523 1.881