Deduce, from the equations employed in Q4 and Q5, the exponent n in the equation: T = k rn where k is a constant and T is the period of a satellite which orbits at a radius r from a massive object in space. Hence, how long is the “year” on Venus if its distance from the Sun is 72.4% of the Earth’s?
The equations I used in the previous equations were simply a = (4(pi^2)r)/T^2 and a = GM/r^2 and basically combinations of the two
The Attempt at a Solution
So I started this question by trying to find the distance of the Earth from the Sun using T^2 = (4pi^2)/Gm (m being mass of the Sun) to which I got the answer 2.75x10^11 km
Then I substituted the r in the Kepler's equation with 0.724Re (to find distance of Venus from the Sun) but my answers seemed to have all been wrong so either I'm making some silly arithmetical error or my entire approach is wrong. Any help and hints would be appreciated, thank you :)