We need to assume that the orbits are circular; this is a very good approximation and do not hesitate to adopt it. We need then to consider the basic equation of circular motion that relates centripetal acceleration, angular velocity, mass, radius and force:
. We also have the basic equation of Newton, F=ma. By checking, we see that for each planet we have that a=v^2*r where v is the angular velocity. v=
where T is the orbital period, hence we have that a=
. Denote with the index 1 the Earth case and with 2 the Mars case. We have then that 
. Substituting the known values in a calculator, we get the result: the centripetal acceleration of earth is 2.32 times greater than that of Mars.
