Analysis of a Pendulum on the Moon

A simple pendulum of length L = 1 m has a period T0 = 2.01 s on Earth (g = 9.8 m/s^2). Explain, detailing the physical reasoning and the calculations, how this period would change if the same pendulum were installed on the Moon (g_moon ~= 1.62 m/s^2). Also discuss the limits of the small-oscillation approximation used here.