Two particles are projected vertically upwards with the same velocity on two different planets with accelerations due to gravity g1 and g2 respectively. If they fall back to their initial points of projection after lapse of time t1 and t2 respectively, then :
t1 t2 = g1 g2
t1 g1 = t2 g2
t1 g2 / t2 g1 = 2
t12 + t22 = g1 + g2