Time Period of a Simple Pendulum: The time period (how long it takes for one swing) of a simple pendulum is given by: T=2π√‌
l
g
This means T depends on 1∕√g, where g is gravity at the pendulum's location. Gravity at a Height: Gravity changes as you go away from the Earth's surface. At height h above Earth, gravity is: g′=‌
g
(1+‌
h
RE
)2
where RE is Earth's radius. Time Period Ratio at Two Heights: Let T1 be the time period at height 2RE and T2 at 3RE. So, h1=2RE and h2=3RE. The ratio is: ‌
T1
T2
=√‌
g2
g1
Calculate Gravity at Each Height: At h1=2RE, gravity is g1=‌