Super-precise Galilei performs free-fall experiments, dropping balls from windows on different floors of the Burj Khalifa tower.

1 What is the accuracy needed on the falling time of the dropped bodies if the purpose of the measurement is to determine the radius of Earth? What formula and graph should one use to evaluate your measurement (for some reason he couldn’t get hold of a computer)?

Assume either that

• there is no atmosphere
• or the air exerts a drag force proportional to the speed of the falling body.

The Earth can be regarded as a regular sphere, the effect of its rotation can be neglected.