Johan Ekenberg

Computer Programmer and Double Bass Player

Lose Weight: Go to the Equator!

A person weighing 75 kg will weigh 250 grams less standing on the equator compared to the north or south pole.

This is caused by the centrifugal force from Earth’s rotation. Earth’s circumference is 40000 km, having a radius of 6370 km. One revolution per 24 hours means a tangential speed of 1670 km/h, or 465 m/s, at the equator.

centrifugal force is given by the formula:

where F is force in Newton (N), m is mass, v is tangential velocity and r is radius. Substituting 75 kg for mass, 465 m/s for velocity, and 6,370,000 m for radius, we get a centrifugal force of 2.54 N. Now, the average gravitational acceleration on Earth is 9.8 m/s2, so 2.54 N equals roughly 250 grams. Go figure!

Now you probably wonder, like I did: How fast would Earth need to rotate for us to weigh nothing, and start drifting off into space? Well, looking at the above equation for centrifugal force, we note that F is proportional to v squared. (If v is doubled, F is quadrupled). The centrifugal force F would need to be 300 times higher (250g * 300 = 75kg). Consequently, v needs to increase by a factor of about 17. ($\sqrt{300}\approx 17$) So: to send us drifting into space, the earth must rotate 17 times faster than now, which is one revolution in about 1 hour 25 minutes.

Of course, this would only be true at the equator. The rotation needs to be quicker the further from the equator you are. Standing at one of the poles, you would run no risk of being spun off the earth no matter how fast the rotation. You might get dizzy but you will stay safe!