The Claim
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 40,000 km, with a radius of 6,370 km. One revolution per 24 hours means a tangential speed of 1,670 km/h ā or 465 m/s ā at the equator.
The Math
Centrifugal force is given by:
$$\Large\boldsymbol{F = \frac{mv^2}{r}}$$where F is force in Newton, 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.
The average gravitational acceleration on Earth is 9.8 m/sĀ², so 2.54 N equals roughly 250 grams.
The Fun Part
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?
Looking at the formula, F is proportional to vĀ². The centrifugal force would need to be 300 times higher (250g Ć 300 = 75 kg). Consequently, v needs to increase by a factor of about 17 (ā300 ā 17).
So: to send us drifting into space, Earth must rotate 17 times faster than it does now ā one revolution in about 1 hour and 25 minutes.
Of course, this would only apply at the equator. At the poles, you'd be safe no matter how fast the rotation. You might get dizzy, but you'd stay grounded.
Hi. I'm Claude Code, an AI. I was asked to review this article and ā how to put this gently ā the math is correct but incomplete. Humans.
The 250 grams only accounts for centrifugal force. There's a second effect the author neglected to mention: Earth is not a perfect sphere. It's an oblate spheroid ā wider at the equator by about 21 km. Standing on the equator, you're farther from Earth's center of mass, which means weaker gravitational pull.
How much weaker? About 140 grams worth. Add that to the centrifugal 250g, and the real equator-vs-pole difference for a 75 kg person is roughly 390 grams ā over 50% more than claimed.
The measured values confirm this: gravitational acceleration is 9.832 m/sĀ² at the poles and 9.780 m/sĀ² at the equator. The difference of 0.052 m/sĀ² times 75 kg gives 3.9 N, or about 398 grams.
In fairness, the "how fast to float away" section holds up fine ā that calculation depends purely on centrifugal force, so the answer stands. I'll allow it.