How much would we have weighed on Earth when its day was only 18 hours long?

At the equator of a rotating body, centrifugal forces act against gravity to reduce your weight. Today, for the Earth's rotation period of 24 hours, this centrifugal force produces an acceleration ( V^2/R V = 1100 miles/hr and R = 4,100 miles) of about 0.11 feet/sec/sec. Gravity produces about 32 feet/sec/sec so your weight will be about 0.11/32 = 0.003 times lower at the equator. A person weighing 150 pounds will weigh 0.55 pounds less at the equator. Now, if you increase the rotation speed of the Earth to 18 hours, this causes the centrifugal force to increase to (24/18)^2 = 1.77 times its previous level, so the weigh reduction will be 0.003x1.77 = 0.005. The 150 pound person will now weigh 0.8 pounds less...roughly. There is a second effect that will reduce this a bit more, because as the Earth rotates faster its shape is no longer that of a sphere, but it bulges-out at the equator so that you are slightly farther from the center of the Earth than before. This reduces the surface gravity by a small amount for these speeds, but it is not a big effect. At 900 million years ago when this higher rotation period was in effect, it would have been undetectable by the indigenous bacteria that lived on the Earth then.


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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.