[Physics] How quickly was the Earth rotating 250 million years ago

earthestimationhomework-and-exercisesrotational-dynamicstidal-effect

The Earth is slowing at a rate of $4.7\times10^{-4}$ miles per second every 100 years due to tidal forces of the moon.

See:

250 million years ago, it would have been spinning at 4.2 million miles per hour! The dinosaurs would have flown off the earth.

If the deceleration rate is inaccurate by 95% (assume it is slowing more slowly), then 250 million years ago, it would be spinning at 213,000 miles per hour.

Also, given the fact that the moon is receding from the Earth, the effect the moon has on the Earth would have been greater in the past.

I don't understand; can someone explain?

Best Answer

The Wikipedia article you linked states:

Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago

If we take this change of 1.7 ms/century and multiply by 2.5 million centuries (250 million years) then we get a change of 4,250 seconds or 1.18 hours. So 250 million years ago the day length would have been 22.82 hours.

The circumference of the Earth around the equator is 40,075 km, so the speed of rotation at the equator would have been about 1,750 km/hr or about 1,092 mph. The current speed is 1,670 km/hr or about 1,040 mph.

Later:

If you're interested, the paper "Geological constraints on the Precambrian history of Earth's rotation and the Moon's orbit", Reviews of Geophysics 38 (1): 37–60, 2000, by George E. Williams discusses the day length changes since the Precambrian. There is a PDF available here. From his figure 2 the estimate of 22.8 hours 250 million years ago looks pretty close.

Related Question