Speed of the umbra during eclipse vs rate of the Earth's rotation

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SUMMARY

The discussion clarifies the relationship between the Earth's rotation and the Moon's orbital speed during a solar eclipse. The Earth rotates at approximately 500 m/s at the equator, while the Moon orbits at about 1 km/s. This means that the shadow of the Moon moves from West to East across the Earth's surface during an eclipse, despite the Earth's faster rotation. The calculations provided confirm that the Earth's rotational speed is consistently slower than the Moon's orbital speed, ensuring the shadow's movement direction remains unchanged.

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The earth rotates faster than the moon orbits. Thus, the moon appears to move from East to West each day. The shadow of the moon during an eclipse as it moves along the curved earth makes it move faster and we see it move West to East.

My question is If a solar eclipse happens near noon and one is directly under the sun-moon alignment, wouldn't the shadow move East to West for a brief moment since the earth rotation is faster at this point? Or is it never faster?
 
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It is never faster. The Earth spin makes the equator move about 500 m/s. The Moon’s orbital speed is about 1 km/s.
 
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To add to that, it is easy to draw this conclusion knowing only the distance to the Moon (ca 384000 km), the radius of the Earth (ca 6300 km) and the periods (28 days and 1 day). As 6300x28 is about 180000, the corresponding equator speed is about half of the Moon’s orbital speed.
 
Thank you. I should have done the calculation first.
 

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