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

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The Earth rotates faster than the Moon orbits, causing the Moon to appear to move from East to West daily. During a solar eclipse, the Moon's shadow moves from West to East across the Earth's surface due to the curvature of the Earth and the relative speeds involved. The Earth’s rotation at the equator is approximately 500 m/s, while the Moon’s orbital speed is about 1 km/s. This means the Earth's spin is never faster than the Moon's orbital speed, confirming that the shadow will not move East to West, even if the eclipse occurs near noon. The discussion emphasizes the importance of understanding the relative speeds and distances involved in these celestial events.
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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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