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

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Discussion Overview

The discussion revolves around the relationship between the speed of the Earth's rotation and the speed of the Moon's shadow during a solar eclipse. Participants explore how these speeds affect the apparent motion of the shadow across the Earth's surface, particularly in relation to the timing of the eclipse.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant asserts that the Earth rotates faster than the Moon orbits, causing the Moon to appear to move from East to West, while its shadow moves from West to East during an eclipse.
  • Another participant claims that the Earth's rotation speed is never faster than the Moon's orbital speed, providing a specific speed of approximately 500 m/s for the Earth's equator and about 1 km/s for the Moon.
  • A third participant supports the previous claim by referencing calculations based on the distances to the Moon and the Earth's radius, suggesting that the equatorial speed is about half of the Moon's orbital speed.
  • A later reply expresses gratitude and acknowledges a lack of prior calculation regarding the speeds discussed.

Areas of Agreement / Disagreement

Participants generally agree on the relative speeds of the Earth and Moon, but there is a question raised about the apparent motion of the shadow during an eclipse that remains unresolved.

Contextual Notes

The discussion includes assumptions about the distances involved and the definitions of speed, which may not be fully explored or agreed upon by all participants.

imsmooth
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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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