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Question

The gravitational attraction of the Sun and the Moon on the Earth produces tides. The Sun’s tidal effect is about half as great as the Moon’s. The direct pull of the Sun on the Earth, however, is about $175$ times that of the Moon. Why is it then that the Moon causes the larger tides?

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2We know that the gravitational force is:

$F = \frac{GMm}{r^2}$

By definition, tidal force is:

$T = - \frac{dF}{dr} R_{earth} = \frac{2GMm}{r^3} R_{earth}$

By analyzing the formula, even though the sun's mass is bigger than the moon's mass, the moon has a smaller distance to the earth compared to the sun. This distance contributes more on the tidal force $T$ that is why the moon causes the larger tides compared to the sun.

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