Chapter 2: Problem 29

The Sun exerts much larger forces on the Earth and its oceans than the Moon does, yet the tides caused by the Sun are much lower than those caused by the Moon. Why?

Short Answer

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Answer: The tides caused by the Sun are much lower than those caused by the Moon due to the larger distance between the Earth and the Sun. Although the Sun exerts a greater gravitational force on the Earth and its oceans, the effect of distance is much more significant in determining the tidal force, which results in the Sun having less of an impact on tides compared to the Moon.

Step by step solution

Gravitational Force

The gravitational force exerted by a celestial body on the Earth depends on its mass and the distance between them. According to Newton's law of universal gravitation, the force can be calculated as: F = G * (m1 * m2) / r^2 where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the celestial bodies (Sun, Moon, and Earth), and r is the distance between the centers of mass of the two bodies.

Gravitational Force of the Sun and the Moon

Due to its much larger mass, the Sun exerts a much larger gravitational force on the Earth and its oceans than the Moon. However, the Sun is also much further away from the Earth compared to the Moon. Since the gravitational force depends on the inverse square of the distance, the force exerted by the Sun gets significantly reduced by the larger distance.

Tidal Forces

The tides are caused by the difference in gravitational force between the near side and the far side of the Earth (the side facing the celestial body and the side facing away). This results in tidal bulges on both sides, leading to high tides, and areas of low tides in between. The tidal force is proportional to the difference in gravitational force across the Earth's radius and can be calculated as follows: Tidal Force ∝ F / r^3 where r is the distance between the Earth and the celestial body.

Comparing the Tidal Forces of the Sun and the Moon

Since the tidal force is proportional to the inverse cube of the distance, the effect of the larger distance between the Earth and the Sun becomes even more significant. Although the Sun's gravitational force on the Earth is much larger than the Moon's, due to its larger mass, the tidal force it creates is lesser than that created by the Moon because of the large distance factor.

Conclusion

The tides caused by the Sun are much lower than those caused by the Moon because of the larger distance between the Earth and the Sun. Although the Sun exerts a greater gravitational force on the Earth and its oceans, the effect of distance is much more significant in determining the tidal force, which results in the Sun having less of an impact on tides compared to the Moon.

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The Sun exerts much larger forces on the Earth and its oceans than the Moon does, yet the tides caused by the Sun are much lower than those caused by the Moon. Why?

Short Answer

Step by step solution

Gravitational Force

Gravitational Force of the Sun and the Moon

Tidal Forces

Comparing the Tidal Forces of the Sun and the Moon

Conclusion

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