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Based on the equation and your knowledge of the Sun-Earth-Moon system, which celestial body (the Sun or the Moon) has a greater influence on Earth's tides? Justify your answer.

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Final answer:

The Moon has a greater influence on Earth's tides than the Sun because, despite the Sun's stronger gravitational pull, the Moon's proximity to Earth causes a larger difference in gravitational pull across Earth's diameter, leading to more significant tidal effects such as high tides and tidal bulges.

Step-by-step explanation:

The Moon has a greater influence on Earth's tides than the Sun. This is because, despite the Sun's gravitational pull being nearly 200 times stronger than that of the Moon, the difference in those forces across Earth's diameter is smaller for the Sun compared to the Moon. This results in the Moon having a greater tidal effect; the fractional change in distance from the near side to the far side of Earth is much greater for the Moon than for the Sun. Additionally, tides are affected by the relative positions of the Sun and Moon to Earth, with spring tides occurring when they are lined up, enhancing the tidal effect, and neap tides occurring when the Moon is at a quarter phase, partially canceling out the Sun's tidal forces.

Ocean tides are an observable result of this phenomenon, with a high tide occurring on the side of Earth closest to the Moon and another on the opposite side. The reason for the second high tide is that Earth itself is pulled toward the Moon more than the water on the far side, creating what is known as a tidal bulge. Overall, the Moon's gravity has a dominant effect on the tides due to its proximity and the significant difference in gravitational pull across Earth's diameter.

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