To determine which two objects exert the greatest gravitational force on each other, we should consider their masses and distances.
The Sun is the most massive object in the solar system, and it exerts a significant gravitational force on all planets. Among the options provided:
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Earth and Neptune: While both are large bodies, their masses are relatively small compared to the Sun.
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the Sun and Neptune: The Sun's massive gravity affects Neptune, but it's not as significant as the relationship with Mercury due to distance.
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the Sun and Mercury: Mercury is the closest planet to the Sun and, therefore, experiences the strongest gravitational pull due to its proximity and the Sun’s immense mass.
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Mercury and Uranus: While both are planets, they are much less massive than the Sun and are also further apart from each other.
Based on this reasoning, the pair that exerts the greatest gravitational force on each other is:
the Sun and Mercury.