The gravitational pull between two objects is described by Newton's law of universal gravitation, which states that the gravitational force (F) is proportional to the product of the masses of the two objects (m1 and m2) and inversely proportional to the square of the distance (r) between them:
\[ F = G \frac{m_1 m_2}{r^2} \]
Where G is the gravitational constant. Let's analyze each situation:
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The Sun doubles in size: Assuming this means the Sun's mass doubles, the gravitational pull would increase because the mass of one of the objects (the Sun) has increased.
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The Sun was farther away from Earth: If the Sun is farther away, the distance \( r \) increases, which means the gravitational pull would decrease because the force is inversely proportional to the square of the distance.
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The Earth becomes closer to the Sun: If the Earth moves closer to the Sun, the distance \( r \) decreases, which means the gravitational pull would increase because the force increases as the distance decreases.
In summary:
- Sun doubles in size: Increase
- Sun is farther away from Earth: Decrease
- Earth becomes closer to the Sun: Increase