To determine how each change affects the gravitational pull between the Earth and the Sun, we can use 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 and inversely proportional to the square of the distance between them. The formula is:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects, and \( r \) is the distance between the centers of the two objects.
Now, let's analyze each change:
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The Sun doubles in size.
- If the Sun doubles in size, it doesn't just change its volume but also approximately doubles its mass (assuming its density remains constant). Since gravitational force is directly proportional to the product of the masses, this would increase the gravitational pull.
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The Sun was farther away from Earth.
- If the Sun is farther away from Earth, the distance \( r \) in the formula increases. Since gravitational force is inversely proportional to the square of the distance, increasing the distance would decrease the gravitational pull.
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The Earth becomes closer to the Sun.
- If the Earth becomes closer to the Sun, the distance \( r \) decreases. This means that the gravitational force increases, because as \( r \) becomes smaller, the force \( F \) becomes larger. Therefore, this would increase the gravitational pull.
In summary:
- The Sun doubles in size: Increase
- The Sun was farther away from Earth: Decrease
- The Earth becomes closer to the Sun: Increase