To understand how these changes affect the gravitational pull between the Earth and the Sun, we can refer to Newton's law of universal gravitation, which states that the gravitational force \( F \) between two objects is given by the equation:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where:
- \( F \) is the gravitational force,
- \( G \) is the gravitational constant,
- \( m_1 \) and \( m_2 \) are the masses of the two objects,
- \( r \) is the distance between the centers of the two objects.
Let's analyze each scenario:
-
The Sun doubles in size:
- The mass of the Sun would also approximately double, since size (volume) is related to mass for a given density.
- This would increase the gravitational pull between the Earth and the Sun.
-
The Sun was farther away from Earth:
- Increasing the distance \( r \) would cause the gravitational force to decrease, since it is inversely proportional to the square of the distance.
- This would decrease the gravitational pull between the Earth and the Sun.
-
The Earth becomes closer to the Sun:
- Decreasing the distance \( r \) would result in an increase in gravitational force, as it is inversely proportional to the square of the distance.
- This would increase the gravitational pull between the Earth and the Sun.
To summarize:
- The Sun doubles in size: Increase
- The Sun was farther away from Earth: Decrease
- The Earth becomes closer to the Sun: Increase
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