The gravitational pull between the Sun and Earth is determined by the masses of both bodies and the distance between them, according to Newton's law of universal gravitation. The formula is:
\[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \]
where \( F \) is the gravitational force, \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two objects (in this case, the Sun and Earth), and \( r \) is the distance between the centers of the two objects.
From the options provided:
- If the sun was twice its size: This would increase the gravitational pull (since mass is increasing).
- If the sun was farther away from Earth: This would decrease the gravitational pull (since the distance \( r \) is increasing).
- If Earth was twice its size: This would increase the gravitational pull (since Earth's mass is increasing).
- If Earth was closer to the sun: This would increase the gravitational pull (since the distance \( r \) is decreasing).
Therefore, the correct choice that would decrease the gravitational pull between the Sun and Earth is:
If the sun was farther away from Earth.