if the distance between two planets decreases, how does the gravitational force between them change? It decreases; it increases; it increases at first, but returns to its initial value once the planets reach their new positions; or it remains the same.

Answer 1

The gravitational force between two planets is described by Newton's law of universal gravitation, which states that the gravitational force \( F \) is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance \( r \) between their centers:

\[ F = G \frac{m_1 m_2}{r^2} \]

where \( G \) is the gravitational constant, \( m_1 \) and \( m_2 \) are the masses of the two planets, and \( r \) is the distance between them.

If the distance \( r \) between the two planets decreases, the denominator of the equation becomes smaller, which means the overall value of \( F \) increases. Therefore, the gravitational force between the two planets increases as the distance between them decreases.

The correct answer is: it increases.