How does the gravitational force between Earth and the Moon change when the distance between the two objects doubles but mass doesn’t change?(1 point)

Question

Responses

The gravitational force between Earth and the Moon would goes up by a proportional amount.
The gravitational force between Earth and the Moon would goes up by a proportional amount.

The gravitational force between Earth and the Moon would completely disappear.
The gravitational force between Earth and the Moon would completely disappear.

The gravitational force between Earth and the Moon would go down by a proportional amount.
The gravitational force between Earth and the Moon would go down by a proportional amount.

The gravitational force between Earth and the Moon would stay the same.

Answer 1

The correct response is:

The gravitational force between Earth and the Moon would go down by a proportional amount.

According to Newton's law of universal gravitation, the gravitational force \( F \) between two masses \( m_1 \) and \( m_2 \) separated by a distance \( r \) is given by the formula:

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

If the distance \( r \) between the Earth and the Moon doubles, the new force \( F' \) would be:

\[ F' = \frac{G \cdot m_1 \cdot m_2}{(2r)^2} = \frac{G \cdot m_1 \cdot m_2}{4r^2} = \frac{1}{4} F \]

Thus, the gravitational force would be reduced to one-fourth of its original value, meaning it goes down by a proportional amount.