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)

Responses

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

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.

1 answer

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 \( m_2 \) is given by the equation:

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

where \( G \) is the gravitational constant and \( r \) is the distance between the centers of the two masses. If the distance \( r \) between the Earth and the Moon doubles, the gravitational force becomes:

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

This shows that the gravitational force would be reduced to one-fourth of its original value.