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 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. The gravitational force between Earth and the Moon would stay the same. 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 goes up 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 go down by a proportional amount.
The correct answer is "The gravitational force between Earth and the Moon would go down by a proportional amount."
To understand why this is the case, we can use Newton's Law of Universal Gravitation, which states that the force of gravity between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
Mathematically, this can be represented as:
F = (G * m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, Earth and the Moon), and r is the distance between the centers of the two objects.
In this question, it is given that the mass of both Earth and the Moon does not change. So, m1 and m2 remain the same.
Now, let's consider what happens when the distance between the two objects doubles. If the original distance is r, then the new distance would be 2r.
Plugging the new values into the equation, we get:
F' = (G * m1 * m2) / (2r)^2
Simplifying this expression, we get:
F' = (G * m1 * m2) / 4r^2
Comparing this with the original equation, we can see that F' is one-fourth of the original force. In other words, the gravitational force between Earth and the Moon is reduced by a factor of four when the distance between them doubles, assuming that their masses remain the same.
Therefore, the correct answer is that the gravitational force between Earth and the Moon would go down by a proportional amount.