Question 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 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.

Question

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

Answer 2

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

Answer 3

To determine how the gravitational force between Earth and the Moon changes when the distance between them doubles but the mass does not change, we can use the formula for gravitational force:

F = (G * m1 * m2) / d^2

Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2/kg^2),
m1 and m2 are the masses of the two objects (Earth and Moon, respectively),
and d is the distance between the centers of the two objects.

In this case, if the distance between Earth and the Moon doubles but both masses remain unchanged, we can express the new distance as 2d. Plugging this into the formula, we get:

F' = (G * m1 * m2) / (2d)^2

Simplifying this expression, we have:

F' = (G * m1 * m2) / 4d^2

We can observe that the denominator of the expression is now four times larger than it was in the original formula for gravitational force. This means that the gravitational force between Earth and the Moon will be four times weaker when the distance between them doubles. Therefore, the correct answer is: "The gravitational force between Earth and the Moon would go down by a proportional amount."