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)%0D%0AResponses%0D%0A%0D%0AThe gravitational force between Earth and the Moon would completely disappear.%0D%0AThe gravitational force between Earth and the Moon would completely disappear.%0D%0A%0D%0AThe gravitational force between Earth and the Moon would go down by a proportional amount.%0D%0AThe gravitational force between Earth and the Moon would go down by a proportional amount.%0D%0A%0D%0AThe gravitational force between Earth and the Moon would goes up by a proportional amount.%0D%0AThe gravitational force between Earth and the Moon would goes up by a proportional amount.%0D%0A%0D%0AThe gravitational force between Earth and the Moon would stay the same.
The gravitational force between Earth and the Moon would go down by a proportional amount.
The gravitational force between two objects is given by the equation 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, and r is the distance between the centers of the two objects.
In this case, the mass of the Earth and Moon doesn't change, but the distance between them doubles. Let's assume that the initial distance between Earth and Moon is d. When the distance doubles, the new distance between them becomes 2d.
To determine how the gravitational force changes, we can substitute the new distance into the equation. So, we have:
F' = G*(m1*m2/(2d)^2)
Simplifying the expression, we have:
F' = G*(m1*m2/4d^2)
Comparing this to the original equation, we can see that the new force F' is one-fourth (1/4) of the original force F. Therefore, the gravitational force between Earth and the Moon would go down by a proportional amount when the distance between them doubles. So, the correct response is: "The gravitational force between Earth and the Moon would go down by a proportional amount."