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 completely disappear. The gravitational force between Earth and the Moon would completely disappear. 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 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 goes up by a proportional amount.
The gravitational force between Earth and the Moon would go down by a proportional amount.
The correct response is: 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 when the distance between them doubles, while the mass of both objects remains the same. To understand why this happens, you can refer to Newton's law of universal gravitation.
According to Newton's law, the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. Mathematically, the equation can be represented as:
F = (G * m1 * m2) / r^2
Where:
- F represents the gravitational force between the two objects.
- G is the gravitational constant, which is a constant value.
- m1 and m2 are the masses of the two objects.
- r is the distance between the centers of the two objects.
Given that the masses of the Earth and the Moon do not change, let's assume they are represented as m1 and m2, respectively. Now, if the distance between them doubles, the new distance can be represented as 2r, where r is the original distance.
Plugging in these values into the equation, we get:
F' = (G * m1 * m2) / (2r)^2
= (G * m1 * m2) / 4r^2
By simplifying this equation, it becomes evident that the gravitational force F' is one-fourth (1/4) of the original force F. Therefore, when the distance between Earth and the Moon doubles while their masses stay the same, the gravitational force decreases by a proportional amount, becoming one-fourth of the original force.