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 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 goes up 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 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, 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 their centers.
Mathematically, the equation can be written 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, and r is the distance between their centers.
In this case, we are assuming that the mass of both Earth and the Moon does not change, but the distance between them doubles. Since the distance between their centers is in the denominator of the equation, when the distance doubles (r becomes 2r), the force of gravity decreases by a factor of (2^2), which is 4.
Therefore, the gravitational force between Earth and the Moon would go down by a proportional amount, specifically by a factor of 4, when the distance between the two objects doubles.