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 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 correct answer is: 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."
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 them.
Mathematically, the formula for the gravitational force between two objects is:
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 them.
In this scenario, the mass of Earth and the Moon does not change, so m1 and m2 will remain the same. However, the distance between them doubles. If we denote the original distance as r1, then the new distance would be 2*r1.
Plugging in the values into the formula, we get:
F1 = G * (m1 * m2) / r1^2 (original gravitational force)
F2 = G * (m1 * m2) / (2*r1)^2 (new gravitational force)
Simplifying F2, we have:
F2 = G * (m1 * m2) / 4 * r1^2
Comparing F1 and F2, we can see that F2 is one-fourth of F1. This means that the gravitational force between Earth and the Moon would go down by a proportional amount when the distance between them doubles but the mass doesn't change.