How does the gravitational force between Earth and the Moon change when the distance between the two objects doubles but mass doesn’t change?
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 completely disappear.
The gravitational force between Earth and the Moon would goes up by a proportional amount.
The correct answer is: The gravitational force between Earth and the Moon would go down by a proportional amount.
According to Newton's law of universal gravitation, the force of gravitational attraction between two objects is inversely proportional to the square of the distance between them. This means that if the distance between Earth and the Moon doubles, the force of gravitational attraction between them would decrease by a factor of four.
The correct answer is: The gravitational force between Earth and the Moon would go down by a proportional amount.
According to Newton's law of universal gravitation, the gravitational force between two objects is inversely proportional to the square of the distance between them. So, if the distance between Earth and the Moon doubles, the gravitational force between them would decrease by a factor of four (since (2)^2 = 4).
The gravitational force between Earth and the Moon can be calculated using Newton's law of universal gravitation, which states that the force 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 gravitational force (F) is:
F = G * (m1 * m2) / r^2
Where 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 both the Earth and the Moon remains constant, but the distance between them doubles. Let's call the initial distance between Earth and the Moon 'd', and the new distance '2d'.
Substituting these values into the formula, we get:
F1 = G * (m1 * m2) / d^2 (initial force)
F2 = G * (m1 * m2) / (2d)^2 (force when distance doubles)
Simplifying F2, we get:
F2 = G * (m1 * m2) / 4d^2
Comparing F1 and F2, we can see that the denominator in F2 is four times larger than in F1. As a result, F2 is one-fourth (1/4) of F1.
Therefore, the correct answer is: The gravitational force between Earth and the Moon would go down by a proportional amount.
So, when the distance between Earth and the Moon doubles but the masses of the two objects remain constant, the gravitational force between them decreases by a factor of four.