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 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 this, we can use Newton's Law of Universal Gravitation, which states that 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 them.
Mathematically, the equation for gravitational force (F) can be written as:
F = (G * m₁ * m₂) / r²
Where:
- F is the gravitational force between the two objects
- G is the gravitational constant
- m₁ and m₂ are the masses of the two objects
- r is the distance between the centers of the two objects
In this case, we are assuming that the masses of Earth and the Moon remain constant. So, let's say the initial distance between Earth and the Moon is d. If the distance doubles, the new distance would be 2d.
To compare the gravitational forces, we can substitute the initial and new distances into the equation:
F₁ = (G * m₁ * m₂) / d²
F₂ = (G * m₁ * m₂) / (2d)² = (G * m₁ * m₂) / 4d²
As you can see, the new gravitational force F₂ is one-fourth (1/4) of the initial gravitational force F₁. In other words, the gravitational force decreases by a proportional amount when the distance between two objects doubles while their masses remain constant.