Question
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 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 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.
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The correct answer is: The gravitational force between Earth and the Moon would go down by a proportional amount.
To understand why, we need to consider Newton's law of universal gravitation. According to this 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 them.
Mathematically, the equation for the gravitational force between two objects is:
F = (G * m1 * m2) / r^2
Where:
F is the gravitational force between the two objects,
G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2),
m1 and m2 are the masses of the two objects, and
r is the distance between the centers of the two objects.
In this case, we know that the mass of the Earth and the Moon doesn't change, but the distance between them doubles. Let's assume that the initial distance between them is d. When the distance doubles, it becomes 2d.
Now, if we plug these values into the equation, we can see the impact on the gravitational force:
F_initial = (G * m1 * m2) / d^2
F_final = (G * m1 * m2) / (2d)^2
Simplifying this, we get:
F_final = F_initial / 4
This means that the gravitational force between Earth and the Moon would decrease by a factor of 4 when the distance between them doubles, assuming the masses of the two objects remain the same.
Therefore, the correct answer is that the gravitational force between Earth and the Moon would go down by a proportional amount.