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)
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 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.
To determine how the gravitational force between Earth and the Moon changes when the distance between them doubles while the mass remains the same, we can use Newton's law of universal gravitation.
According to this law, 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 equation for the gravitational force (F) is given by:
F = (G * m1 * m2) / r^2
Where:
F represents the gravitational force,
G is the gravitational constant (approximately 6.67430 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the two objects (in this case, Earth and the Moon), and
r is the distance between them.
In this scenario, when the distance between Earth and the Moon doubles but their masses remain constant, we can see that the value of 'r' in the equation will increase by a factor of 2.
Since r is squared in the denominator of the equation, the net effect is that when 'r' doubles, the denominator of the equation becomes four times larger (2^2 = 4).
This means that the gravitational force between Earth and the Moon will decrease by a factor of four (1/4) when the distance between them doubles but mass remains constant.
Therefore, the correct answer is:
The gravitational force between Earth and the Moon would go down by a proportional amount.