If the distance between two objects is tripled, by what factor will the
gravitational force between them change?
1/(3^2) = ?
That's called using the inverse square law.
but what is the 3^2 for? If the 3 is for the distance being tripled...what about the exponent 2?
Oh nvm, you mean
F = 1/d^2
Got it...thanks.
1/(3^2) = 1/9
Square the distance ratio and put it in the denominator
if the separation distance b/w two objects is tripled is increased by a factor of 3,then the force of gravitation is decreased by a factor of 6
To determine the factor by which the gravitational force between two objects changes when the distance between them is tripled, we need to use Newton's law of universal gravitation. According to this law, the gravitational force (F) between two objects is directly proportional to the product of their masses (m1 and m2) and inversely proportional to the square of the distance (r) between them.
The equation for gravitational force is:
F = G * (m1 * m2) / (r^2)
Where:
F = Gravitational force between two objects
G = Universal gravitational constant
m1, m2 = Mass of the two objects
r = Distance between the two objects
If we triple the distance between the two objects, the new distance (r') will be three times the original distance (r).
So, r' = 3r
Now, let's consider the ratio of the gravitational forces before and after the distance is tripled:
(F') / F = (G * (m1 * m2) / (r'^2)) / (G * (m1 * m2) / (r^2))
We can simplify this ratio by canceling out the common terms:
(F') / F = (r^2) / (r'^2)
Substituting the values of r' and r in terms of each other:
(F') / F = (r^2) / ((3r)^2)
= (r^2) / (9r^2)
= 1/9
Therefore, the gravitational force between the two objects will decrease by a factor of 1/9 (or 0.111) when the distance between them is tripled.