Question

Two asteroids exert a gravitational force, F, on each other. Some time later, the asteroids are now three times as far from each other as before. Which of the following represents the gravitational force at this distance?​

Answer 1

Given:

Two asteroids exert a gravitational force, F, on each other. Some time later, the asteroids are now three times as far from each other as before.

To find:

New Gravitational force.

Calculation:

Let's assume that the asteroids were separated by a distance of d.

According to NEWTON'S LAW OF GRAVITATION:

$\therefore \: F = \dfrac{G(m1)(m2)}{ {d}^{2} }$

Now , the distance has been tripled; Let new force be F_(2):

$\therefore \: F_{2} = \dfrac{G(m1)(m2)}{ {(3d)}^{2} }$

$= > \: F_{2} = \dfrac{G(m1)(m2)}{ 9{d}^{2} }$

$= > \: F_{2} = \dfrac{1}{9} \times \dfrac{G(m1)(m2)}{ {d}^{2} }$

$= > \: F_{2} = \dfrac{1}{9} \times F$

$= > \: F_{2} = \dfrac{F}{9}$

So, final answer is:

$\boxed{ \bf{\: F_{2} = \dfrac{F}{9} }}$

Answer 2

When two asteroids are three times as far from each other as before then the gravitational force at this distance would be F/9.

Explanation:

A gravitational force is that force that exists between two objects having a significant weight and mass.

The formula is

F = G m1 m2 / d^2

F2 = Gm1 x m2 / (3d)^2

F2 = Gm1m2 / 9d^2

F2 = Gm1m2 / ^2 x 1/9

F2 = F / 9

Thus the value of gravitational force will be F/9.