Question

According to Newton's Universal Law of Gravitation, when the distance between two interacting objects doubles, the gravitational force is

Answer 1

If the distance doubles, the gravitational force is divided by 4

Step-by-step explanation:

Newton’s Universal Law of Gravitation

Objects attract each other with a force that is proportional to their masses and inversely proportional to the square of the distance.

`\displaystyle F=G{\frac {m_(1)m_(2)}{r^(2)}}`

Where:

m1 = mass of object 1

m2 = mass of object 2

r = distance between the objects' center of masses

G = gravitational constant: 6.67\cdot 10^{-11}~Nw*m^2/Kg^2

If the distance between the interacting objects doubles to 2r, the new force F' is:

`\displaystyle F'=G{\frac {m_(1)m_(2)}{(2r)^(2)}}`

Operating:

`\displaystyle F'=(1)/(4)G{\frac {m_(1)m_(2)}{r^(2)}}`

Substituting the original value of F:

`\displaystyle F'=(1)/(4)F`

If the distance doubles, the gravitational force is divided by 4