Answer:
If the distance doubles, the gravitational force is divided by 4
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.
[tex]\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}[/tex]
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:
[tex]\displaystyle F'=G{\frac {m_{1}m_{2}}{(2r)^{2}}}[/tex]
Operating:
[tex]\displaystyle F'=\frac{1}{4}G{\frac {m_{1}m_{2}}{r^{2}}}[/tex]
Substituting the original value of F:
[tex]\displaystyle F'=\frac{1}{4}F[/tex]
If the distance doubles, the gravitational force is divided by 4
