gravitational attraction

inverse square law the attraction between two objects is = G(m1m2)/r2 thererfore...
CHANGES IN THE DISTANCE
double the distance (2 x)...
new force  vs old force
 G(m1m2) ------------ (2r)2

vs

 G(m1m2) ----------- r2

 1 x G(m1m2) ------------ (2r)x(2r)

vs

 1 x G(m1m2) ----------- 1r2
1/4 to 1

and the new force = 1/4 x the old force, or 4 times smaller

triple the distance (3 x)...
new force  vs old force
 G(m1m2) ------------ (3r)2

vs

 G(m1m2) ----------- r2

 1 x G(m1m2) ------------ (3r)x(3r)

vs

 1 x G(m1m2) ----------- 1r2
1/9 to 1

and the new force = 1/9 x the old force, or 9 times smaller

quadruple the distance (4 x) and the new force is 16 times smaller
5x , 25 times smaller and so on.
halve the distance (.5 x) ...
new force  vs old force
 G(m1m2) ------------ (r/2)2

vs

 G(m1m2) ----------- r2

 1 x G(m1m2) ------------ (1 x r/2)x(1 x r/2)

vs

 1 x G(m1m2) ----------- 1r2
4 to 1

and the new force = 4 times the old force, or 4 times bigger

make the distance 3 times less (1/3 x) ...and the new force = 9 times the old force, or 9 times bigger

make the distance by 4 times less (1/4 x) ...and the new force = 16 times the old force, or 16 times greater

divide distance by 5, force increases by 25 times

CHANGES TO THE MASSES
double either one of the masses (2 x)
new force  vs old force
 G(2m1m2) ------------ (r)2

vs

 G(m1m2) ----------- r2

 G(2m1m2) ------------ 1

vs

 1 x G(m1m2) ----------- 1r2
2 to 1

and the new force = 2 times the old force

double both of the masses

new force  vs old force
 G(2m12m2) ------------ (r)2

vs

 G(m1m2) ----------- r2

 G(2m1 x 2m2) ------------ 1 r2

vs

 1 x G(m1m2) ----------- 1r2
4 to 1

and the new force = 4 times the old force

triple either one and the force will be 3 times greater, and so on...

Triple both of the masses and the new force will be 9 times greater

The table below is provided for reference, do not try to memorize it. Make one yourself to help understand how to figure a new combination out.

 change what... multiplier m1 m2 r r2 Fnew/Fold increase distance byand force decreases 1 1 1 1 1 1 2 1 1 2 4 1/4 3 1 1 3 9 1/9 4 1 1 4 16 1/16 6 1 1 6 36 1/36 9 1 1 9 81 1/81 10 1 1 10 100 1/100 change what... multiplier m1 m2 r r2 Fnew/Fold decrease (divide) distance by __ and force increases by the square 1 1 1 1 1/1 1 2 1 1 1/2 1/4 4 4 1 1 1/4 1/16 16 5 1 1 1/5 1/25 25 6 1 1 1/6 1/36 36 9 1 1 1/9 1/81 81 10 1 1 1/10 1/100 100 change what... multiplier m1 m2 r r2 Fnew/Fold change one mass by ____ and the force increases by the same factor 1 x 1 1 1 1 1 2 x 2 1 1 1 2 1 2 1 1 2 3 x 3 1 1 1 3 3 1 1 1 3 4 x 4 1 1 4 1 4 1 1 4 5 x 5 1 1 1 5 10 x 1 10 1 1 10 change what... multiplier m1 m2 r r2 Fnew/Fold change both  masses by ____ and the force increases by the square of the factor 2 x 2 2 1 1 4 3 x 3 3 1 1 9 4 x 4 4 1 1 16 5 x 5 5 1 1 25 6 x 6 6 1 1 36 9 x 9 9 1 1 81 10 x 10 10 1 1 100