Consider two planets in space that gravitationally attract each other if the mass of one of them stays the same and the mass of the other is doubled and the distance between them is doubled, then the force between them changes by what factor? a. doubled
b. quadrupled
c. tripled
d. half as much

D. half as much

Explanation:

let m and M be the mass of the planets and r be the distance between them.

then: the force of attraction between them is given by,

F = G×m×M/(r^2)

if we keep one mass constant and double the other and also double the distance between them.

the force of attraction becomes:

F1 = 2G×m×M/[(2×r)^2]

   = 2G×m×M/[4×(r)^2]

   = (1/2)G×m×M/(r^2)

   = 1/2×F

therefore, when you double one mass and keep the other mass constant and double the distance between the masses you decrease the force by a factor of 1/2.

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more than, less

less than, more