Roger N. answered • 07/29/21

. BE in Civil Engineering . Senior Structural/Civil Engineer

the gravitational force assuming the same objects mass m1 = m2 = m and same distance is F1 = k (m1m2)/ r^{2} or

F1 = k (m^{2})/ r^{2} . If one of the objects is three times in mass than the other then m2 = 3m1 = 3m and if it moves 3 times the distance then r = 3r

substituting you get F2 = k( m1)(3m1)/ (3r)^{2} = k(m)(3m)/( 9r^{2}) = k ( 3m^{2})/ 9r^{2} simplifying you get

F2 = k (m^{2}) / 3 r^{2} , comparing this with original equation F1 = k (m^{2})/ r^{2} and F2 = k (m^{2}) / 3 r^{2} divide F1 by F2 you get F1 / F2 = k (m^{2})/ r^{2} / k (m^{2}) / 3 r^{2} simplifying , F1 / F2 = 3 and F2 = 1/3 F1 , therefore the force is reduced to 1/3 of the original force