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The force, written as an equation, is:

F = G (m1)(m2) / r2, where

  • F is the Force between the masses
  • G is the gravitational constant (~= 6.674 x 10-11 N m2/kg2)
  • m1 is one of the masses
  • m2 is the other mass
  • r is the distance between the masses (center to center)
Take the formula, and solve for r (I'll show the steps):

Fold = G (m1)(m2) / r2.

(r2)(Fold)= G (m1)(m2)

(r2)= G (m1)(m2) / (Fold)

r= √ [ G (m1)(m2) / (Fold) ]


Plug the formula into itself, but remember, r = 3r (it tripled).
Fnew= G (m1)(m2) / (3r)2.

Fnew= G (m1)(m2) /(3√ [ G (m1)(m2) / (Fold) ])2.

Fnew=G (m1)(m2)/(

32G (m1)(m2) / (Fold) ) <-- G, m1 and m2 cancel

Fnew= 1/( 9

/ Fold) = Fold/ 9 <-- just rewrote the equation


Fnew = (1/9)Fold, or

The force was reduced by a ninth when the distance between the objects tripled.


Try to do this by hand, because it's sometimes hard to follow equation steps in this form.

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12y ago

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