SOLUTION: The Gravitational attraction, G, between two objects is directly proportional to the product of the masses, m and n, and inversely proportional to the square of the distance, d, be

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Question 1105280: The Gravitational attraction, G, between two objects is directly proportional to the product of the masses, m and n, and inversely proportional to the square of the distance, d, between their centers of gravity. How is the gravitational attraction between two objects affected if the distance between the objects is two-thirds of its original value?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Think "reciprocal" when dealing with inverse variation. The gravitational force varies inversely as the square of the distance, so if the distance is reduced to 2/3 of its original value, the factor by which the force is increased is the reciprocal of the square of 2/3:
1%2F%282%2F3%29%5E2+=+1%2F%284%2F9%29+=+9%2F4

The gravitational force is increased by a factor of 9/4 when the distance is decreased to 2/3 of its original distance.

I think it is awkward to try to see this if you use the whole formula; here is what it might look like.

Let the original force be F1: F1+=+%28m1%2Am2%29%2Fd%5E2

The new force F2, with the distance cut to 2/3 of the original distance, is

So the force F2 is F1, increased by a factor of 9/4.