Two planets each feel a gravitational force F due to the other at a distance of 1 AU apart.?

Question

What gravitational force would each planet feel due to the other in terms of F if the same planets were at a distance of

A) one-half an AU apart

B) 2 AU apart

Show or describe how you obtained your answer.

Answer 1

Gravitational force is proportional to 1/R^2, where R is the distance between the planets.

If you reduce R to half its former value, the gravitation force becomes 4 times as large.

If you increase R to twice its former value, the gravitational force becomes 1/4 as larg..

Answer 2

The force of gravity varies as the inverse square of the distance.  If they're closer, it's stronger, if they're farther apart, it's weaker.  At half the distance, the force is 4 times greater, and at twice the distance, the force is 4 times smaller.  So, A: 4F, B: 0.25F.

Now, to prove that this is a class assignment.  We let P be the probability that the student understands math enough to express a question mathematically.  We let L be the probability that the student doesn't grasp how gravity works so intuitively that the answer isn't so obvious that asking Yahoo Answers doesn't take longer than just writing down the answer.  Since L is clearly one, P must be less than L, which corresponds to a class assignment.  Now let F be the grade assigned if this answer is handed in verbatim.