Question

Suppose that Two planets are sitting 3 AU apart in their respective orbits. eventually they reach a point where they are only 1 AU apart how did the gravitational force change from 3 AU to 1 AU? A) It increased by 4XB) it Decreased by 9XC) Increased by 9XD) The gravitational force did not change

Answer 1

Given:

Initial distance between the two planets is 3 AU

Final distance between the two planets is 1 AU

Required: Change in gravitational force.

Explanation:

The relation between gravitational force and distance is

$F\propto\frac{1}{r^2}$

The initial gravitational force is

$F_i\propto\frac{1}{9\text{ AU}}$

The final gravitational force is

$F_f\propto\frac{1}{1\text{ AU}}$

As the force is inversely proportional to the distance squared.

Thus, the force is increased by 9x.

Final Answer: The gravitational force increased by 9x