Barron's 2nd Edition DT Q40

Barron's Book

40) This problem acts us to compare the force of gravity acting on planet m and that of planet 2m. The universal gravitational force equation is different from the equation we approximate for objects on Earth. Here is the equation.

Where F is force, G is the universal constant of gravity, m is mass, and r is distance between planet and central star

The next step would be to write a proportion for planet m.

Where F is force, G is the universal constant of gravity, m is mass, and r is distance between planet and central star

Now, we can also apply this proportion to planet 2m.

Where k is a constant, F is force, G is the universal constant of gravity, m is mass, and r is distance between planet and central star

To finish the problem, let's pull out all the constants and solve for k. Then we can compare the proportion for planet m and planet 2m.

Where k is a constant F is force, G is the universal constant of gravity, m is mass, and r is distance between planet and central star

Answer: D