A planet with mass m = 2.00 times 1024 kg and a second with mass M = 5.00 times

Question

A planet with mass m = 2.00 times 1024 kg and a second with mass M = 5.00 times lO24 kg are separated by a distance d = 4.06 times 1011 m. What is the strength of the gravitational force (N) which in exerts on M? What is the strength of the gravitational force (N) which M exerts on m? A third planet with mass m3 = 5.00 x 1023 kg happens to be midway between M .and m. What is the net gravitational force (magnitude in N) on m3 due to the other two planets? Is the net force toward or away from the smaller mass (m)? Where could the third planet be positioned (distance from the larger planet M in meters) so that the net gravitational force is zero?

Explanation / Answer

now lets say we are a distance x from M then the net force will be given by G M m3 / (x)^2 - G m m3 /(d-x)^2=0 or M (d-x)^2 - m x^2=0 if d=4.06 E11, 5E24 * (4.06E11-x)^2-2E24*x^2=0 solve for x and get x=2.49E11

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