Suppose that three astronomical objects

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To solve the problem, the gravitational forces acting on object 2 from objects 1 and 3 need to be analyzed. The net force on object 2 will be zero when the gravitational pull from object 1 equals that from object 3. Using the formula F = (G x m1 x m2) / r^2, the masses of the objects can be substituted in terms of each other. The distances between the objects must be expressed in relation to D to find the specific distance between objects 1 and 2. A clear diagram can aid in visualizing the forces and distances involved in the calculation.
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Homework Statement


Suppose that three astronomical objects (1, 2, and 3) are observed to lie on a line, and that the distance from object 1 to object 3 is D. Given that object 1 has 1.5 times the mass of object 3 and seven times the mass of object 2, find the distance (in terms of D) between objects 1 and 2 for which the net force on object 2 is zero.
____ D m


Homework Equations


F = (G x m1 x m2) / r^2


The Attempt at a Solution


I drew a diagram of this, and had no luck figuring out what to do next.
 
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