Suppose that three astronomical objects

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SUMMARY

The discussion centers on a physics problem involving three astronomical objects aligned on a line, with specific mass relationships and a defined distance D between objects 1 and 3. Object 1 has a mass 1.5 times that of object 3 and seven times that of object 2. The objective is to determine the distance between objects 1 and 2 such that the net gravitational force on object 2 is zero, utilizing the gravitational force equation F = (G x m1 x m2) / r^2.

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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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