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6.21.Set Up:When we take the ratio of the forces and at andthe masses of the two objects divides out.Solve: (a)The orbit is sketched in Figure 6.21. Figure 6.21(b)so Reflect:The force is greater when Sedna is closer to the sun.6.22.Set Up:Use coordinates where is to the right. Each gravitational force is attractive, so is toward the massexerting it. Treat the masses as uniform spheres, so the gravitational force is the same as for point masses with thesame center-to-center distances. The free-body diagrams for (a) and (b) are given in Figures 6.22a and b.Figure 6.22Solve: (a)The net force on Ais to the right.(b)The net force on Ais to the left.6.23.Set Up:The two masses are sketched in Figure 6.23a. Let the 3Mmass be to the right of M. For the net forceto be zero, the forces and due to Mand 3Mmust be equal in magnitude and opposite in direction. The twoforces will be opposite in direction only at points between the two masses. Consider a point Pthat is a distance dfrom M, so from 3M. Let the third object, at
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