Serway & Jewett — Universal Gravitation: Problem 6

(a) Compute the vector gravitational field at a point \(P\) on the perpendicular bisector of the line joining two objects of equal mass separated by a distance \(2a\) as shown in Figure P13.6. (b) Explain physically why the field should approach zero as \(r \to 0\). (c) Prove mathematically that the answer to part (a) behaves in this way. (d) Explain physically why the magnitude of the field should approach \(2GM/r^{2}\) as \(r \to \infty\). (e) Prove mathematically that the answer to part (a) behaves correctly in this limit.