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NASA/JPL Section 13.3 Analysis Model: Particle in a Field (Gravitational) 14. (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 P13.14. (b) Explain physically why the field should approach zero as r â 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/r2 as r ââ. (e) Prove mathematically that the answer to part (a) behaves correct in this limit. Figure P13.14 15. Three objects of equal mass are located at three corners of a square of edge length â, as shown in Figure P13.15. Find the magnitude and direction of the gravitational field at the fourth corner due to these objects. Figure P13.15 16. A spacecraft in the shape of a long cylinder has a length of 100 m, and its mass with occupants is 1 000 kg. It has strayed too close to a black hole having a mass

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