Two identical spherical asteroids each of mass are fixed in space with their centres apart

PHYSICS · Subjective · CBSE · Physics · Gravitation · Gravitation

Problem

Two identical spherical asteroids each of mass 3.0×1012 kg3.0\times10^{12}\,\text{kg} are fixed in space with their centres 1.0×105 m1.0\times10^{5}\,\text{m} apart. A research satellite of mass 500 kg500\,\text{kg} is placed exactly midway between the two asteroids on the line joining their centres. (a) Calculate the magnitude of the gravitational force exerted on the satellite by one asteroid. Take G=6.67×10−11 N m2 kg−2G = 6.67\times10^{-11}\,\text{N\,m}^2\,\text{kg}^{-2}. (b) What is the magnitude and direction of the net gravitational force acting on the satellite? (c) If the distance between the centres of the asteroids is increased to 2.0×105 m2.0\times10^{5}\,\text{m} while the satellite remains midway, determine the new magnitude of the net gravitational force on the satellite. (d) Find the percentage change in the net gravitational force on the satellite as a result of the change described in part (c).

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