It is the proportionality constant of Newton's law of gravitation. It is constant over the entire universe and hence gravitational force is independent of location.
The value of the gravitational constant G entering the Universal law of gravitation can be determined experimentally and this was first done by English scientist Henry Cavendish in 1798. The apparatus used by him is schematically shown in figure.
Explanation : The bar AB has two small lead spheres attached at its ends. The bar is suspended from a rigid support by a fine wire.
Two large lead spheres are brought close to the small ones but on opposite sides as shown. The big spheres attract the nearby small ones by equal and opposite force as shown. There is no net force on the bar but only a torque which is clearly equal to F times the length of the bar,where F is the force of attraction between a big sphere and its neighboring small sphere. Due to this torque, the suspended wire gets twisted till such time as the restoring torque of the wire equals
the gravitational torque .
If θ is the angle of twist of the suspended wire, the restoring torque is proportional to θ, equal to τθ. Where τ is the restoring couple per unit angle of twist. τ can be measured independently e.g. by applying a known torque and measuring the angle of twist.
The gravitational force between the spherical balls is the same as if their masses are concentrated at their centers. Thus if d is the separation between the centers of the big and its neighboring small ball, M and m their masses, the gravitational force between the big sphere and its neighboring small ball is.(8.4)
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