The story started with an apple. Apple was the forbidden fruit which tempted eve. Apple was the fruit which propelled Newton to discover the law of gravitation.
At the age of 44, Newton found out the Law of Universal Gravitation, which states that any two objects attract each other with a force given by
F = G (M1 * M2)
R2
Newton estimated this constant of proportionality, called universal gravitational constant G, from the gravitational acceleration of the falling apple and an approximate guess for the average density of the Earth. However, more than 100 years elapsed before G was first measured in the laboratory.
It was in 1798 that Cavendish and co-workers obtained a value for G of 6.67 x10-11 Newton.m2kg-2, accurate to about 1%.
The recent official value for G is (6.67259±0.00085)x10-11 Newton.m2kg-2
The new values using the best laboratory equipment to-date disagreed wildly to the point that many doubt about the constancy of this parameter and some are even postulating entirely new forces to explain these gravitational anomalies.
It was proposed that the force between two masses can be better represented by
F = G (M1 * M2) [1+ (1+ r /lamda) alpha e-r/lamda] / R2
with alpha = -0.007 and lamda ~ 200 m
As alpha is -ve, the 2nd term in the bracket represents a repulsive force.
For r >> 200 m,
F = G (M1 * M2)
R2
which is the force operating between the earth and other objects.
For r << 200 m,
F = G (M1 * M2)(1+alpha)
R2
= G`(M1 * M2)
R2
Where G`= G (1+ alpha)
And, therefore, the value of G for small distance is about 1% less than the value of G for large distance.
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P.s. sorry for hybrid typing
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