establish a relation between acceleration due to gravity and gravitational constant
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The value of g on earth is 9.81 m/s^2 or N/kg. However, G denotes the gravitational constant, an empiricalphysical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation (F = Gm1m2/r^2) and in Albert Einstein's general theory of relativity.
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Let g be the acceleration due to gravity and G be the gravitational constant.
Force = Gm1m2 / r^2
For two objects with the same mass,
F = Gm^2 / r^2
But, force = mg
Therefore, mg = Gm^2 / r^2
Thus, g = Gm / r^2
Force = Gm1m2 / r^2
For two objects with the same mass,
F = Gm^2 / r^2
But, force = mg
Therefore, mg = Gm^2 / r^2
Thus, g = Gm / r^2
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