Explain newton's law of gravitation by mathematically
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In modern language, the law states the following:
Every point mass attracts every single other point mass by a force pointing alongthe line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:[2]
F = G m 1 m 2 r 2 {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\ }
where:
F is the force between the masses;G is the gravitational constant (6.674×10−11 N · (m/kg)2);m1 is the first mass;m2 is the second mass;r is the distance between the centers of the masses.
Error plot showing experimental values for big G.
Assuming SI units, F is measured in newtons(N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10−11 N m2 kg−2.[29] The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientistHenry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G.[3] This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton'sPrincipia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force.
Every point mass attracts every single other point mass by a force pointing alongthe line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them:[2]
F = G m 1 m 2 r 2 {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}}\ }
where:
F is the force between the masses;G is the gravitational constant (6.674×10−11 N · (m/kg)2);m1 is the first mass;m2 is the second mass;r is the distance between the centers of the masses.
Error plot showing experimental values for big G.
Assuming SI units, F is measured in newtons(N), m1 and m2 in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674×10−11 N m2 kg−2.[29] The value of the constant G was first accurately determined from the results of the Cavendish experiment conducted by the British scientistHenry Cavendish in 1798, although Cavendish did not himself calculate a numerical value for G.[3] This experiment was also the first test of Newton's theory of gravitation between masses in the laboratory. It took place 111 years after the publication of Newton'sPrincipia and 71 years after Newton's death, so none of Newton's calculations could use the value of G; instead he could only calculate a force relative to another force.
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