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Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws , where force is inversely proportional to the square of the distance between the bodies.
The Cavendish experiment, performed in 1797–1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory [1] and the first to yield accurate values for the gravitational constant.
Newton's laws are often stated in terms of point or particle masses, that is, bodies whose volume is negligible. This is a reasonable approximation for real bodies when the motion of internal parts can be neglected, and when the separation between bodies is much larger than the size of each.
In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations , it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress ...
A newton is defined as 1 kg⋅m/s 2 (it is a named derived unit defined in terms of the SI base units). [1]: 137 One newton is, therefore, the force needed to accelerate one kilogram of mass at the rate of one metre per second squared in the direction of the applied force. [2]
Force measured in a 2010 experiment by perturbing 60 beryllium-9 ions [4] [5] 10 −18 attonewton (aN) 10 −17: 30 aN Smallest force of gravity measured [6] [7] 10 −15 femtonewton (fN) 10 −14 ~10 fN Brownian motion force on an E. coli bacterium averaged over 1 second [8] ~10 fN Weight of an E. coli bacterium [9] [10] 10 −13 ~100 fN
(A diagram showing the forces exerted both on and by a body is likely to be confusing since all the forces will cancel out. By Newton's 3rd law if body A exerts a force on body B then B exerts an equal and opposite force on A. This should not be confused with the equal and opposite forces that are necessary to hold a body in equilibrium.)
At this time, Newton developed his theory of gravitation which is based on attraction, and although Huygens agreed with the mathematical formalism, he said the model was insufficient due to the lack of a mechanical explanation of the force law. Newton's discovery that gravity obeys the inverse square law surprised Huygens and he tried to take ...
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