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where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant. The first test of Newton's law of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry ...
The first equation shows that, after one second, an object will have fallen a distance of 1/2 × 9.8 × 1 2 = 4.9 m. After two seconds it will have fallen 1/2 × 9.8 × 2 2 = 19.6 m; and so on. On the other hand, the penultimate equation becomes grossly inaccurate at great distances.
A common misconception occurs between centre of mass and centre of gravity.They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts.
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 ...
is the radial coordinate of the observer within the gravitational field (this coordinate is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate; the equation in this form has real solutions for >), is the speed of light,
[12] [13]: 150 The physics concept of force makes quantitative the everyday idea of a push or a pull. Forces in Newtonian mechanics are often due to strings and ropes, friction, muscle effort, gravity, and so forth. Like displacement, velocity, and acceleration, force is a vector quantity.
The force of attraction or repulsion between two electrically charged particles, in addition to being directly proportional to the product of the electric charges, is inversely proportional to the square of the distance between them; this is known as Coulomb's law. The deviation of the exponent from 2 is less than one part in 10 15. [8]
where and are any two masses, is the gravitational constant, and is the distance between the two point-like masses. Two bodies orbiting their center of mass (red cross) Using the integral form of Gauss's Law , this formula can be extended to any pair of objects of which one is far more massive than the other — like a planet relative to any ...