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History of gravitational theory. In physics, theories of gravitation postulate mechanisms of interaction governing the movements of bodies with mass. There have been numerous theories of gravitation since ancient times. The first extant sources discussing such theories are found in ancient Greek philosophy.
The equation for universal gravitation thus takes the form: F = G m 1 m 2 r 2 , {\displaystyle F=G{\frac {m_{1}m_{2}}{r^{2}}},} 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 .
René Descartes theorized that the tides (alongside the movement of planets, etc.) were caused by aetheric vortices, without reference to Kepler's theories of gravitation by mutual attraction; this was extremely influential, with numerous followers of Descartes expounding on this theory throughout the 17th century, particularly in France.
According to Descartes, this inward pressure is nothing other than gravity. He compared this mechanism with the fact that if a rotating, liquid filled vessel is stopped, the liquid goes on to rotate. Now, if one drops small pieces of light matter (e.g. wood) into the vessel, the pieces move to the middle of the vessel.
Newton's first law expresses the principle of inertia: the natural behavior of a body is to move in a straight line at constant speed. A body's motion preserves the status quo, but external forces can perturb this. The modern understanding of Newton's first law is that no inertial observer is privileged over any other.
The folium of Descartes is related to the trisectrix of Maclaurin by affine transformation. To see this, start with the equation. and change variables to find the equation in a coordinate system rotated 45 degrees. This amounts to setting In the plane the equation is. If we stretch the curve in the direction by a factor of this becomes.
In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mutually tangent circles. The theorem is named after René Descartes, who stated it in 1643.
At a fixed point on the surface, the magnitude of Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. [2] [3] At different points on Earth's surface, the free fall acceleration ranges from 9.764 to 9.834 m/s 2 (32.03 to 32.26 ft/s 2 ), [4] depending on altitude , latitude , and longitude .