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Gravitation is the tendency of masses to move toward each other.
The first mathematical formulation of the theory of gravitation was made by Sir Isaac Newton and proved astonishingly accurate. He postulated the force of "universal gravitational attraction".
Newton's theory has now been replaced by Albert Einstein's theory of General relativity but for most purposes dealing with weak gravitational fields (for example, sending rockets to the moon or around the solar system) Newton's formulae are sufficiently accurate. For this reason Newton's law is often used and will be presented first.
Gravity in a room: the curvature of the Earth is negligible at this scale, and the force lines can be considered being parallel
Newton's law of universal gravitation states the following:
Considering only the magnitude of the force, and momentarily putting aside its direction, the law can be stated symbolically as follows.
where
Strictly speaking, this law applies only to point-like objects. If the objects have spatial extent, the force has to be calculated by integrating the force (in vector form, see below) over the extents of the two bodies. It can be shown that for an object with a spherically-symmetric distribution of mass, the integral gives the same gravitational attraction on masses outside it as if the object were a point mass.
This law of universal gravitation was originally formulated by Isaac Newton in his work, the Principia MathematicaNewton's own copy of his Principia with hand written corrections for the second edition. The Philosophiae Naturalis Principia Mathematica ( Latin: "mathematical principles of natural philosophy", often Principia or Principia Mathematica for short) is a th ( 1687Events March 19 The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. July 5 Isaac Newton's Philosophiae Naturalis Principia Mathematica is published. December 31 The first Huguenots set sail). The history of the gravitation as a physical concept is considered in more detail below.
Newton's law of universal gravitation can be written as a vectorA vector in physics and engineering typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a "magnitude" and a "direction". The word vector is also now used for more general concepts ( equationAlgebra This article is about equations in mathematics. For equations in chemistry, see chemical equation. In mathematics, one often (not quite always) distinguishes between an identity which is an assertion that two expressions are equal regardless of th to account for the direction of the gravitational force as well as its magnitude. In this formulation, quantities in bold represent vectors.
As before, m1 and m2 are the masses of the objects 1 and 2, and G is the gravitational constant.
It can be seen that the vector form of the equation is the same as the scalarAbstract algebra Algebra Linear algebra The concept of a scalar is used in mathematics and physics. The concept used in physics is a more concrete version of the same idea that goes by that name in mathematics. In mathematics, the meaning of scalar depend form, except for the vector value of F and the unit vector. Also, it can be seen that F12 = − F21.
Gravitational acceleration is given by the same formula except for one of the factors m:
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