Gravity

:For other senses of the words gravity and gravitation, see gravity (disambiguation).

Newton's law of universal gravitation

Newton's law of universal gravitation states the following:

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:Every object in the Universe attracts every other object with a force directed along the line of centers of mass for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects.

Related Topics:
Universe - Force - Line - Proportional - Square

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Considering only the magnitude of the force, and momentarily putting aside its direction, the law can be stated symbolically as follows.

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:F = - G rac{m_1 m_2}{r^2}

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where:

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:F is the magnitude of the gravitational force between two objects

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:G is the gravitational constant, that is approximately : G = 6.67 × 10−11 N m2 kg-2

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:m1 is the mass of first object

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:m2 is the mass of second object

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:r is the distance between the objects

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Remember that the force F is always negative, this stands for attractive force. The sign minus is useful to hold the same value meaning as in the Coulomb's Law, where a positive force as result means repulsion between two charges.

Related Topics:
Coulomb's Law - Charges

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Thus gravity is proportional to the mass of each object, but has an inverse square relationship with the distance between the centres of each mass.

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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.1

Related Topics:
Integrating - 1

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This law of universal gravitation was originally formulated by Isaac Newton in his work, the Principia Mathematica (1687). The history of gravitation as a physical concept is considered in more detail below.

Related Topics:
Isaac Newton - Principia Mathematica - 1687 - Below

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Vector form

Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formulation, quantities in bold represent vectors.

Related Topics:
Vector - Equation

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:

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mathbf{F}_{12} =

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G {m_1 m_2 over r_{21}^2}

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, mathbf{hat{r}}_{21}

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or

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mathbf{F}_{12} =

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