Changes

=== Newtonian Gravitation ===

=== Newtonian Gravitation ===

In 1687, [[Sir Isaac Newton]] published his [[Philosophiæ Naturalis Principia Mathematica|''Principia Mathematica'']], an exhaustive work that laid the foundation for what we know today as classical mechanics. In this work, Newton advanced the [[Law of Universal Gravitation|law of universal gravitation]] that had been previously published by Hooke and others. Whereas Galileo described gravitation in terms of motion, Newton described it in terms of a [[force]]. Gravitation itself went from the natural tendency of objects to fall to a vector [[field theory]] in which the force between two objects was inversely proportional to the square of the distance between them.

In 1687, [[Sir Isaac Newton]] published his Principia Mathematica, an exhaustive work that laid the foundation for what we know today as classical mechanics. In this work, Newton advanced the [[Law of Universal Gravitation|law of universal gravitation]] that had been previously published by Hooke and others. Whereas Galileo described gravitation in terms of motion, Newton described it in terms of a [[force]]. Gravitation itself went from the natural tendency of objects to fall to a vector [[field theory]] in which the force between two objects was inversely proportional to the square of the distance between them.

Newton's vector equation for gravitation states that each particle in the [[universe]] attracts another particle with a force directly [[proportion]]al to the product of their masses and inversely proportional to the [[exponentiation|square]] of the distance between them,<ref>Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition</ref> or:  

Newton's vector equation for gravitation states that each particle in the [[universe]] attracts another particle with a force directly [[proportion]]al to the product of their masses and inversely proportional to the [[exponentiation|square]] of the distance between them,<ref>Serway and Beichner, Physics for Scientists and Engineers, Fifth Edition</ref> or:  

Where:

Where:

*'''''F''''' is the gravitational force vector.

*<math>\mathbf{F}</math> is the gravitational force vector.

*''m''₁ and ''m''₂ are the object's masses.

*<math>m_1</math> and <math>m_2</math> are the object's masses.

   

   

*'''''r''''' is the vector that separates the objects' centers of mass.

*<math>\mathbf{r}</math> is the vector that separates the objects' centers of mass.

* <math>\mathbf{\hat{r}}</math> is the unit vector of '''''r'''''; <math>\mathbf{r} = \vert {\mathbf{r}} \vert \  \mathbf{\hat{r}}</math>

* <math>\mathbf{\hat{r}}</math> is the unit vector of <math>\mathbf{r}</math>; defined as <math>\mathbf{\hat{r}} =\mathbf{r}/ {\vert {\mathbf{r}} \vert}</math>

*''G'' is the [[gravitational constant]]: <math>\frac{6.67428 \times 10^{-11} N m^2}{kg^2}</math>

*<math>G</math> is the [[gravitational constant]]: <math>\frac{6.67408(31) \times 10^{-11} N m^2}{kg^2}</math><ref>http://physics.nist.gov/cgi-bin/cuu/Value?bg</ref>

Another way to express this equation, that is more convenient for programming and expansion into power series, is:

Another way to express this equation, that is more convenient for programming and expansion into power series, is: