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→Newtonian Gravitation
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:
:<math>\mathbf{F} = G \frac{m_1 m_2}{\mathbf{r}^2}</math>
:<math>\mathbf{F} = -G \frac{m_1 m_2}{\vert {\mathbf{r}} \vert ^2} \mathbf{\hat{r}}</math>
Where:
Where:
*''<b>F</b>'' is the magnitude of the gravitational force.
*''<b>F</b>'' is the gravitational force vector.
*''m''<sub>1</sub> and ''m''<sub>2</sub> are the object's masses.
*''m''<sub>1</sub> and ''m''<sub>2</sub> are the object's masses.
*''<b>r</b>'' is the vector that separates the objects' centers of mass.
*''<b>r</b>'' is the vector that separates the objects' centers of mass.
* <math>\mathbf{\hat{r}}</math> is the unit vector of ''<b>r</b>''.
*''G'' is the [[gravitational constant]]: <math>\frac{6.67428 \times 10^{-11} N m^2}{kg^2}</math>
*''G'' is the [[gravitational constant]]: <math>\frac{6.67428 \times 10^{-11} N m^2}{kg^2}</math>