Editing Lagrange point (section)

===L<sub>3</sub>===
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The location of L<sub>3</sub> is the solution to the following equation, gravitation providing the centripetal force:
<math display="block">\frac{M_1}{\left(R-r\right)^2}+\frac{M_2}{\left(2R-r\right)^2}=\left(\frac{M_2}{M_1+M_2}R+R-r\right)\frac{M_1+M_2}{R^3}</math>
with parameters ''M''<sub>1</sub>, ''M''<sub>2</sub>, and ''R'' defined as for the L<sub>1</sub> and L<sub>2</sub> cases, and ''r'' being defined such that the distance of L<sub>3</sub> from the center of the larger object is ''R''&nbsp;−&nbsp;''r''. If the mass of the smaller object (''M''<sub>2</sub>) is much smaller than the mass of the larger object (''M''<sub>1</sub>), then:<ref>{{Cite web|url=https://ocw.mit.edu/courses/aeronautics-and-astronautics/16-07-dynamics-fall-2009/lecture-notes/MIT16_07F09_Lec18.pdf |title=Widnall, Lecture L18 - Exploring the Neighborhood: the Restricted Three-Body Problem}}</ref>

<math display="block">r\approx R\tfrac{7}{12}\mu.</math><!-- in the source the factor that appears in the equation is 5/12, but that is the distance from L3 to the center of mass, here we are showing the distance between L3 and the orbit of the smaller object -->

Thus the distance from L<sub>3</sub> to the larger object is less than the separation of the two objects (although the distance between L<sub>3</sub> and the barycentre is greater than the distance between the smaller object and the barycentre).