Editing Lagrange point (section)

==={{L2|nolink=yes}}===
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[[File:L2 rendering.jpg|thumb|right|upright=1.35|The Lagrangian L<sub>2</sub> point for the [[Sun]]–[[Earth]] system]]
The location of L<sub>2</sub> is the solution to the following equation, gravitation providing the centripetal force:
<math display="block">\frac{M_1}{(R+r)^2}+\frac{M_2}{r^2}=\left(\frac{M_1}{M_1+M_2}R+r\right)\frac{M_1+M_2}{R^3}</math>
with parameters defined as for the L<sub>1</sub> case. The corresponding quintic equation is
<math display="block">x^5 + x^4 (3 - \mu) + x^3 (3 - 2\mu) - x^2 (\mu) - x (2\mu) - \mu = 0</math>

Again, 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 L<sub>2</sub> is at approximately the radius of the [[Hill sphere]], given by:
<math display="block">r \approx R \sqrt[3]{\frac{\mu}{3}}</math>

The same remarks about tidal influence and apparent size apply as for the L{{sub|1}} point. For example, the angular radius of the Sun as viewed from L<sub>2</sub> is arcsin({{sfrac|{{val|695.5e3}}|{{val|151.1e6}}}})&nbsp;≈&nbsp;0.264°, whereas that of the Earth is arcsin({{sfrac|6371|{{val|1.5e6}}}})&nbsp;≈&nbsp;0.242°. Looking toward the Sun from L<sub>2</sub> one sees an [[annular eclipse]]. It is necessary for a spacecraft, like [[Gaia (spacecraft)|Gaia]], to follow a [[Lissajous orbit]] or a [[halo orbit]] around L<sub>2</sub> in order for its solar panels to get full sun.