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==Explanation==
 
==Explanation==
  
In celestial mechanics, the {{w|Lagrange point}}s are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Or in simpler terms, positions in space where objects can float motionless relative to the defining bodies.
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In celestial mechanics, the {{w|Lagrange point}}s are points of equilibrium for small-mass objects under the influence of two massive orbiting bodies. Or in simpler terms, positions in space where objects can float motionless relative to the defining bodies. The L<sub>1</sub>, L<sub>2</sub>, and L<sub>3</sub> points are unstable, as any drifting off the point (e.g. due to the gravity of other bodies) might quickly increase the tendency to depart the area. However, there are quasi-stable {{w|Halo orbit}}s around these points, like the one used by the {{w|James Webb Space Telescope}}. The L<sub>4</sub> and L<sub>5</sub> points can actually retain objects stably over long periods, resulting in the Sun-Jupiter L<sub>4</sub> and L<sub>5</sub> points capturing the {{w|Trojan (celestial_body)|Trojan Asteroids}}.
  
There are five traditional Lagrange points. Two form equilateral triangles with the two massive objects (in this case the Earth and the Sun), and three more are collinear with the massive objects. The L<sub>1</sub>, L<sub>2</sub>, and L<sub>3</sub> points are unstable, as any drifting off the point (e.g. due to the gravity of other bodies) might quickly increase the tendency to depart the area. However, there are quasi-stable {{w|Halo orbit}}s around these points, like the one used by the {{w|James Webb Space Telescope}}. The L<sub>4</sub> and L<sub>5</sub> points can actually retain objects stably over long periods, resulting in the Sun-Jupiter L<sub>4</sub> and L<sub>5</sub> points capturing the {{w|Trojan (celestial_body)|Trojan Asteroids}}.
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There are five traditional Lagrange points. Two form equilateral triangles with the two massive objects (in this case the Earth and the Sun), and three more are collinear with the massive objects. Randall claims that a sixth Lagrange point has been discovered outside of {{w|Cleveland}}, {{w|Ohio}}. This is pretty obviously farcical,{{Citation needed}} as this would be part of the Earth and thus not gravitationally balanced between Earth and the Sun, though it is balanced by the countering forces that hold anything stable on the surface of any body: {{w|gravity}} and {{w|electromagnetism}}. The joke here is that there actually is a small village named {{w|LaGrange, Ohio|LaGrange, OH}} (population 2,595 in 2020) just outside Cleveland ([https://www.google.com/maps/place/Lagrange,+OH+44050/ map]). However, the village name is spelled with a capital G, unlike {{w|Joseph-Louis Lagrange}} after which the Lagrange points were named.
 
 
Randall claims that a sixth Lagrange point has been discovered outside of {{w|Cleveland}}, {{w|Ohio}}. This is pretty obviously farcical,{{Citation needed}} as this would be part of the Earth and thus not gravitationally balanced between Earth and the Sun, though it is balanced by the countering forces that hold anything stable on the surface of any body: {{w|gravity}} and {{w|electromagnetism}}. The joke here is that there actually is a small village named {{w|LaGrange, Ohio|LaGrange, OH}} (population 2,595 in 2020) just outside Cleveland ([https://www.google.com/maps/place/Lagrange,+OH+44050/ map]). However, the village name is spelled with a capital G, unlike {{w|Joseph-Louis Lagrange}} after which the Lagrange points were named.
 
  
 
There is, however, a {{w|Lagrange,_Maine|Lagrange in Maine}}, a {{w|Lagrange,_Virginia|Lagrange in Virginia}} and a {{w|Lagrange_Township,_Bond_County,_Illinois|Lagrange Township in Illinois}} which all use the lower case g in their spelling like Joseph-Louis Lagrange.  There are also {{w|https://en.wikipedia.org/wiki/Lagrange_(disambiguation)|twenty-six other communities}} in the United states with a spelling of LaGrange or La Grange, as well as four in France and two in Australia with one of the three spellings.  This includes {{w|La_Grange,_Texas|La Grange, Texas}} which became famous as the title of a {{w|La_Grange_(song)|ZZ Top song}}.
 
There is, however, a {{w|Lagrange,_Maine|Lagrange in Maine}}, a {{w|Lagrange,_Virginia|Lagrange in Virginia}} and a {{w|Lagrange_Township,_Bond_County,_Illinois|Lagrange Township in Illinois}} which all use the lower case g in their spelling like Joseph-Louis Lagrange.  There are also {{w|https://en.wikipedia.org/wiki/Lagrange_(disambiguation)|twenty-six other communities}} in the United states with a spelling of LaGrange or La Grange, as well as four in France and two in Australia with one of the three spellings.  This includes {{w|La_Grange,_Texas|La Grange, Texas}} which became famous as the title of a {{w|La_Grange_(song)|ZZ Top song}}.

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