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The three collinear Lagrange points (L 1, L 2, L 3) were discovered by the Swiss mathematician Leonhard Euler around 1750, a decade before the Italian-born Joseph-Louis Lagrange discovered the remaining two.
Joseph-Louis Lagrange [a] (born Giuseppe Luigi Lagrangia [5] [b] or Giuseppe Ludovico De la Grange Tournier; [6] [c] 25 January 1736 – 10 April 1813), also reported as Giuseppe Luigi Lagrange [7] or Lagrangia, [8] was an Italian mathematician, physicist and astronomer, later naturalized French.
L 4 is the Sun–Earth Lagrange point located close to the Earth's orbit 60° ahead of Earth. Asteroid (706765) 2010 TK 7 is the first discovered tadpole orbit companion to Earth, orbiting L 4 ; like Earth, its mean distance to the Sun is about one astronomical unit .
After Newton, Joseph-Louis Lagrange attempted to solve the three-body problem in 1772, analyzed the stability of planetary orbits, and discovered the existence of the Lagrange points. Lagrange also reformulated the principles of classical mechanics, emphasizing energy more than force, and developing a method to use a single polar coordinate ...
In the calculus of variations and classical mechanics, the Euler–Lagrange equations [1] are a system of second-order ordinary differential equations whose solutions are stationary points of the given action functional. The equations were discovered in the 1750s by Swiss mathematician Leonhard Euler and Italian mathematician Joseph-Louis Lagrange.
c. 1750 – The three collinear Lagrange points (L1, L2, L3) were discovered by Leonhard Euler, a decade before Joseph-Louis Lagrange discovered the remaining two. [110] [111] 1752 – Benjamin Franklin conducts his kite experiment, successfully extracting sparks from a cloud, showing that lightning bolts are huge natural electrical discharges ...
In the special case of the circular restricted three-body problem, these solutions, viewed in a frame rotating with the primaries, become points called Lagrangian points and labeled L 1, L 2, L 3, L 4, and L 5, with L 4 and L 5 being symmetric instances of Lagrange's solution.
These leading and trailing points are called the L 4 and L 5 Lagrange points. [11] [Note 1] The first asteroids trapped in Lagrange points were observed more than a century after Lagrange's hypothesis. Those associated with Jupiter were the first to be discovered. [2]