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Just what are Lagrange Points
The three body problem is inherently chaotic, basically unsolvable, the mathematical solution defeating even Issac Newton. Continued study led to perubation theory, and by reducing the three body problem where the third body is very small compared to the other two, you can derive Lagrange points.
Lagrange points are positions in space where the gravitational
forces of two large celestial bodies, like the Sun and Earth,
balance the centrifugal force of a third smaller object,
such as a spacecraft or asteroid, allowing it to remain in a
fixed position relative to the two large bodies.
There are five L-points for any two large masses, with L1, L2,
and L3 located along the line connecting the two bodies,
these three are unstable. The James Webb Space Telescope is
parked at L2 which allows its sunshield to block the light
and heat from the Sun, Earth, and Moon simultaneously.
In the 1760s, Swiss mathematician Leonhard Euler explored a
restricted version of the three-body problem, in which one
of the bodies has negligible mass compared to the other two.
He discovered the three collinear solutions, today known as
L1, L2, and L3, where all three bodies lie on a straight line.
In 1772, Italian-French mathematician Joseph-Louis Lagrange
published his "Essay on the three-body problem," building on
Euler's work. He identified all five equilibrium points,
including the two triangular ones (L4 and L5), where the
three bodies form an equilateral triangle. This discovery
completed the theoretical foundation for the points that
now bear his name. L4 and L5 form equilateral triangles
with the two large bodies, and are stable or semi-stable
"parking spots" in space, used by satellites for constant
observation or uninterrupted communication.
There are Lagrange points for pairs of large masses,
Sun-Earth System, Sun-Jupiter System, and the Sun Neptune
System. In the Sun-Earth system, the regions around the
L4 and L5 points are roughly 500,000 miles wide.
The largest stable regions in the solar system belong to
Neptune. Its L4 and L5 zones are estimated to be
about 2 billion miles across.
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Version History:
Sunday Sep 14, 2025 (V00b) Posted
Sunday Aug 31, 2025 (V00a) Created