Lagrange Points:A Special locations in Space

Do you know that when a spacecraft placed in an orbital path around a huge mass body orbits in the same orbit with stability, that is what is known as Lagrange Point, which was given by the French mathematician Joseph Louis Lagrange, who had published three body problems A Lagrange point is an exact solution for a three-body problem, and it is a point where all the forces are balanced.Lagrange showed all five locations where, if we placed a particle of zero mass with the right velocity, it would remain in the same path relative to a high-mass body.The force of gravity and the centrifugal force are forces acting on the lagrange points.All five points were actually discovered by Leonard Euler, namely L1, L2, L3, L4, and L5.The most brief of all points is L1, which sits between two bodies on the saddle point between two gravity wells (gravity of two mass bodies).Similarly, L2 is on the far side of the low-mass body and is an unstable point that needs regular maintenance if we place an object right there, and L3 is on the far side of the higher-mass body.But the objects rotating in L4 and L5 remain in the same orbit due to the coriolis force (rotating environment) at 90 degrees to the direction of motion of the object.The main concept of stabilizing the L4 and L5 points is the effect of changing the mass ratio of two mass bodies, such as Sun-Earth, Sun-Jupiter, etc.Since three body problems, i.e., the sun, planet, and satellite, are complex body problems, a lagrange point is best suited to solve three body problems by placing an object on the point where two mass bodies' gravity cancels out.