I have tried reading about them and I have understood how L1,2&3 are made. That was pretty easy to get. But L4 and L5 I am not able to. If anyone could give me a source to read or explain it to me. Thanks.
In: 4
So imagine you have an equilateral triangle with a small satellite A, a heavy mass B, and a medium mass C at the three corners. The satellite A is equally far from the heavy and medium masses (by definition of an equilateral traingle), so B and C will pull A towards each of them in proportion to their masses. If the heavy mass is 99x as heavy as the medium mass, it pulls exactly 99x as hard, so if you imagine the line segment BC divided up into 100 equal portions, satellite A’s net force will be directed towards the point at the end of the first portion, exactly one unit away from B and 99 units away from C.
That point is *also* the center of mass of the BC orbital system, for the same reason, that if B is 99x more massive, the center of mass must be 99x closer to B. B and C are both going to be orbiting that point.
So you have a situation where the two massive objects are both going to maintain an orbit around a certain center of mass point, the third satellite is also experiencing a centripetal acceleration directly toward that center of mass point, and the orbit is stable because the object is orbiting as the same rate around the point as the medium mass C is. (If it were an isosceles triangle and A were closer or further away, A would need a greater or lesser orbital velocity than C, and couldn’t maintain the equilateral triangle).
That creates two points where it is conceivable for A to remain in a stable orbit around B thanks to the offsetting pull by C.
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