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
[Hard to do without a diagram.]
Consider a world with two massive bodies rotating around each other.
Look at the world in a rotating frame of reference, so the two bodies are at fixed positions.
Draw a line, put marks for the two bodies (M1, M2) and a third for the center of mass of the system (CM); let’s say that’s close to the left body.
If you do the math, the L4 point is going to be the third corner of an equilateral triangle with the two bodies, so put a little mark there.
At every point in the system, a third body is going to feel three forces: gravitational attraction toward M1, which decreases with increasing distance from M1; gravitational attraction toward M2; and the centrifugal force, which *increases* with increasing distance from the CM.
Now, consider a point to the upper right of L4.
The gravitational force from M1 is a little less, and the centrifugal force is a little greater, so the *net* force, compared to that at L4, is to the upper right.
Next, consider a point to the lower right of L4.
The gravity from M2 is a little more, so the net force, compared to that at L4, is to the lower right.
Similarly, you can work out that the net forces at points to the upper left and lower left of L4 are away from L4.
So *somewhere* in between those four points, there has to be a place where the three forces are in balance, so there’s no net force … and it turns out to be at L4.
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