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I have just found an article talking about the L1 to L5 equilibrium positions of gravitation around stars, planets, etc. As far as I could learn from this website and other research I have done the gravitational attraction is not a force is a deformation of time space fabric

Ouestion: could you please help me understand how is it possible for the space-time to be deformed in stable and non-stable ways?

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  • $\begingroup$ Lagrange points are not stationary. For example, a Lagrange point for the Earth is always at the same distance from the Earth, but this point still rotates around the Sun along with the Earth. It does not surprise you that the Earth can rotate around the Sun. Why should it surprise you that a satellite in a Lagrange point also can rotate around the Sun? The only caveat here is that this satellite rotates with the same period as the Earth, but this is simply because the gravity of the Earth also pulls it along. $\endgroup$ – safesphere Aug 22 '18 at 22:09
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I think you are confused about stability. It does not matter about the nature of the gravitational field, what matters is whether the resulting orbits are relatively stable or relatively unstable. That is, how likely they are to remain close to those points.

It's a bit like being in a hill or a valley. In a valley you're more likely to remain in the valley - it's harder to get out and easy to stay in. On the top of a hill it's easy to roll off and hard to stay up. One is stable place to be, the other is not a stable place to be.

The fact that spacetime distorted by mass and energy is how gravity arises does not change this. Spacetime is not the thing that is stable or unstable, it is the nature of the orbit the objects are in that either makes it more likely or less likely to stay near a particular Lagrange point.

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