Understanding the Lagrange Points: What's Going Wrong with L2 and L3?

[Imager]

The Wiki article shows 5 Lagrange points. I can “see” how the points L1, L4 and L5 points would be balanced by the gravitation of the two bodies, but not the L2 and L3.

For L2 and L3, it looks to me like the combination of the Sun’s and Earth’s gravity increase pull and make less stable. So where am I going wrong?

https://en.wikipedia.org/wiki/Lagrangian_point

 

[Orodruin]

You are forgetting that this is a rotating system. Consequently, there is also a contribution from the ficticious centrifugal force in the rotating frame.

 

[Imager]

You are forgetting that this is a rotating system. Consequently, there is also a contribution from the ficticious centrifugal force in the rotating frame.

So I could think of it like another small planet in orbit around the sun?

 

[Orodruin]

So I could think of it like another small planet in orbit around the sun?

Essentially. The "big" thing here is that the presence of the second large body (the Earth) has the effect that at the angular velocity only is the same at a few points. In other places, the gravitational effect of the Earth will destabilise the orbit.

Edit: Also note that this third body needs to be significantly lighter than the Earth in order not to influence the Earth orbit as well.

 

[Chalnoth]

The Wiki article shows 5 Lagrange points. I can “see” how the points L1, L4 and L5 points would be balanced by the gravitation of the two bodies, but not the L2 and L3.

For L2 and L3, it looks to me like the combination of the Sun’s and Earth’s gravity increase pull and make less stable. So where am I going wrong?

L1, L2, and L3 are all unstable equilibrium points. You can park a satellite there, if you're careful, but it won't stay forever: it will eventually get kicked out of the orbit. It's rare to find natural satellites at these points. L4 and L5 are stable, so there's lots of asteroids and whatnot around those Lagrange points.

 

[Imager]

Great answers, thank you!

Another proof that my intuition gets it backwards when in come to Physics and my golf swing.