# Earth-Sun Lagrange points L4/L5 existence

Why do Lagrange points L4 and L5 exist at all?

Consider the mass of Jupiter equals 320 Earth masses, and distance from Lagrange point to Jupiter is about 4-6 A.U. We get that the gravity of Jupiter is by the order of magnitude greater than that of Earth at these points. Shouldn't it perturb the orbit of the body enough to force it out of the Lagrange point?

The difference with L1/L2/L3 is that L4 and L5 are stable equilibrium points(for the mass ration $M_1/M_2 \geq 25$), while L1-L3 are unstable. Stable means that, if you place an object there and then move it a little bit, it will go back to where you placed it. Unstable means the opposite.