Lagrange points solved one of physics' biggest problems
The formulation that the forces “cancel out” at the Lagrange points bothers me, even though it’s not technically wrong.<p>At each of the five points, there’s a net gravitational force towards the sun (to be more precise: towards the common barycenter). This is easiest to see at L2 and L3 where the gravitational forces pull in the same direction.<p>There are now two ways to look at this combined gravitational force:<p>1. In an inertial reference frame (the one we imagine when we say the Earth revolves around the Sun), this combined gravitational force acts as a centripetal force. At the Lagrange points, it has precisely the correct value to keep the object in an orbit with period 1 year.<p>2. In the reference frame where Sun and Earth don’t move (that is, the reference frame that rotates at 1&#x2F;year around the barycenter), every point experiences an apparent centrifugal force. At the Lagrange point, this centrifugal force cancels with the gravitational forces to keep the object stationary in this reference frame.<p>The math is completely the same (x=y vs. x-y=0). I personally just find the first view to be more intuitive.