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In defining the effective force using the effective potential, you have just considered L as a constant! L is actually a function of r. This only makes a difference in the change of sign in this particular case. And while the equation of force is the correct one, since the force (centrifugal) is repulsive, meaning that it has a positive sign, tracing it back to the potential using L's dependence on r should make the centrifugal potential negative. It is required to be negative so that it falls as you go farther, which is gives rise to the Lagrangian points. Tushar Shrotriya (talk) 11:09, 21 February 2014 (UTC)