Equilibrium in a rotating configuration
In the Sun–Earth system, a small object at an equilibrium position can move with Earth’s angular rate and preserve the relative configuration. Combined gravity supplies the required centripetal acceleration, rather than necessarily vanishing.
Stationary consequently refers to the rotating frame. In an inertial description the object still moves under gravity; these are not permanently fixed coordinates in space.
Three collinear and two triangular points
L1, L2 and L3 lie on the line through the primary bodies. For Sun–Earth, L1 lies between them, L2 beyond Earth away from the Sun and L3 beyond the Sun; L4 and L5 complete equilateral configurations ahead and behind.
The three collinear Sun–Earth points are unstable and nearby spacecraft require corrections. Small motions around L4 and L5 can be stable when the mass ratio meets the relevant condition; stability is not unconditional for every pair and perturbation.
Webb orbits near L2 rather than occupying a pin
Webb operates near Sun–Earth L2, roughly 1.5 million kilometers from Earth. While orbiting the Sun, it follows a roughly six-month orbit around the L2 neighborhood instead of continuously occupying the mathematical equilibrium point.
This geometry keeps the Sun, Earth and Moon broadly on the sunshield side and avoids their shadows, supporting power and thermal conditions. The choice concerns dynamics, shielding and communication rather than an absence of gravity.
References: [2]