Nearest-point distanceJacobi deviation
THE PHYSICS
Five balances in a rotating system.
In the frame rotating with the two massive bodies, gravity, centrifugal effects and Coriolis acceleration create five equilibrium locations. L1–L3 are unstable; L4 and L5 can support bounded motion when the mass ratio is small enough.
C = 2Ω(x,y) − (ẋ² + ẏ²)Jacobi constant in the ideal model
These collinear points are dynamically unstable. Real missions nearby follow halo or Lissajous-like orbits and require station-keeping.
Located 60° ahead and behind the secondary body, these triangular regions can be stable and host Trojan populations.
JWST operates near Sun–Earth L2, while solar observatories use the L1 region. Neither location is a place where a craft simply remains motionless forever.