Lagrange PointsSpin your frame with two orbiting bodies and gravity plus centrifugal force combine into a landscape of hills and valleys. Five spots are perfectly level — a spacecraft parked there just co-orbits forever. L4 and L5, sixty degrees ahead and behind, sit in broad basins that trap dust and asteroids (the Trojans). The glowing curve is the edge of where a drifting particle of a given energy can go.In the rotating frame the motion conserves one number, the Jacobi constant. Setting speed to zero gives 2Ω(x,y) = C, the boundary you can't cross; as C drops, gateways open at L1, then L2, then L3 — the maths behind cheap interplanetary transfers.