Space is not an empty void but a landscape of invisible gravitational hills, valleys, and ridges. This episode explores Lagrange points, the five spots in any two-body system where gravity and the centrifugal pseudo-force cancel out, first calculated by Leonhard Euler around 1750 and Joseph-Louis Lagrange in 1772. We explain the restricted three-body problem, why an object at L1 can sit closer to the sun than Earth yet keep a one-year orbit, and how L1, L2, and L3 behave like saddle points that require halo orbits and station keeping to stay put.

From there we look at real missions and future plans: DSCOVR watching for coronal mass ejections at Sun-Earth L1, the James Webb Space Telescope hiding behind a single sunshield at L2, why a counter-Earth at L3 is ruled out by Venus's orbit, and the stable L4 and L5 points that trap Jupiter's milli ...