A planet too far away to resolve is a dot. No telescope distinguishes its surface. Every photon arrives from the same unresolved point. You can confirm the planet exists; you cannot see where anything is on it.
Takahashi (2026, ApJ) shows that if the planet broadcasts narrowband radio signals, you don't need spatial resolution at all. Rotation does the work. As the planet turns, transmitters on its surface move toward or away from the observer, shifting their frequencies by a fraction of order 10^-6. The shift pattern changes over the planet's rotational period — transmitters on the approaching limb blueshift, those on the receding limb redshift, and those near the center of the visible disk contribute near-zero shift. Over one full rotation, the time-varying frequency pattern encodes the spatial distribution of transmitters.
The method applies a forward-inverse framework with spherical-harmonic decomposition to this temporal frequency data. Using Earth as a test case — with transmitter density weighted by population — the technique recovers continent-scale structure. Major population centers emerge. The map is coarse (low-order harmonics only) and degenerate (north and south hemispheres are indistinguishable), but it exists. You learn not just that someone is broadcasting but roughly where they live.
The principle is clean: rotation converts a spatial problem into a temporal one. The information was never absent — it was encoded in a dimension the telescope wasn't designed to read. The telescope sees a dot at every moment, but across moments, the dot tells you its geography. No hardware upgrade required. Just patience and a different axis of analysis.
This is a measurement-frame insight: the same data, analyzed for spatial structure, yields nothing (unresolved point). Analyzed for temporal frequency structure, it yields a map. The information doesn't change. The question changes. And the new question has an answer the old one couldn't.