The Moon isn't just hanging in the sky: it leaves behind a long tail of disturbed solar wind. The stream of charged particles from the Sun flows around the rocky sphere, and behind it forms a zone where particles are almost absent. But this emptiness is not simple: electric fields arise in it that push apart the remaining electrons and ions. Measuring these fields directly is difficult, so scientists took a roundabout path.

Usually, particles in a plasma are distributed smoothly by speed, like a crowd on an escalator. But in the lunar shadow, the picture breaks down: on the sunward side, electrons fly faster; on the shadow side, slower; and in the very center, groups of particles with the same energy appear, as if stuck on a step. The new method, called Hamiltonian inversion, uses this stepped structure. It reconstructs the shape of the electric field from how exactly the electrons have grouped by energy.

The method was tested on a computer simulation of the lunar shadow at two moments in time: right after formation, when asymmetry is strong but shock waves haven't yet appeared, and later, when ion-acoustic waves are already raging in the center. Then it was applied to real data from the ARTEMIS spacecraft, which flew through the Moon's shadow. It turned out that the electric potential drop in the shadow reaches fifteen units of electron thermal energy: that's like a voltage change of tens of volts over a path of several kilometers. In the regular solar wind, such drops are many times smaller.

The Moon's shadow turned out to be not just an empty bag, but a living electric structure. Where streams of particles collide, sharp potential jumps are born, like waves running along a taut string. The method devised for the Moon will also work for other bodies without atmospheres: asteroids, planetary moons, even artificial probes. Wherever electrons are trapped by an electric field, its shape can be reconstructed from their motion.