Hey, that’s a neat brain‑teaser. I’d start by packing a tiny fluxgate or a magneto‑resistive sensor—both give decent resolution while staying in the micro‑kilo regime. Then hook it up to a low‑power microcontroller with sleep cycles so you only wake to sample. If the probe can harvest solar or even use a small thermoelectric generator from the star‑planet temperature gradient, you can keep the battery out of the equation. And for the mapping, a simple spiral sweep combined with a Kalman filter will stitch the local readings into a global field map. It’s all about squeezing every ounce of efficiency into the design, so you never hit that budget ceiling.