The solar wind carries the interplanetary magnetic field toward Earth at speed v. A stronger wind compresses the day-side magnetopause and stretches the night-side magnetotail, both scaled by k = (v−300)/600. The planetary Kp geomagnetic index is approximated as Kp = 2.1 + 6.4k, and the auroral-oval boundary moves equatorward as Kp -> higher latitude coverage: oval colatitude = 72° − 12k°. Charged particles funnel down open field lines near the poles, so the two aurora rings brighten and widen with k while streaming particles cross the bow shock and pile up on the compressed day side.