Magnetic connectivity between a Mars orbiter and Jupiter under Parker-spiral IMF geometry. (a) Example heliocentric configuration showing the Parker spiral connecting Jupiter to a highly elliptical Mars orbit, with connected epochs indicated along the spacecraft trajectory. (b) Mean per-orbit connectivity duty cycle as a function of the RAAN for three solar-wind speeds (350, 450, and 550 km s⁻¹). Two symmetric connectivity windows separated by approximately 180° are observed. (c) Dependence of the optimal RAAN and peak connectivity duty cycle on solar-wind speed, illustrating the systematic shift and broadening of connectivity windows as the Parker-spiral geometry varies.