Based on helioseismological measurements (1996–2017), the entire Sun shrinks during solar maximum and regrows during the next solar minimum by about a few km (~10−5 effect). Here, we observe, for the first time, that the solar radius variation resembles a 225-day relationship that coincides with Venus’ orbital period. We show that a remote link between planet Venus and Sun’s size must be at work. However, within known realms of physics, this is unexpected. Therefore, we can only speculate about its cause. Notably, the driving idea behind this investigation was some generic as-yet-invisible matter from the dark Universe. In fact, the 11-year solar cycle shows planetary relationships for a number of other observables as well. It has been proposed that the cause must be due to some generic streaming invisible massive matter (IMM). As when a low-speed stream is aligned toward the Sun with an intervening planet, the IMM influx increases temporally due to planetary gravitational focusing, assisted eventually with the free fall of incident slow IMM. A case-specific simulation for Venus’ impact supports the tentative scenario based on this investigation’s driving idea. Importantly, Saturn, combined with the innermost planets Mercury or Venus, unambiguously confirms an underlying planetary correlation with the Sun’s size. The impact of the suspected IMM accumulates with time, slowly triggering the underlying process(es); the associated energy change is massive even though it extends from months to several years. This study shows that the Sun’s size response is as short as half the orbital period of Mercury (44 days) or Venus (112 days). Then, the solar system is the target and the antenna of still unidentified external impact, assuming tentatively from the dark sector. If the generic IMM also has some preferential incidence direction, future long-lasting observations of the Sun’s shape might provide an asymmetry that could be utilized to identify the not isotropic influx of the assumed IMM.