Tidal Demise: The Evolution and Fate of a Hypothetical Venus Moon

Abstract

Venus possesses no natural satellite, raising the question whether a formed moon could have survived. We explore the tidal evolution of a Venus-moon system, coupling Venus's spin to the satellite's orbit under tides from the moon and Sun. We survey spin period ($P_0 = 5$--100~hr), moon mass ($M_m = 0.01$--$10~M_{\rm Moon}$), eccentricity, quality factor, and initial semi-major axis under both constant-$Q$ and constant time lag models. Survival depends on competition between outward migration ($\propto M_m$) and synchronous radius expansion ($\propto M_m^2$): for circular orbits around rapidly spinning Venus ($P_0 \lesssim 12$~hr), a lunar-mass satellite survives the age of the Solar System in both models. For $P_0 \lesssim 10$~hr, eccentricity pumping can destabilize low-mass satellites, while for $P_0 \gtrsim 15$~hr or $M_m \gtrsim 2~M_{\rm Moon}$ the synchronous radius overtakes the orbit and drives Roche destruction within $\sim$0.03--1.7~Gyr in the constant-$Q$ model. The constant time lag model instead permits quasi-synchronous survival for massive moons at fast spin. Explaining Venus's present state requires satisfying two constraints simultaneously: loss of the satellite and despinning of an initially rapid rotator. Both are met only within a restricted region of parameter space, favoring moderate post-impact spin periods and lunar-to-super-lunar masses. Giant impact simulations predict spin periods $\gtrsim$12~hr for Venus's present rotation, placing a lunar-mass satellite at the survival boundary. For last-impact conditions within this region, the present absence of a Venusian satellite arises through tidal evolution alone; a subsequent catastrophic stripping event, while capable of removing a moon, is not required.