Summary
A numerical study finds that a hypothetical Venusian moon could have been destroyed by tidal evolution, depending on Venus’s early spin, the moon’s mass and the planet’s tidal response.
Venus has no natural satellite today, but a new study finds that a moon formed around the planet could have been lost through tidal evolution alone. The result comes from coupled numerical models of Venus’s rotation and a hypothetical moon’s orbit, rather than from an observation of a former satellite.
The simulations show that the outcome depended mainly on Venus’s initial spin period, the moon’s mass, its starting orbit and the poorly constrained tidal response of Venus’s interior. Under some conditions, the moon would migrate outward and survive for the 4.5-billion-year age of the Solar System. Under others, Venus’s slowing rotation would cause the moon to spiral inward and break apart at the Roche limit.
Contents
How a Venusian moon would evolve
The study models a prograde moon, orbiting in the same direction as Venus’s initial rotation. Tidal forces transfer angular momentum between the planet’s spin and the satellite’s orbit. If Venus rotates faster than the moon orbits, the moon initially moves outward. At the same time, Venus loses spin angular momentum and its synchronous radius expands. This is the orbital distance at which a satellite’s orbital period matches the planet’s rotation period.
A moon that falls inside the synchronous radius migrates inward instead. If it crosses the Roche limit—the distance inside which tidal forces can overcome the satellite’s self-gravity—the moon is expected to be disrupted into debris that can later reaccrete onto Venus.
The researchers surveyed initial Venus spin periods from 5 to 100 hours, moon masses from 0.01 to 10 times the mass of Earth’s Moon, starting distances of 3.5 to 25 Venus radii, tidal quality factors from 10 to 100, and initial orbital eccentricities from zero to 0.5. Most calculations used a starting distance of five Venus radii.
For that orbit, the critical initial spin period is 16.1 hours. A slower-spinning Venus places the moon inside the synchronous radius from the beginning, producing rapid inward migration. In the constant-quality-factor model, such moons reached the Roche limit in less than about 1 million years, regardless of satellite mass.
A narrow survival window
For a circular, lunar-mass satellite, an initial Venus spin period of roughly 12 hours or less allowed survival through the full 4.5-billion-year integration in both tidal models. The moon first moved outward, while Venus spun down, and later approached a long-lived near-synchronous state.
The survival margin became much smaller for more massive moons. In the constant-quality-factor model, satellites of at least about two lunar masses could be destroyed after Venus’s synchronous radius overtook their orbits. Depending on the initial spin and mass, the calculated destruction times ranged from about 0.03 to 1.7 billion years. A five-lunar-mass moon was destroyed within about 100 million years even when Venus initially rotated rapidly.
The assumed tidal model changed some outcomes substantially. The constant-quality-factor model treats dissipation as frequency-independent, while the constant-time-lag model allows the tidal torque to weaken smoothly as the planet and moon approach synchronous rotation. For an initial spin period of eight hours and a two-lunar-mass moon, the first model predicted Roche-limit destruction after about 1.7 billion years; the second predicted long-term quasi-synchronous survival. At a 12-hour initial spin, the corresponding constant-quality-factor destruction time was about 33 million years, while the constant-time-lag model again produced survival.
Orbital eccentricity added another pathway to instability. With an eight-hour initial spin, low-mass moons could have their eccentricity increased by tides and be driven outward toward Venus’s Hill-sphere stability boundary. The calculations found that this could occur even for an initial eccentricity of 0.01. At a 12-hour initial spin, eccentricity was generally damped for moderate starting values, although values above about 0.5 increased tidal dissipation enough to drive destruction.
Why the result matters for Venus
The model offers a way to connect Venus’s present lack of a moon with the planet’s early rotational history. In the study’s calculations, the moon’s tidal torque on Venus was about 3 million times stronger than the solar tidal torque at the starting configuration. The moon itself therefore controlled most of the early spin-orbit evolution.
This creates a feedback process. A more massive moon transfers angular momentum more strongly and can slow Venus faster, expanding the synchronous radius more quickly. Although the moon’s outward migration also accelerates with mass, the expansion of the synchronous radius can overtake it. The resulting balance produces a narrow region in which a moon is both lost and Venus is substantially despun.
The authors conclude that a moon-forming event followed by tidal destruction could account for Venus’s current satellite-free state without requiring a later catastrophic stripping event. The conclusion remains model-dependent. Venus’s tidal dissipation is not directly measured, and the study omits atmospheric thermal tides, which are important to Venus’s present spin and could shorten the calculated satellite lifetimes. The constant-quality-factor and constant-time-lag calculations also represent different idealised descriptions of the planet’s interior; a more realistic frequency-dependent rheology could produce outcomes between them.