Young Venus could have sent a hypothetical moon racing outward before gradually catching up with it as the planet lost its spin. As Venus slowed, its synchronous orbit expanded until, in some cases, it overtook the moon and reversed its migration, sending the satellite inward toward destruction. The outcome depended strongly on how fast Venus was initially rotating, how massive the moon was, and how the planet’s interior dissipated tidal energy.
Venus and Earth are similar in mass and radius, but their satellite systems are dramatically different. Earth has a large Moon that has migrated outward over billions of years. Venus has no natural satellite and now rotates retrograde once every 243 days.
The absence of a Venusian moon has several possible explanations. Venus may never have formed one. A giant impact may have created a moon that was later destroyed by tidal evolution. Or a later impact could have stripped a moon away.
The study by Stephen R. Kane, Franck Selsis, Jérémy Leconte and Sean N. Raymond examined the second possibility: if a moon had formed around Venus, under what conditions could it have survived?
Rather than model one particular formation event, the researchers constructed a semianalytical model of the coupled evolution of Venus’s rotation and a hypothetical prograde satellite. They varied the planet’s initial spin period, the moon’s mass, its starting distance from Venus, its orbital eccentricity and Venus’s tidal quality factor. The calculations were performed using two different descriptions of tidal dissipation, known as the constant-Q and constant-time-lag models.
The calculations covered initial Venus spin periods from 5 to 100 hours and satellite masses from 0.01 to 10 times the mass of Earth’s Moon. The standard starting distance was five Venus radii, with additional cases ranging from 3.5 to 25 Venus radii. Venus’s tidal quality factor was varied from 10 to 100, while eccentricity was explored from zero to 0.5.
The equations were integrated with a fourth-order Runge-Kutta scheme using adaptive time steps. The calculations ended if the moon crossed Venus’s Roche limit, moved beyond the critical stable-orbit radius, or survived for 4.5 billion years. The model was also checked against the present Earth-Moon system. Using Earth’s measured tidal parameters, the calculation reproduced the observed lunar recession rate to within 3% and the observed increase in Earth’s length of day to within 11%.
The critical race between the moon and Venus
The central process is a competition between two changing distances.
A moon orbiting outside Venus’s synchronous radius tends to move outward because tidal interactions transfer angular momentum from the planet’s rotation to the satellite’s orbit. As Venus loses rotational angular momentum, however, its synchronous radius moves outward as well.
The researchers found that these two processes do not scale in the same way with moon mass. The outward migration rate increases roughly in proportion to the moon’s mass, while the expansion of the synchronous radius caused by Venus’s despinning scales with the square of that mass. A sufficiently massive moon can therefore slow Venus down so efficiently that the synchronous radius catches up with the moon.
Once that happens in the constant-Q model, the direction of tidal migration reverses. The moon begins moving inward instead of outward and can eventually cross Venus’s Roche limit, where tidal forces destroy it.
This produces a sharp boundary between long-term survival and destruction. The boundary shifts with both the initial spin of Venus and the mass of the satellite.
For a one-Moon-mass satellite beginning five Venus radii away, the difference can be substantial. With an initial Venus spin period of 8 or 12 hours, the satellite survives the full 4.5-billion-year calculation in the constant-Q model. With a 15-hour initial spin, the same satellite is destroyed after about 0.97 billion years. A 24-hour initial spin places the moon inside the synchronous radius from the beginning, leading to Roche-limit destruction in roughly 1 million years.
The effect is also visible when the starting orbital distance is changed. For a one-Moon-mass satellite and a 12-hour initial spin, moons beginning at 5, 8 and 12 Venus radii all survive for 4.5 billion years, although they reach different maximum distances. Moons starting closer to Venus experience stronger tidal torques and therefore migrate outward more rapidly.
A narrow survival region emerges
The broader parameter survey shows why simply asking whether Venus could once have had a moon does not have a single answer.
At the fiducial tidal quality factor of 50, satellites with masses of roughly one Moon or less can survive for 4.5 billion years when Venus begins with a sufficiently rapid rotation. More massive satellites become progressively harder to retain in the constant-Q calculations.
Satellites of about two Moon masses or more can be destroyed through synchronous reversal on timescales ranging from about 30 million years to 1.7 billion years, depending on their mass and Venus’s initial spin. If Venus begins with a spin period longer than the critical value at which the moon starts inside the synchronous radius, destruction occurs within roughly 1 million years regardless of satellite mass.
The assumed tidal quality factor changes the timing but not the basic structure of the result. Increasing Venus’s quality factor from 50 to 100 roughly doubles the calculated lifetimes and shifts the survival boundary toward more massive moons. Reducing it to 10 shortens the lifetimes and moves destruction toward lower satellite masses.
The researchers also found that the moon itself would dominate Venus’s despinning in these calculations. Its tidal torque on Venus is about 3 million times stronger than the solar tidal torque. That makes the satellite, rather than the Sun, the principal agent controlling Venus’s spin evolution in the modeled Venus-moon system.
This behavior differs from the Earth-Moon system. In a comparison beginning with a five-hour planetary spin and a satellite at 3.5 planetary radii, Earth’s Moon continues moving outward over 4.5 billion years and reaches about 60 Earth radii. In the analogous Venus calculation, the moon also initially moves outward, but Venus’s synchronous radius expands much more rapidly and progressively approaches the moon’s orbit. For the one-Moon-mass case, the synchronous radius reaches about half the moon’s orbital distance after 4.5 billion years, compared with about 15% in the Earth calculation.
The tidal model changes the fate of massive moons
One of the study’s most important qualifications is that the answer changes depending on how Venus’s tidal response is modeled.
The constant-Q model assumes that tidal dissipation is independent of the frequency of the tidal forcing. The constant-time-lag, or CTL, model instead makes the tidal torque vary with the difference between Venus’s spin rate and the moon’s orbital rate.
That distinction becomes especially important near synchronization.
For a one-Moon-mass satellite at an initial spin of eight hours, both models predict long-term survival. But for a two-Moon-mass satellite under the same initial conditions, they diverge sharply. The constant-Q calculation produces Roche-limit destruction after about 1.7 billion years, while the CTL calculation allows the moon to approach a quasi-synchronous state and survive for the age of the solar system.
For a five-Moon-mass satellite, the constant-Q model produces destruction within about 100 million years across the modeled spin periods, whereas the CTL model can still produce quasi-synchronous equilibrium for sufficiently rapid initial rotation.
The authors caution that neither tidal prescription fully captures the rheology of a rocky planet. Real planetary interiors are expected to have more complicated, frequency-dependent responses. They note that models such as Andrade or Sundberg-Cooper rheologies could produce behavior between the two limiting cases explored here.
There is also a numerical qualification specific to the constant-Q calculations. Because the constant-Q torque changes sign discontinuously at synchronization, the calculated lifetimes near the survival boundary can depend on the numerical treatment of that sign reversal. The CTL model changes smoothly through synchronization and therefore gives a more robust treatment near that state.
Eccentricity can destroy a moon that would otherwise survive
The orbit does not have to be circular for the moon to be lost.
The researchers used the full eccentricity-dependent tidal equations to examine initial eccentricities up to 0.5. For a rapidly rotating Venus, tidal interactions can initially increase rather than decrease the moon’s orbital eccentricity.
At small eccentricity, the transition occurs when the ratio between Venus’s spin frequency and the moon’s orbital frequency reaches about 18/11, or 1.636. For a moon beginning five Venus radii from the planet, this corresponds to an initial Venus spin period of roughly 10 hours.
An eight-hour initial spin places the system in this eccentricity-pumping regime. The outcome then depends on satellite mass.
A massive moon, roughly two Moon masses or more, can despin Venus quickly enough to move the system below the eccentricity-pumping threshold before its eccentricity grows substantially. The eccentricity then begins to damp and the moon can survive.
Lower-mass moons behave differently. Satellites of about half a Moon mass or less leave Venus spinning above the threshold for much longer. Their eccentricities can grow, increasing tidal dissipation and accelerating further orbital evolution. In the calculations, these moons can be driven toward the outer stability boundary of Venus’s Hill sphere and lost from the system. This can happen even when their initial eccentricity is only 0.01.
At a 12-hour initial spin, the system begins below the eccentricity-pumping threshold. Moderate eccentricities, up to about 0.3, do not qualitatively change the survival boundary. At still larger eccentricities, enhanced tidal dissipation can instead drive a surviving moon inward toward the Roche limit.
For a 24-hour initial spin, the moon starts inside the synchronous radius, so the outcome is rapid Roche-limit destruction regardless of its initial eccentricity.
Taken together, the calculations place a one-Moon-mass satellite in a particularly restricted region. The authors find that survival requires an initial Venus spin of approximately 10 to 12 hours when the initial eccentricity is low.
The possible impact history narrows the possibilities
The tidal calculations can then be compared with simulations of giant impacts on Venus, although the authors emphasize that this comparison has important limitations.
The survival calculations require a lunar-mass satellite to form around a rapidly rotating Venus, with an initial spin period of roughly 12 hours or less. Recent impact simulations cited by the authors found that impact scenarios consistent with Venus’s present rotation generally leave the planet spinning more slowly, with postimpact periods of at least about 12 hours.
Those same simulations found that some impact geometries produce debris disks inside the synchronous orbit. Such material would reaccrete onto Venus rather than form a long-lived moon. Other impact geometries can put debris outside the synchronous orbit, where a moon could form, but these cases tend to leave Venus rotating more slowly and therefore put the satellite near the boundary between survival and destruction.
The authors stress that the impact simulations did not systematically explore Venus’s preimpact spin, used a fully differentiated initial Venus, and were primarily designed to reproduce Venus’s present rotation directly rather than through later moon-driven tidal evolution. They therefore treat their spin-period results as indicative rather than definitive.
Within those qualifications, the combined calculations suggest two possible pathways to Venus’s present satellite-free state. The impact that produced Venus could have generated debris that never formed a stable moon, or a moon could have formed and later been destroyed through tidal evolution. The authors conclude that their results do not require a separate later catastrophic stripping event to remove a moon.
A young moon would not necessarily have lasted
The timing matters because the surface of Venus is much younger than the planet itself.
The authors note that Venus has a globally young surface, with a crater-retention age of several hundred million years. If a large moon had been destroyed and its debris had subsequently reaccreted onto Venus, a sufficiently recent event would be expected to leave a detectable surface signature. The study therefore places any such moon-loss event early in Venus’s history, before the most recent major resurfacing interval.
That timing is compatible with the sub-billion-year destruction timescales found for many of the modeled systems, although it does not establish that such a moon actually existed.
If a moon did survive for part of Venus’s early history, the authors note that it could have influenced the planet’s early environment. A satellite of roughly lunar mass could stabilize Venus’s obliquity, while strong tidal interactions could influence rotation and ocean tides. If that moon were eventually destroyed at the Roche limit, the resulting event would also release substantial energy and deliver silicate debris to the planet.
These consequences are discussed as possible implications of an early Venusian moon rather than as demonstrated features of Venus’s actual history.
The model leaves out an important Venusian tide
There is a significant limitation to the calculations: they include gravitational body tides raised by the moon and the Sun but not atmospheric thermal tides.
Solar heating drives atmospheric tides on Venus, and previous work cited by the authors indicates that these tides can contribute significantly to the planet’s spin evolution. Adding that effect would provide an additional torque that accelerates Venus’s despinning and therefore causes the synchronous radius to expand more quickly.
The authors say that including atmospheric tides would shorten the calculated satellite lifetimes and further narrow the region in which a moon could survive. The results presented in the study should therefore be regarded as conservative with respect to this omitted process.
The study also does not treat every possible history of Venus’s formation. Its calculations are specifically calibrated to Venus’s mass, radius and present orbital distance. The authors caution that their numerical results should not be interpreted as a general survey of all Venus-like exoplanets.
They do, however, point to a qualitative extension of the result. Slowly rotating terrestrial planets in the inner parts of planetary systems should have difficulty retaining large satellites because their synchronous radii can lie beyond the region where stable satellites can orbit. For a Venus-like planet receiving comparable stellar illumination while orbiting a 0.3-solar-mass star at 0.1 astronomical units, the study estimates that the critical spin period would be about 10 times shorter than for Venus, making moon survival effectively impossible for plausible postimpact spins.
A possible trace of a lost moon
The authors also identify a potential way to investigate the moon-loss scenario observationally.
If a Venusian moon had spiraled inward and crossed the Roche limit, some of its silicate material would ultimately have been deposited onto Venus’s surface and into its atmosphere. The authors suggest that measurements of noble gases and isotopic ratios could potentially help constrain such a scenario.
They emphasize, however, that identifying such a signal would be difficult because any material from a disrupted moon would have to be distinguished from Venus’s indigenous volatile inventory, later volcanic outgassing and atmospheric escape. They propose detailed mass-balance modeling as a necessary next step for determining whether a disruption signature could be detectable.
The resulting picture is therefore not that Venus simply could or could not have had a moon. Instead, the calculations describe a system in which the fate of a hypothetical moon was highly sensitive to its starting conditions. A rapidly rotating Venus could allow a lunar-mass satellite to move outward and survive for billions of years, while a modestly slower initial rotation or a substantially more massive satellite could cause the synchronous radius to overtake the orbit and ultimately destroy the moon. Orbital eccentricity adds another route to instability, while the assumed tidal rheology can change the fate of massive satellites near synchronization.
The study was published in The Astrophysical Journal.
