Venus's Enigmatic Motions:
The Cheshire  Moon Hypothesis

An Unexplained Coincidence

Venus orbits the sun counterclockwise (seen from the sun’s north pole) every 225 days and rotates clockwise on its axis every 243 days. Because of these two motions, a point on Venus’s surface that passes directly beneath the sun does so every 116.75 days.

Venus most closely approaches the Earth every 584 Earth days. This is almost exactly five times 116.75 days, and means that Venus shows almost exactly the same face to Earth at every closest approach.

People have speculated that this synchrony results from gravitational locking between Venus and Earth—but no one has plausibly explained such locking.This is what my hypothesis attempts.


Scientific Background

It might seem preposterous that two such distant objects as Earth and Venus could influence each other, but scientific investigations have shown that entrainment between oscillators takes surprisingly little energy. Entrainment or synchronization was first described between pendulum clocks by Christian Huygens, and has since been described in many other systems, both physical and biological.

Planetary orbits and rotations are periodic oscillators, potentially entrainable by gravity’s transfer of energy between them. Because gravitational attraction between two objects decreases as the square of their distance, attraction between two planets seems likely to synchronize their closest approach.

Presumably, even very small exchanges of energy can synchronize two oscillators if enough time is allowed. If the Earth and Venus are each 5 billion years old, and remain in roughly their original orbits, they have passed each other more than 3 billion times. Two pendulums whose movements coincided every three seconds would take 297 years to coincide that many times. By comparison, the juxtaposed pendulum clocks described by Huygens always achieved synchrony within 30 minutes.

The suspicion that planetary orbits might sometimes become entrained is
confirmed by bodies in our solar system. As one example, Neptune and Pluto are in a 3:2 orbital resonance with each other. In the time that it takes Neptune to orbit the sun 3 times, Pluto goes around twice.

A second example of orbital synchrony involves Jupiter’s moons Ganymede, Europa, and Io. For every orbit of Ganymede, Europa orbits Jupiter twice and Io orbits Jupiter 4 times.

A third example involves Earth and Venus, in an orbital synchrony entirely different from the one described above. Venus orbits the sun more frequently than does Earth and, as mentioned above, passes the Earth every 584 days. It takes exactly 8 revolutions around the sun for Venus to pass the Earth 5 times.

These observations suggest that Venus and Earth might influence each others' orbits. But, how could Earth’s
orbit influence Venus’s rotation?


Suggestion 1: Venus once had a large moon whose orbit coincided with Venus’s rotation. This large moon provided a “handle” for the Earth to influence Venus’s rotation.

Venus’s rotation is puzzling in several ways. First, why is its rotation synchronized with Venus’s closest approach to Earth? Second, why is its rotation clockwise while its orbit is counterclockwise? Third, since Venus and Earth have nearly the same mass, how might Earth have affected Venus’s rotation, while Venus has had no such effect on Earth?

All of these oddities could be explained if Venus once had a large moon whose orbit coincided with Venus’s rotation. This essay will be clearer if I name this hypothetical moon. For reasons given below, I call it
Cheshire.

Cheshire was captured by Venus, and circled Venus is a clockwise orbit (
see Figure 1). Over time, tidal interactions between Cheshire and Venus slowed Venus’s natural counterclockwise rotation—eventually turning it into a clockwise rotation.

Two massive bodies orbiting each other exchange energy through
tidal interactions. Their rotations and orbits approach synchrony, a state where they always show the same face to each other. The larger a body is, the faster its orbit and the rotational speed of its partner converge.

As an example, the Earth and Luna (our moon) orbit a point 1100 miles beneath the Earth’s surface. The smaller body, Luna, now rotates at a speed equal to its orbit around the Earth, and hence always shows the same face to Earth. By contrast, although the Earth’s rotation has been slowed by interaction with Luna, the Earth still rotates much faster than Luna orbits around us.

If Cheshire could slow and then reverse Venus’s rotation, Cheshire must have been quite large. I suggest that Cheshire provided a “handle” that enabled Earth’s gravity to influence Venus’s rotation, while Venus had no such influence on the Earth.

I imagine that Cheshire behaved the way a magnet clinging to the surface of a smooth metallic sphere would behave. It could move relative to Venus’s surface, but was inclined not to.


Suggestion 2: The large moon was slowed by a trip around the sun, which allowed it to be captured by Venus.

I suggest (see below) that Cheshire originated in the Solar System’s outer reaches. So, how was Cheshire captured? A body that falls into a planet’s gravitational field acquires enough momentum to take it back out again. An object falling in from the outer solar system would have enormous momentum. What slowed it down, so that Venus could capture it?

The only thing I can think of is a trip around the sun (see Figure 1). The slowing was either by friction as Cheshire passed through the sun’s outer layers, or by tidal effects or both. Although I have drawn Figure 1 to show capture of Cheshire after only a single pass around the sun, multiple passes around the sun before capture are more likely.

I suppose that tidal effects are the
deus ex machina of orbital mechanics, the standard way of widening the constraints on nearly any theory enough to make the theory plausible. However, conversion of momentum to heat and mechanical strain by tidal effects DOES happen. Jupiter’s moon Io is bursting with volcanoes caused by tidal effects.


Suggestion 3: The large moon was made of volatile material. It persisted for ages, but eventually evaporated and disintegrated.

Venus has no moon. If Cheshire once existed, where did it go?

Tidal forces might cause a moon to
spiral into a planet’s surface, but a big moon in a large surface-stationary orbit would not do that. It would orbit Venus forever, unless something knocked it out of the sky—in which case, it would leave a huge ring of orbiting debris. Venus has no such ring of debris.

I suggest that Cheshire was composed of substances that are volatile at room temperature and standard atmospheric pressure. Cheshire originated from the material that orbits the sun out beyond Pluto, and which provides us with an occasional comet. Parts of this huge band of material are called the Oort Cloud, the Hills Cloud, the Kuiper Belt, and the Scattered Disk… Anyhow, there seems to be quite a lot of material out there—perhaps more than contained in the known planets. There is more than enough to provide Venus with a Mars-sized moon. Cheshire, my imaginary moon, was essentially a hyper-humongous comet.

So, what happened to Cheshire? Most astronomers assume that a body of cometary material trapped near the sun would heat up and vaporize within just a few years. But, I argue that a large body of such material might be stable for a long time, with most of the internal material remaining solid even at high temperature.

Under high pressure and increasing temperature, the methane and ammonia of Cheshire’s core might have formed more complex organic molecules. This would have liberated hydrogen gas, which might slowly have made its way to Cheshire’s surface.

Cheshire had no metallic core and hence no self-generated magnetic field to shield it from the solar wind. Unless Venus had a magnetic field large enough to shield Cheshire (Venus has no magnetic field now), the solar wind (which was probably stronger then than it is now) carried away hydrogen that evaporated from the surface. The surface of Cheshire, and eventually deeper layers as well, became hydrogen-depleted. Evaporation of hydrogen, while it lasted, may have cooled Cheshire’s surface.

Ultraviolet radiation from the sun might have acted on the methane and ammonia of Cheshire’s outer layers to produce a tarry goo. If this material remained near Cheshire’s surface, it might have retarded the escape of hydrogen.

As hydrogen escaped, and water decomposed, free oxygen—destroyer of all things organic—would also have built up. The oxygen would likely have degraded the tarry outer layer, forming carbon dioxide and liberating a lot of heat. This might have happened slowly, but it is more fun to imagine huge fires raging across Cheshire’s surface.

As Cheshire lost mass, its gravity decreased, and the rate of mass loss increased. Eventually, Cheshire came apart (see Suggestion 4, below).

Cheshire's properties would have differed from those of other bodies in the inner solar system. First, Venus's gravity would have raised enormous tides on Cheshire, affecting tidal locking between the two. Second, as mentioned above, the steady evaporation of hydrogen and other gases from Cheshire might have cooled its surface. Third, the steady loss of mass from Cheshire, coupled with ongoing Venus-Cheshire-Earth gravitational interactions might have caused Cheshire to fade into an object large enough to
maintain locking between Venus's rotation and Earth's orbit, but too small to have promoted it ab initio.

Like the Cheshire Cat of Alice in Wonderland, which faded slowly into invisibility until nothing was left but the smile, the
Cheshire Moon faded away until nothing was left except Venus's characteristic rotational momentum.


Suggestion 4: Most of the moon’s material escaped into interplanetary space. A small amount fell to Venus’s surface, melting the surface and slightly increasing Venus’s clockwise rotation.

Most of Cheshire’s material somehow escaped into interplanetary space, taking with it most of Cheshire’s angular momentum. A small part fell to Venus’s surface, increasing Venus’s retrograde rotation slightly, the way that a twirling ice skater increases her speed by pulling in her arms. This spoiled Venus’s perfect rotational synchrony with Earth’s orbit. (Venus actually rotates a tiny bit too fast to show exactly the same face to the Earth at every closest approach.)

If even a small part of a gaseous body the size of Mars fell onto a planet, it would enormously thicken the atmosphere and melt the planet’s surface. In fact, Venus has an enormously thick atmosphere, and some unexplained heat source probably melted Venus’s surface some 800 million years ago.

If Venus’s present atmosphere consists mainly of material from Cheshire, then the atmosphere’s elemental composition should match the elemental composition of comets. Venus’s atmosphere is much richer in carbon dioxide (96.5%) than in nitrogen (3.5%). Whether this is consistent with comet compositions is not yet known.

If Cheshire really existed, remnants of it might still orbit Venus. Diamonds and other solid materials too large to be pushed out of orbit by the sun's radiation pressure might be present.


Afterword        

So that’s my theory. It explains (1) Venus’s retrograde rotation, (2) Venus’s rotational synchrony with Earth’s orbit, and (3) the melting of Venus’s surface hundreds of millions of years ago.

Did I mention that nominations for this year's Ig Nobel prize in Astronomy—
Most Farfetched Theory By A Rank Amateur—are still open. Oh, wait… there is no Ig Nobel Prize for Astronomy. Too bad.


Bibliography

Grinspoon, David Harry   (1997) Venus Revealed: A New Look Below the Clouds of Our Mysterious Twin Planet.  New York: Addison-Wesleygy

Earth and its sister planet Venus dance an intricate orbital tango. Venus, in particular, seems to have been strongly influenced by the Earth. Here is my explanation.