Simulating Moons Around Terrestrial Planets

by Paul Gilster on May 31, 2011

Just how the Moon originally formed is under renewed scrutiny given the finding that it contains larger amounts of water than previously thought. We’ll look at that issue in depth another time, because it’s far from resolved. The generally accepted account of the Moon’s formation involves a giant impact with a planetary embryo that has been called Theia. The name is a nod to the Greek story of the titan that gave birth to Selene, the Moon goddess. After its formation, the Moon would have been closer to a much more quickly rotating Earth, inducing huge tidal forces that may have had repercussions on the evolution of the earliest life on the planet.

All of this has a further bearing on life’s emergence because a large moon can affect the tilt of a planet’s rotation relative to its orbit around the star. The term for this degree of tilt is ‘obliquity,’ and its effects on global climate can be profound. If there is little or no tilt, the poles become colder and heat flows in their direction. Increasing the obliquity means that the poles get more sunlight during half of the year while the equatorial regions cool twice a year. The influence on climate is inescapable, as is the fact that obliquity will be unique for each planetary situation.

A new paper by Sebastian Elser (University of Zurich) looks at this issue in terms of the Earth’s history and the probability of giant impacts among planets in general. What we know now is that the Earth’s tilt varies about 1.3 degrees around the figure of 23.3 degrees, with a period of roughly 41,000 years. Elser and team note that without the Moon, the Earth’s obliquity would experience large variations. Venus, which has no moon, shows a retrograde spin, which the Elser paper finds may have been induced by spin-orbit resonances and tidal effects.

Obliquity can vary enormously with time. The tilt of Mars’ rotation ranges from 0 to 60 degrees in less than 50 million years, and earlier work has indicated that the obliquity of an Earth without its Moon would range from 0 to as much as 85 degrees (complete references on these numbers can be found in the paper, cited below). Large moons, then, may be a major player in keeping climatic conditions stable. The Elser paper explores the impact history of planets to see how many would be likely to have a companion like the Moon, using simulations of planets forming in the habitable zone. The history and evolution of such Moons is then modeled.

The results show that large moons are not unlikely:

Under these restrictive conditions we identify 88 moon forming events in 64 simulations… On average, every simulation gives three terrestrial planets with different masses and orbital characteristics and we have roughly 180 planets in total. Hence, almost one in two planets has an obliquity stabilizing satellite in its orbit. If we focus on Earth-Moon like systems, where we have a massive planet with a final mass larger than half of an Earth mass and a satellite larger than half a Lunar mass, we identify 15 moon forming collisions. Therefore, 1 in 12 terrestrial planets is hosting a massive moon.

Assuming, then, that an Earth-class planet forms in the habitable zone around another star, the chances of its being orbited by a moon large enough to stabilize its orbital tilt is roughly 10 percent. The simulations used here, based on 2010 work by Ryuji Morishima (Swiss Federal Institute of Technology) and colleagues, produce numerous habitable ‘Earths,’ so the question of the importance of the Moon’s stabilizing influence becomes significant. We also have to untangle the issue of the water content of lunar magma, called into play by new work by Erik Hauri (Carnegie Institution of Washington). We’re looking at water levels 100 times higher than first supposed, challenging the giant impact theory of the Moon’s formation, which predicted very low lunar water content. Clearly, untangling all this will involve, among other things, sample returns from planets and other bodies that will teach us more about our system’s history.

Hauri speaks to this question himself:

“Water plays a critical role in determining the tectonic behavior of planetary surfaces, the melting point of planetary interiors and the location and eruptive style of planetary volcanoes. I can conceive of no sample type that would be more important to return to Earth than these volcanic glass samples ejected by explosive volcanism, which have been mapped not only on the Moon but throughout the inner solar system.”

The paper on planet/moon simulations is Elser et al., “How common are Earth-Moon planetary systems?” accepted for publication in Icarus (preprint). On the issue of water on the Moon, see Hauri et al., “High Pre-Eruptive Water Contents Preserved in Lunar Melt Inclusions,” published online by Science on 26 May 2011 (abstract). On the Moon’s stabilizing effects in general, see Laskar et al., “Stabilization of the Earth’s Obliquity by the Moon,” Nature 361, 615-617 (1993). Abstract available.

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Adam May 31, 2011 at 16:17

Of course there’s other ways to make a moon. According to Nayakshin’s tidal downsizing cosmogony, the Earth-Moon could have formed as a binary within their common proto-planet envelope, without the angular momentum loss questions of George Darwin’s original binary fission theory.

Alternatively, there’s Malcuit’s suggestion of capture, which is made feasible by massive tidal energy dissipation during the initial encounter. A retro-grade Moon capture by Venus caused eventual merger of the two and the end state we observe today.

Of course anything not forbidden is mandatory in physics, so if the alternatives can happen they’ve happened somewhere in the Galaxy – the vexing question is how to tell which applies in the case of our Moon.

Eric May 31, 2011 at 18:49

I wonder what the odds would be for a double planet, with two bodies of more or less Earth mass orbiting each other. They’d probably be tidally locked, but would be really impressive to see in their respective skies.

I’m sure they’d also be a big motivator for intelligent beings to develop space travel. Interesting thought!

Michael Simmons May 31, 2011 at 20:01

There is a study that indicates that a moon isn’t always require to Stabilize Obliquity
“Obliquity Variations of a Moonless Earth”
http://www.abstractsonline.com/Plan/ViewAbstract.aspx?sKey=4deb0dbb-3eb9-4dde-ba24-65b00b23a616&cKey=6f1002f1-290f-4069-a80f-8353719a5ac8&mKey={E29B4337-1CDD-49F2-9083-C1E105E02454}

A manuscript on this study is being worked on but has yet to be released (email from Lissauer).

But if you combine “Planet Formation: Statistics of spin rates and obliquities of extrasolar planets” http://arxiv.org/abs/1004.1406 with Laskar et al work then you can see that this is possible.

Also realise that other solar systems might not have jupiter size outer planets to affect the inner planets obliquity.

Rob Henry May 31, 2011 at 23:01

If our moon stabilises obliquity and through it climate, and the Snowball Earth episodes really did trigger the Cambrian explosion, wouldn’t the more likely outcome of removing our moon been an earlier onset of animal life.

If the K-T meteorite impact really was needed to tilt evolutionary pressures in favour of smaller fauna that had a more flexible intelligence, couldn’t we have expected that result earlier if we had a much less stable climate.

Does our experience really show that having a large moon advances life, or does the bulk of evidence point the other way, yet we just want intelligent life to need a large moon so as to alleviate the paradox (and because its such a cool idea!).

Frank June 1, 2011 at 8:24

Interesting results. For many years, I’ve read that having a large moon like earth’s would be a rare event and thus adding to the “rare earth” hypothesis.

Alex Tolley June 1, 2011 at 11:56

@Rob Henry,
I think that there is a lot of “just so” thinking about the need for a moon. Just consider the climate issue. We know that biomes reestablish themselves very quickly in geologic terms with the flow of ice ages. Therefore if the planet tilts over millions of years, one can expect those biomes to move with that tilt. Now it may prove difficult for some forms to migrate successfully due to ocean or continent barriers, but that will just bias some forms over others. However we also know that continental drift has moved continents all over the surface of the earth too, a process that mimics obliquity changes, without apparently causing a problem for the evolution of life.
I’d want to see some effect of planetary tilt that would be antithetical to the evolution of life, even as we know it.

kurt9 June 1, 2011 at 12:19

My question is why is it only now that they are finding all of this water in the moon, and the moon rocks. The last moon rocks were brought back on Apollo 17 nearly 40 years ago. Why didn’t they find it then?

Mike June 1, 2011 at 22:04

Could not the Late Heavy Bombardment have re-supplied the Moon with volatiles long after its’ theorized formation from a collision event?

Ronald June 10, 2011 at 7:10

Adding to Adam, Micheal, Rob and Alex, I have also read that the climatic variations on an earthlike planet as a result of moonlessness induced obliquity, even if it occurred, would play out over many millions of years and hence in many cases being slower/smaller than many other climatic changes.

The importance of a (large) moon at least partly seems to be a deterministic or ‘reversed engineering’ thing: it must be very important, because we have one, also typical of the Rare Earth Hype. It is also, not surprisingly, a recurring theme in creationism.

John P Curtin June 12, 2011 at 22:48

At the time of Jupiters migration inward in which it robbed Mars of potential mass it also disturbed a Ceres size object that impacted a Mars size Earth forming the proto Earth -Moon system. Subsequent impacts grew both bodies to their present size, explaining why both have similiar amounts of internal water.

Wondering June 28, 2012 at 16:39

What if we had, say, 3 Moons? What effect would that have on Day Length, on Winds, on Tides? I can’t seem to find stuff that covers what would happen if the moon was larger, or smaller, or more, or fewer….

Paul Gilster June 28, 2012 at 16:56

Neil Comins’ book What If the Earth Had Two Moons may have thoughts on all this, though I haven’t read it yet:

http://www.amazon.com/What-Earth-Had-Moons-Thought-Provoking/dp/0312598920

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