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Big Bang, New Moon

Theoretical and computational simulations at SwRI could soon explain how the Earth came to have its orbiting neighbor.

by Robin Canup, Ph.D.

About 4.45 billion years ago, a young planet Earth -- a mere 50 million years old at the time -- experienced the largest impact event of its history. Another planetary body with roughly the mass of Mars had formed nearby with an orbit that had, by chance, placed it on a collision course with Earth. When young Earth and this rogue body collided, the energy involved was 100 million times larger than the much later event believed to have wiped out the dinosaurs. The early giant collision destroyed the rogue body, likely vaporized the upper layers of Earth's mantle, and ejected large amounts of debris into Earth orbit. From this debris our moon coalesced, possibly on a time scale as short as one to 100 years.

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Dr. Robin Canup, a senior research scientist in the Boulder, Colorado, office of the SwRI Instrumentation and Space Research Division, specializes in models relating to the origin of the Earth-moon system, the formation of terrestrial planets, and the origin of planetary ring and satellite systems. Contact Canup at (303) 546-6856.


This giant impact scenario of lunar formation represents an important piece of our overall understanding of the origin of the terrestrial, or Earth-like, planets in the solar system, which include Mercury, Venus, Earth, and Mars. In turn, understanding the origins of planets in our solar system is the key to determining the likelihood of habitable planets in extrasolar systems.

A research group in the Space Studies Department of the Southwest Research Institute (SwRI) Instrumentation and Space Research Division studies the origins of planetary bodies using both theoretical and computational methods. The group includes the author, Institute Scientist Dr. William Ward, Space Studies Department Director Dr. Alan Stern, Principal Scientist Dr. Harold Levison, Senior Research Scientist Dr. Luke Dones, and Postdoctoral Researcher Dr. Daniel Durda. Recently, research and computational facilities funded by NASA, the National Science Foundation, and SwRI's internal research program have been directed toward developing improved models of an impact-triggered formation of the moon and examining the related implications for the likelihood of similar planet-moon systems around other stars.

Evolving theories of lunar origin

Compared to other moons and their planets, the Earth's moon is unusual in several respects. It is large relative to the Earth, with a density that is abnormally low compared to the terrestrial planets, indicating that it lacks high-density iron. Recent findings even suggest that the moon's core constitutes only 2-4 percent of its total mass, compared to a terrestrial core with about 30 percent of the Earth's mass. The Earth-moon system also has an abnormally large angular momentum per unit of mass, contained in both the Earth's spin and the moon's orbit, compared to other planet-satellite systems.

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SwRI researchers use the smoothed-particle hydrodynamics method and N-body integrations to model the giant impact scenario of lunar formation.


Prior to the 1970s, there were three main theories regarding the origin of the moon. The first involved a fission event, in which the moon broke off from a rapidly spinning Earth. A co-formation theory proposed that the Earth and moon formed contemporaneously as a gravitationally bound pair. The third theory suggested that the moon formed as an independent planetary body that was later "captured" by the Earth during a close pass. Each theory had deficiencies. For example, it was difficult in both the capture and co-formation models to account for the lack of a large lunar iron core, because both predicted that the moon formed from the same mix of materials as the terrestrial planets, which typically contain a more substantial abundance of iron.

One of the main scientific objectives of the Apollo space program was to differentiate between these theories to resolve the question of lunar origin. However, the analysis of lunar samples raised new questions and challenges. Relative to terrestrial samples, lunar material was discovered to be deficient in volatile materials -- those that vaporize and escape easily when heated -- implying that the moon had undergone some intense thermal processing compared to that experienced by the Earth. In addition, the abundance of siderophile, or "iron-liking," elements in lunar rocks suggested that the moon was derived from material that had once been part of the mantle of a larger body with a sizeable iron core.

In 1976 and 1977, two groups* proposed a new theory for lunar origin: the giant impact scenario. The idea was that an off-center impact of a roughly Mars-sized body with early Earth could provide Earth with its high initial spin, needed to explain the current system's angular momentum, and eject enough debris into orbit to form the moon. If the ejected material came primarily from the mantles of the Earth and the impactor, the lack of a sizeable lunar core was easily understood, and the energy of the impact could account for the extra heating of lunar material required by lunar volatile depletions.

For nearly a decade, the giant impact theory was heavily critiqued. The idea that the moon was the result of a particular large impact event was considered too arbitrary, and did not fit in well with the existing view of a quiescent planet formation process. In 1984, a conference devoted to lunar origin prompted critical comparison of the existing theories. The giant impact theory emerged from this conference with nearly consensus support, enhanced by new models of planet formation that suggested large impacts might indeed be common events in the end stages of terrestrial planet formation. Such models demonstrated that the relatively quiescent stage of planetary growth continued only until young planets grew to sizes ranging from lunar to Mars-sized, and that the final stages of growth were characterized by collisions among tens to hundreds of these large, planet-sized bodies. In the course of the many impacts apparently required to yield the final four terrestrial planets, it did not then seem so unreasonable that one of the impacts would be of the type required to yield the moon.


page9.gif (24517 bytes)A time sequence computer simulation (beginning top left) shows a potential moon-forming impact modeled using the smoothed-particle hydrodynamics method. The mantles of the Earth and impactor are represented by red particles that change to orange when heated, while the iron cores are shown with blue particles that change to green with increasing temperature. The initial impact imparts a counterclockwise spin to the Earth, and part of the impacting body temporarily re-coalesces before colliding with the Earth a second time.

After the second hit, material primarily from the impactor's mantle is sheared into a disk of debris; the total amount of iron left in orbit is consistent with the moon's small core. The total time simulated by this run is about a day. Simulations such as this one demonstrated that a Mars-sized body colliding with the Earth with something close to the current Earth-moon system angular momentum could leave roughly a lunar mass worth of material in orbit. (Courtesy Dr. Alastair Cameron, Harvard University)


Modeling the moon-forming impact

Clearly the impact of a Mars-sized body with Earth cannot be reproduced experimentally. For this scale of an event, researchers must rely on computer simulations that can be compared with experimental results at small sizes and then extrapolated to the larger scales of interest with relative confidence. For modeling the moon-forming collision, impact energies of interest are high enough to cause excessive heating and phase changes, and a hydrodynamic treatment with an appropriate equation of state is required. The self-gravity of the material involved in the impact must also be tracked explicitly because of the large total mass and the deformation of the bodies that occurs during an impact. Finally, a simulation must be able to both achieve high spatial resolution at the point of contact between the two planets when they initially collide, and track the dynamics and thermal properties of material ejected into distant orbits.

The method typically used to simulate planet-scale collisions is the smoothed-particle hydrodynamics (SPH) method. Using this technique, the material in a simulation is represented by a finite number (typically 10,000 or so) of discrete, overlapping particles that approximate a continuous distribution of matter. Each particle has a mass, internal energy, and three-dimensional spatial density probability distribution. At a given point in space, the local density of material is then calculated by summing over the contributions from the nearby particles. The evolution of the particles is tracked individually, so that the computational resolution effectively follows the material wherever it goes. At each time-step in the simulation, forces such as pressure and gravity are calculated, and the particles are accelerated accordingly. The equation of state relates pressure to internal energy and density, taking into account such factors as latent heat of phase changes.

An SPH simulation of a potential moon-forming impact requires months of computational time on a single workstation. However, faster simulation speeds and increased resolution with greater numbers of particles are possible through the use of parallel computing. SwRI scientists are currently collaborating with Dr. Erik Asphaug, of the University of California at Santa Cruz, in the development of parallelized SPH methods.

Forming the moon

To model the accumulation of the moon from the impact-ejected debris, SwRI researchers track the interactions between particles as they orbit the Earth. This is typically done by using an N-body integration method, which explicitly calculates the gravitational force on each particle caused by every other particle in the simulation at each time-step. When orbiting particles collide with low enough impact energies, the result is a gravitationally bound aggregate. Such aggregates continue to grow in size as they collide, forming larger and larger bodies in a process called accretion.

Based on this model, the first question to be addressed was, why would a swarm of debris orbiting close to the Earth yield a single large moon when we find systems of multiple moons and rings around the gas giant planets? For a pre-lunar debris swarm, most of the accretion simulations predict the formation of one large moon orbiting at a characteristic distance of about 3-5 Earth radii (12,500-20,000 miles) from the center of the Earth. The moon's current distance is about 60 Earth radii (240,000 miles). However, we know that the tidal interaction between the Earth and moon that gives rise to our twice-daily oceanic tides has also caused the lunar orbit to expand. Thus the moon was much closer to the earth when it formed, appearing more than 10 times larger in the sky than it does today.

Putting it all together: The devil is in the details

While the models of lunar accumulation easily account for why the Earth has only one moon, they also suggest that the accretion process is very inefficient, with always less than half of the initially orbiting debris incorporated into the final moon. This, in turn, means that a more massive initial debris cloud -- one containing at least two times the lunar mass -- must have been produced by the impact to yield a lunar-sized moon. For the past two years, SwRI staff have collaborated with Dr. Alastair Cameron, a professor at Harvard University in Cambridge, Massachusetts, to identify which sizes and velocities of impactors, as well as which impact angles, are capable of producing sufficiently massive debris disks to form the moon.

One class of impacts that characteristically places sufficient amounts of material into orbit involves bodies with three times the mass of Mars and more than twice the current system angular momentum. These impacts yield an Earth with a moon of the correct size, but leave the system spinning too rapidly. From the basic laws of physics, it is known that the angular momentum of the Earth-moon system has been very nearly conserved over the age of the solar system, with a small amount (less than 10 percent) lost to interaction with the sun. Thus, for these extremely high angular momentum impacts, one must invoke some mechanism to significantly slow the Earth's spin after the moon-forming event, such as perhaps a second massive impact.

Another class of possible impacts that could produce an appropriately sized moon yields the correct total angular momentum, but results in an Earth that is only 60 percent of its current mass. This scenario is also problematic: If the Earth continued to accumulate solar-orbiting material in large amounts after the moon was formed, it would have been difficult to prevent the moon from becoming contaminated with iron-rich material imported in such collisions as well. Researchers have thus yet to identify a set of impact conditions that yields the Earth-moon system in the most widely accepted paradigm for lunar origin.

Fortunately for the impact theory, there are still many avenues to explore. SwRI researchers are using an algorithm developed by Levison to conduct the first highly accurate simulations of the final stages of terrestrial planet formation that will explicitly track the dynamics of the largest impact events. To date, results from this work suggest that Earth-like planets could experience several large impact events and that the final masses and angular momentum of the Earth-moon system may be the combined result of more than one impact. Simulations have also shown that Earth probably had a significant spin prior to the moon-forming event, and this could affect the ejecta yield predicted by the SPH simulations that, to date, have assumed Earth was not rotating prior to the impact event.

These results suggest that new regions of parameter space need to be modeled using impact and accretion simulations to develop a consistent, plausible model for the origin of the Earth-moon system. Such research can then be applied to models of the formation of the Pluto-Charon system -- also believed to be the result of an impact event -- as well as to the formation of planets and moons in solar systems around other stars.

Conclusions

As we detect other planetary systems that are quite different from our own, the question that drew many astronomers and planetary scientists into the field even as children arises: Are there other Earths? By learning more about the moon, we become increasingly aware of its interactions with our planet. In particular, we now know that the presence of our large moon acts to stabilize the variation of the Earth's rotational axis, a fact that was first discovered in 1974 by SwRI Institute Scientist Dr. William Ward, who was then at the Harvard Center for Astrophysics. Were it not for the moon, the influence of the giant planets in our system would cause Earth's obliquity -- the angle between the Earth's equator and the plane of its orbit, whose current value is 23.5 degrees -- to vary wildly with values as extreme as 0 to 80 degrees. Such variation would probably cause extreme climatic changes that would render the planet uninhabitable. Thus having a large moon may be one of the key characteristics necessary for a habitable Earth-like planet -- making it all the more important to resolve questions about the origin of our Earth and moon. v

* Dr. William Hartmann and Dr. Don Davis (both of the Planetary Science Institute), and Dr. Alastair Cameron (Harvard University) and Dr. William Ward (currently at SwRI, but then at the Jet Propulsion Laboratory), first proposed the giant impact scenario in 1976 and 1977.

Published in the Spring 1999 issue of Technology Today®, published by Southwest Research Institute. For more information, contact Maria Stothoff.

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