By J. Richard Gott
The standard theory for the origin of the Moon is that a Mars-sized planet (named Theia) collided with the Earth about 4.5 billion years ago, and that the splash debris formed the Moon. This theory can explain why the Earth and Moon have identical oxygen isotope abundances (as discovered by the Apollo astronauts) while being so different in iron. The Earth is about 30% iron by weight while the Moon is about 3%. Collision simulations by Robin Canup show that Theia must have hit the Earth when it was about 95% formed. Thus there had been time for the iron in both Earth and Theia to sink to form iron cores. The Canup simulations show that the splash material that formed the Moon comes from mostly Theia mantle material poor in iron. But there is a remaining mystery. Why are the oxygen isotope abundances in the Earth and Moon identical That makes it look like they came from exactly the same position in the solar system, 1 Astronomical Unit (1 AU) away from the Sun. Mars, which is farther away, has quite different oxygen isotope abundance ratios. As the Earth grew by gravitational accretion of planetesimals we would expect it to have gobbled up material near 1 AU first, and the last thing to fall in, like a fully formed Theia, would seem likely to have come from halfway between us and Mars (or halfway between us and Venus). But that scenario would give Theia quite different oxygen isotope abundance ratios. Also the collision dynamics required to form the Moon require Theia to fall in at very low velocity, not from a very eccentric orbit. Is there any place to form Theia at 1 AU from the Sun where it would not be swept up by the Earth early-on before it had had time to grow.
Ed Belbruno and I wrote a paper saying there was such a place for Theia to originate, namely, either of the stable Lagrange points L4 or L5 in Earth’s orbit situated either 60 degrees ahead or behind the Earth as it circles the Sun. Debris can accumulate in stable orbits at such Lagrange points. Numerous Trojan asteroids are located at L4 and L5 in Jupiter’s orbit. Belbruno and I proposed that Theia formed out of debris at either L4 or L5 in Earth orbit.
The Lagrange points in Earth’s orbit. L1, L2, and L3 are unstable equilibria. Objects can be placed there (like the WMAP satellite at L2, or the SOHO satellite at L1) but will eventually drift away. L4 and L5 by contrast are stable. Objects can circulate around L4 or L5 and remain stable indefinitely. Belbruno and Gott propose that the giant impactor Theia originated from debris at either L4 or L5. Gravitational perturbations by other planetesimals then sent Theia onto a horseshoe orbit that circulated through L5, L3, L4, and back again. Finally it was perturbed onto a chaotic circulating orbit that sent it on a collision course with Earth.
Theia would remain stable there and could grow large. It would have the same oxygen isotope abundances as Earth because it was accreting material from exactly the same regions as Earth. Eventually, we argued, perturbations by other remaining planetesimals knocked Theia out of L4 or L5 into an oscillating tadpole orbit, and then onto a horseshoe orbit that made close approaches to Earth. Finally, we showed how it would be kicked out onto a chaotic, circulating orbit with a high probability of colliding with Earth, giving just the sort of low velocity collision that would be likely to form the Moon!
We found other examples of this phenomenon occurring in the solar system, which we pointed out in our 2005 Astronomical Journal paper. Saturn’s Moon Tethys is accompanied by two Trojan moons in its orbit: Telesto (leading) and Calypso (trailing), while Saturn’s moon Dione is also accompanied by two Trojan moons: Helene (leading) and Polydeuces (trailing). Saturn’s moon Janus has a moon Epimetheus co-orbiting with it in a horseshoe orbit, exactly like the horseshoe orbit that Belbruno and I had calculated for Theia to have been perturbed onto before its ultimate collision with Earth. This analysis led us to a new theory for the origin of Saturn’s rings. The standard theory was that Saturn’s rings were formed when an errant moon of Saturn’s wandered inside the Roche limit where tidal forces from Saturn ripped it apart and formed the rings. But all the icy moons of Saturn out to Titan are in nice well-behaved circular orbits. We argue that Saturn’s rings (made of icy particles) were originally much larger, and that outside the Roche limit, gravitational accretion was able to form icy moons out of the ring debris. Inside the Roche limit, tidal forces simply prevent the formation of large moons and we are left with the rings. This implies that the rings are old, consistent with recent Cassini satellite data.
Belbruno and I pointed out that asteroid 2002AA29 follows a horseshoe orbit with respect to the Earth that looks just like the ones we found for objects that have escaped from L4 or L5. Perhaps it was part of some primordial debris that originated at the other stable Lagrange point that Theia did not occupy. In that case it would be expected to have the same amount of iron as Earth and the same oxygen isotope abundances as Earth, having formed also at 1 AU from the Sun. That could be tested in a future space mission. I reasoned that if there are asteroids out there with this primordial composition, there should be meteorites with this composition as well. I have found that the EH (Enstatite chondrite) meteorites have about the same iron content as the Earth and have identical oxygen isotope abundances. So it would be interesting to see if asteroid 2002AA29 has a spectrum that resembles EH meteorites. If it did, that would support our theory. Independently, M. Javoy has proposed that the Earth formed out of EH (Enstatite chondrite) material, so such an observation would support his theory as well.
People sometimes wonder if the Apollo missions to the Moon discovered anything important. They did. The oxygen isotope data they brought back led astronomers to our current theory for the origin of the Moon as formed by a giant impact from a Mars-sized object we now call Theia. If the Apollo program allowed astronomers to figure out how the Moon was formed, what greater scientific accomplishment could one hope for! Those same oxygen isotope abundance data also point toward an origin for Theia at 1 AU and, therefore, to an origin at one of Earth’s Lagrange points. Theia would have appeared in the early Earth’s sky as either a morning or evening star stationed 60 degrees away from the sun. Then, perturbed by other planetesimals, it would have started to move, eventually looming large.
Belbruno, E.; Gott, J. R. Where did the Moon come from Astronomical Journal, Vol. 129, pp. 1724-1745 (2005). http://arxiv.org/abs/astro-ph/0405372
Canup, R., Simulations of late lunar-forming impact, Icarus, Vol. 168, pp. 433-456 (2004).
Chown, Marcus. The planet that stalked the Earth. New Scientist, August 14, 2004, pp. 26-30. http://www.newscientist.com/article/mg18324605.200-the-planet-that-stalked-the-earth.html
Gott, J. R. Lagrange L4/L5 Points and the Origin of Our Moon and Saturn’s Moons and Rings. Annals of the New York Academy of Sciences, Vol. 1065, New Trends in Astrodynamics, pp. 325-335 (2005).
Javoy, M. The integral enstatite chondrite model of the earth. Geophysical Research Letters, Vol. 22, pp. 2219-2222 (1995).
Vanderbei, R. J. Horsing Around on Saturn. In New Trends in Astrodynamics and Applications, Vol.1065, pp. 336-345. NY Academy of Sciences, 2005.
More information about J. Richard Gott’s new book is available at http://sizinguptheuniverse.com
By J. Richard Gott
J. Richard Gott is Professor of Astrophysics at Princeton University where he received his doctorate. He is known for his work in cosmology and General Relativity. He and his work have been profiled in Time, Newsweek, The New Yorker, National Geographic, and the New York Times. In 1991 he discovered an exact solution to Einstein’s equations for the geometry around two moving cosmic strings, a solution of particular interest because it allows time travel to the past. His measurement of the Sloan Great Wall of galaxies (1.37 billion light-years long) with Mario Juric was entered into the Guinness World Records 2006 as the ‘largest structure in the universe,’ a record it still holds today. His new book Sizing Up the Universe, co-authored with Robert Vanderbei includes his remarkable Map of the Universe, showing for the first time the entire visible universe in a single map. The Los Angeles Times called it ‘arguably the most mind bending map to date.’