Einstein’s Gravity Protects Earth

If the universe obeyed Newton's laws of gravity, there would be about a 60% chance that Mercury would head toward the Sun or Venus during the Sun’s lifetime. But according to a new study, corrections to Newton's laws using Einstein's theory of gravity (general relativity) lower these chances to about 1%. That’s good news, because if Mercury had a near miss with Venus or the Sun, it could wreak havoc on Earth.

Artist's concept of a collision between Venus and Earth.
J. Vidal-Madjar / IMCCE / CNRS
Jupiter, the solar system's most massive planet, affects Mercury's trajectory. Drastic consequences for Mercury are possible, if its orbit elongates into a highly eccentric ellipse, allowing it to reach beyond Venus.

If that happens, Mercury would likely smash into Venus or the Sun, according to a new study by Jacques Laskar and Mickael Gastineau (Paris Observatory, France), published in the June 11th issue of Nature.

For all of Jupiter’s mass, sending Mercury farther out than Venus requires an "alignment of planets" of sorts — a near-perfect geometry that physicists call a resonance — allowing a small effect to build up over time.

In the case of Jupiter and Mercury, the accidental matching is provided by the speed at which their elliptical orbits move around the Sun — the precession of their perihelia — which happens to be nearly synchronized. But the warping of space-time near the Sun predicted by general relativity introduces a slight mismatch, by speeding up Mercury’s precession. So the resonance is less likely to happen.

We can thank Einstein once more (and Laskar too) for informing us that Mercury has only a 1% chance of going out of whack. Laskar's estimate following Newtonian gravity was 60%. "[The Newtonian calculation] had to be wrong," says Jack Lissauer (NASA/Ames Research Center), arguing that, with such high probabilities, Mercury would already have hit Venus or the Sun during the past few billion years.

Example of long-term evolution of the planetary orbits: Mercury (white), Venus (green), Earth (blue), Mars (red). Time is indicated in thousands of years (kyr). (a) In the vicinity of the current state, the orbits become distorted under the influence of planetary perturbations, but without allowing close encounters or collisions. (b) In about 1% of cases, the orbit of Mercury may be distorted enough to allow a collision with Venus or the Sun in less than 5 billion years. (c) In one of the trajectories, the eccentricity of Mars increases sufficiently to allow for a close encounter or collision with Earth. (d) This leads to a destabilization of the terrestrial planets and collision between Venus and Earth.
ASD / IMCCE / CNRS
"The interesting thing is that it can still happen quite a long time after planets have formed," says John Chambers (Carnegie Institution of Washington). "We’re sort of changing the idea that planetary systems are formed, and then stay the same."

Mercury's demise brings little consequences for Earth, unless Venus tidally disrupts Mercury, sending fragments our way. "There would be a lot of these chunks, and they could hit Earth," says Lissauer.

If Mercury goes haywire but misses Venus and the Sun on its new, highly eccentric trajectory, Mercury can perturb the orbits of Mars, Venus, or Earth; the more massive outer planets would remain unaffected.

It's difficult to know whether this will happen, because the solar system is chaotic. "That the system is chaotic doesn't mean anything can happen," Laskar explains, but relates to the "butterfly effect." All the planets and smaller bodies gravitationally influence each other, meaning that any imprecision on today’s trajectory is multiplied by ten every 10 million years.

Because of this chaos, astronomers will never be able to predict the positions of planets beyond a few hundred million years, and nobody can guarantee that Earth will even orbit the Sun so far in the future. "We can never overcome this limitation," says Laskar, even if the inaccuracy started out less than a trillionth of a trillionth of an inch.

"If I jump in the air, Earth moves more than that," Laskar says. So instead of aiming for the unknown exact trajectory of Mercury, Laskar and Gastineau went for a random sampling of what might happen. Modifying Mercury's current position in steps of 0.38 millimeters, they created 2,501 trajectories. These tiny variations could be thought of as due to Laskar jumping up, an asteroid or star passing by, the influences of tides, or the finite size of the planets. We can't tell the 2,501 trajectories apart today, but as they diverge in the future, they provide a sample of the innumerable possible outcomes.

The result is expressed in terms of probabilities, yielding the 1% for Mercury going haywire, and only a small fraction of this percent for it going haywire but missing Venus or the Sun. If it misses, Mercury can then send Mars or Venus hurling toward Earth, with dramatic consequences. Even without a direct hit, Earth's orbit can be enormously modified, Laskar says, "In all these cases, we have very strong climate change."

Mercury may cause chaotic events in the future, says Renu Malhotra (University of Arizona), but it might even owe its current eccentricity, inclination, and high density to some previous collision. Maybe this isn't a coincidence after all…

See a movie on Jacques Laskar's website. For an expert's opinion, read the News & Views in Nature by Greg Laughlin (University of California, Santa Cruz).

11 thoughts on “Einstein’s Gravity Protects Earth

  1. Rod

    A neat report here. If Mercury orbited the Sun for 1E+9 years, that could involve > 4E+9 revolutions and over 4.5 billion years > 18E+9. Ruling out the Newtonian calculation because it does not fit with 4.5 billions years is an interpretation. Could this also be interpreted that the planets simply have not been orbiting the Sun for billions of years?

  2. Eric F. Diaz

    In working with Laplace-Lagrange (LL) secular theory, we used to talk about the long-term instability inherent in all planetary systems and the likelihood that Mercury would most probably one day slam into the Earth. You don’t know how good it is to hear that that probability has been reduced down to only 1%. Thank you, Albert Einstein!

    P.S.

    I always did like that guy!

  3. Richard

    This is an interesting article but the “what ifs” are so pervasive and overwhelming that they don’t really mean anything at all. Of course, any theories that predict a 60% chance or a 1% chance of something happening in the extreme past or future never affect reality at all but only describe someone’s faulty perceptions of reality.
    So… it may be best not to thank the theorists who generate all this smoke and mirrors but rather the ONE who designed and built it all in the first place.

  4. Michael C. Emmert

    I’ve played with GravitySimulator a bunch. If you run it too fast or your computer is too slow, various mathematical errors can creep into your calculations. It doesn’t do relativity, anyway, that would just slow it down too much. I think Renu Malhotra is right about a previous collision giving Mercury an eccentric orbit; the object was formed in the Sun/Mercury L4 or L5 point and plunged into the Sun, the other L5 or L4 object formed Caloris Basin. It’s become apparent that other solar systems generally have larger planets than ours, if you replace the masses of the gas giants of our solar system with 10 Jupiter masses, the Solar System falls apart immediately. This might be a partial answer to the Fermi Paradox (“If there are aliens, where are they?”). It’s best to carefully construct simulations to answer generalized situations.

  5. Rod

    In reference to Michael Emmert’s comments, exoplanet.eu website shows 353 exoplanets. The table indicates 146 have semi-major axis 1-8 AU, the average mass is a little more than 4 Jupiters, average semi-major axis 2.26 AU and average eccentricity is 0.3087. 102 of the 353 listed are apparently hot Jupiters. This configuration here could make for some chaos at home.

  6. Grant Miller

    Regarding the first comment by Rod-It’s very unlikely. General relativity has been proven extremely reliable and the other lines of evidence(geology, radiometric dating, etc.) indicate an Earth that is about 4.5 byo. Also, Big Bang cosmology has much evidential support. This is not necessarily in conflict w/Christian scripture(assuming that is where you are coming from). reasons.org

  7. Rod

    Grant Miller, interesting points raised. A problem I see is that radiometric ages cannot be shown to represent true orbital revolutions around the Sun, only circular reasoning supports the interpretation. Case in point, Mercury needs some 18 billion revolutions to experience 4.5 billion years of radiometric dating.

  8. Marc

    In reference to Michael Emmert and Rod’s comments, one should not forget that the current sample of exoplanets cannot be assumed to be representative of all planetary systems in the sun’s neighbourhood, or indeed the rest of the universe. This is simply because the methods used to detect exoplanes are strongly biased to detecting planets with relatively large masses which orbit close to their parent star. If our models of planet formation are correct (and there is currently no real fundamental reason to believe that they are not) there will be plenty of planetary systems out there that resemble our solar systems. However, our current techniques are simply not sensitive enough to detect these.

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