Jupiter: Friend or Foe?

Διὸς δ᾽ ἐτελείετο βουλή — Homer, Iliad, I 5

Jupiter was once thought to play a protective role in our Solar System, preventing comets from the outer Solar System from reaching the region of the terrestrial planets, and Earth in particular, where they pose a threat to the survival of complex life by colliding with the planet. The destructive power of such collisions is evident from the Chixulub crater in Yucatán, created by the impactor that probably caused the extinction of the dinosaurs. A large enough impactor would be sufficient to destroy all the biosphere save perhaps a few hardy micro-organisms, and a planetary system where such impacts were frequent would be inimical to the survival or even emergence of complex life.

The existence of Jupiter as a “shield”, protecting our planet from dangerous bodies, is one of the pillars of the “Rare Earth Hypothesis” promulgated by Ward & Brownlee. This states that planets with complex multi-cellular life are extremely rare in the cosmos, because the conditions that allow such life to develop and survive are hard to fulfil. For example, a planet must support liquid water on its surface, and hence cannot be too close to nor too far from its star (This region is known as the Habitable Zone). Its spin axis must be fairly well-aligned with its orbital axis, so as to avoid excessive seasonal temperature variations; our own Moon stabilises the Earth’s rotation axis, keeping it only moderately misaligned with the orbital axis. And the planet must not be subjected to too large a flux of dangerous asteroids and comets; it was thought that Jupiter plays a protective role in our Solar System by clearing out dangerous comets. Hence, Ward & Brownlee argued that the suitability of a planet for hosting complex life is exquisitely sensitive to the properties of other planets in its solar system. In particular, they argued that a Jupiter-like gas giant must exist for a terrestrial planet to support complex life, and that such giant planets are not common, so nor will complex life-bearing planets be.

In a series of papers, Horner & Jones have set out to test this latter argument: the hypothesis that Jupiter does actually protect our planet from impactors. They is reason to be skeptical of this claim, since while Jupiter may throw some bodies out of the Solar System or remove them by colliding with them, it may equally well destabilise others and send them onto Earth-crossing orbits. “What Jupiter gives with one hand, it may take away with the other.” The authors test the hypothesis by numerically integrating the orbits of hypothetical comets and asteroids under the gravitational influence of the planets, and counting how many hit the Earth (The size of Earth is artificially `inflated’ to ensure good statistics, since the real Earth is a very small target). There are two related questions that need answering: first, does the very existence of Jupiter enhance or reduce impact flux, and second, does changing the mass and orbit of Jupiter change the impact flux. Horner & Jones’ first three papers examined the role of changing Jupiter’s mass on three populations of impactors: asteroids from the Main Belt between Mars and Jupiter; Centaurs, which have unstable orbits crossing the giant planets’; and long-period comets from the Oort cloud. Their newest paper looks at the role of changing Jupiter’s orbital eccentricity and inclinations on the Asteroid Belt and Centaurs. Let us, like the authors, take each of these in turn.

I: The Asteroids

The effect of Jupiter on a hypothetical Asteroid Belt. The plots show histograms of the number of asteroids per semi-major axis bin. The initial population is shown in the bottom panel. The population remaining after 10 million years is shown in the upper two panels. The top panel shows the effects of the real Jupiter, while the bottom shows the effects of a "Jupiter" whose mass is only a quarter that of the real Jupiter. Notice the depletion of bodies at resonant locations in the Belt.

The first paper looks at the efficiency of Jupiter-type planets at destabilising bodies in the Asteroid Belt. A hypothetical primordial Asteroid Belt was placed between the orbits of Mars and Jupiter (shown in the lower panel of the above plot), and the evolution of the asteroids’ orbits followed for 10 million years. The shape of the belts that remained at the end of the integration, for the real Jupiter and a “Jupiter” reduced to a quarter of its real mass, are shown in the upper two panels. Both belts show cleared regions associated with mean motion resonances with “Jupiter”, where the asteroids’ orbital periods are close to an integer ratio with “Jupiter’s” and the asteroids experience strong perturbations and are destabilised. These are known as Kirkwood Gaps after their discoverer. There is also a broader cleared region at the inner edge of the belt, at 2 AU for the Jupiter and 2.5 AU for the quarter-Jupiter. This is due to another type of resonance called a secular resonance, which again destabilises the asteroids.

The location of the secular resonance moves closer to “Jupiter’s” location, where there are more asteroids, at lower masses of the “Jupiter”. This means that, somewhat counterintuitively, the lower-mass “Jupiters” may destabilise more asteroids. The numbers of bodies hitting Earth for a whole range of “Jupiter” masses are shown below:

The total number of asteroids hitting the (inflated) Earth, as a function of "Jupiter's" mass. The lines show the cumulative number of impactors at 1, 2, 5 and 10 million years. The real Jupiter is more dangerous than very large or very small "Jupiters", but less dangerous than an intermediate-sized "Jupiter".

It is clear that very small “Jupiters” do not result in many impactors since they do not perturb the Asteroid Belt significantly. Larger “Jupiters”, up to around 0.3 Jupiter masses, result in significantly more disruption to the Belt, while as “Jupiter’s” mass is increased beyond this the number of Earth impactors falls again. Hence, the hypothesis the Jupiter acts as a shield is indeed only partly true: while the real Jupiter provides more protection than one only half or a third of the size, more protection would be afforded by one either more massive or significantly less massive.

II: The Centaurs

The Centaurs are a population of bodies whose orbits in the outer Solar System intersect the giant planets’. As such they are highly unstable, and many are sent into the inner Solar System to become short-period comets. The population is thought to be ultimately replenished by objects from the Kuiper Belt beyond Neptune.

In their second paper the authors looked at the number of Earth impactors coming from the Centaur population as a function of Jupiter’s mass. The same pattern is seen as for the Main Belt Asteroids: the impact risk is small for small masses of “Jupiter”, rises to a maximum at around 0.2 Jupiter masses, and then falls as “Jupiter’s” mass is increased further:

The number of Short-Period Comets hitting Earth as a function of "Jupiter's" mass. Lines show the cumulative number after 2, 4, 6, 8 and 10 million years.

In this case, the danger posed by “Jupiter” is due to a balance between its ability to destabilise the Centaur bodies and its ability to remove them from the Solar System. Planets around a quarter of Jupiter’s mass are good at the former but bad at the latter, explaining why they are most dangerous. The fact that the impact flux peaks at about the same mass for both Asteroids and Centaur populations appears to be a coincidence.

III: The Oort Cloud

Long-Period Comets hail from the Oort Cloud, the swarm of bodies on very wide (many thousands or tens of thousands of AU) orbits which surrounds the planetary regions of the Solar System. Bodies in the Oort Cloud suffer perturbations from extra-Solar sources such as nearby stars, and the changes to their orbits can bring their pericentres to within a few AU of the Sun where they can interact with the planets.

The these objects, the cause of injection onto Earth-crossing orbits is effects from outside the Solar System, while the role of Jupiter and the other giant planets is simply to eject ones that encounter them, an outcome which is more likely for higher planetary masses. Hence, this population is the only one from which Jupiter acts unambiguously as a shield, since there is a decreasing number of Earth-crossing comets as “Jupiter’s” mass is increased. Indeed, the efficiency of Jupiter removing such comets was the origin of the idea that Jupiter acts as a shield in the first place.

Number of Long-Period Comets from the Oort Cloud that cross Earth's orbit, as a function of time. The different lines show different values of "Jupiter's" mass: from top to bottom, the masses are 0, 0.25, 0.5 1 and 2 times Jupiter's mass. Here Jupiter is unambiguously a shield: the impact flux would be much greater if it were absent or smaller.

So far we have seen that Jupiter definitely acts as a shield from Long-Period Comets, but for both Main Belt Asteroids and Centaurs its role is more ambiguous: while a slightly decreased Jovian mass would result in a significantly higher impact flux, either a larger or a very small Jovian mass, or no Jupiter at all, would result in fewer impactors. In the past it was thought that Long-Period Comets posed the greatest impact risk to Earth. If true, this would mean that Jupiter on the whole acts as a shield. However, the greatest impact threat is now thought to come from the Asteroids, a threat which would be much lower if Jupiter were much smaller.

IV: The Jovian Eccentricity and Inclination

As well as varying Jupiter’s mass, one should ask what are the effects of varying its orbital eccentricity and inclination, to see whether our own Jupiter has a particularly fortuitous combination of these elements or not. This the authors did in their latest paper. They tested the effects of varying these parameters on the impact flux from the Asteroid Belt and Centaurs. Increasing Jupiter’s eccentricity and inclination has a strong destabilising effect on the Asteroid Belt, resulting in noticeably more impacts:

The effects of varying "Jupiter's" mass and eccentricity on Earth impactors from the Asteroid Belt. The upper line shows a high-eccentricity "Jupiter" with e=0.1. The middle line shows the real Jupiter with e=0.049. The lower line shows a low-eccentricity "Jupiter" with e=0.01.

This is largely through the destabilising effects of the stronger mean motion and secular resonances at higher eccentricity. However, the effect on the Centaur population is rather weak. Similarly increasing “Jupiter’s” inclination also increases the number of impactors.

The conclusion of this study then is that Jupiter’s current eccentricity and inclination are not optimal for protecting the Earth from impactors, but the situation could be a lot worse.

Conclusions

Taken together, these papers show that the old idea of Jupiter being a protector of the Earth is somewhat naïve. Jupiter only plays an unambiguous protective role in the case of Oort Cloud comets, which are not now thought to constitute the major impact hazard.

The implications of this for the Rare Earth hypothesis are not entirely clear. While it is the case that, if Jupiter were to not exist, the impact flux suffered by Earth would be much less, it is also the case that Jupiter could be much more hostile to life on Earth, if its mass were a little lower or eccentricity a little higher. Knowledge of the proportion of Earth-like planets with impact regimes suitable for sustaining complex life will doubtless have to await a thorough census of the numbers and orbital properties of both Earth-like planets and their giant planet companions.

An additional complication is that, if “Jupiter” were much different from the real Jupiter, the populations of small bodies in the Solar System may be very different, since their present locations are determined by the formation and evolution of the Solar System as a whole. Properly the vulnerability of a planet to impactors should be determined within the context of a full model of Solar System evolution, but as Horner & Jones say, we are a long way from the conceptual knowledge and computational power required to simulate this…

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Trojan

The space surrounding Earth’s orbit is far from empty. Small meteoroids can be seen as they enter Earth’s atmosphere and disintegrate, leaving wakes of incandescent gas. Comets leave extensive debris trails as they approach the Sun. There is also, unseen to the naked eye, a large population of asteroids whose orbits are in the vicinity of Earth’s.

Last week, one such asteroid, 2010 TK7was announced to be the first known member of a special class of asteroid known as Trojans. While Trojans relating to other planets such as Jupiter were known previously, this is the first example of one associated with Earth. The distinguishing feature of Trojan asteroids is that they are located close to one of the Lagrange points of the planet-Sun system, shown below:

Lagrange points

Image credit: Wikipedia

The contours show the gravitational potential due to the Earth and Sun. This is in a rotating reference frame, so the Earth remains fixed at the right as it orbits the Sun. Since it is a rotating reference frame, particles will feel fictitious forces, since they want to remain on a straight trajectory in the inertial frame. One of these forces is the centrifugal force, which is included in the contours. The behaviour of a particle due to the gravitational and centrifugal forces can be visualised by imagining that the contours represent a system of hills and valleys, with particles rolling “downhill” under the action of gravity. There are 5 points where the gravitational and centrifugal forces exactly balance, labelled L1 to L5. If a particle were located exactly at one of these points, there would be no net force, just as if it were located exactly at the top of a hill, and it would remain there.

However, the existence of such equilibrium points does not tell the whole story. Equilibria may be stable or unstable, depending on whether a particle placed close to one will move towards or away from it. Thinking again in terms of a landscape, the top of a hill and the bottom of a valley are both equilibria, but only the second is stable.

2010 TK7 is located close to but not at the L4 Lagrange point. Despite being a “hill” in the contour plot, suggesting instability, the L4 point is actually stable. This is due to the effects of another fictitious force, the Coriolis force. This is the force that governs the rotation of weather systems on Earth. The Coriolis force acts only on moving bodies, and so cannot be captured in a static description of forces as shown in the above figure. The effects are best shown in an animation:

Coriolis effect

Animation credit: Wikipedia

On the left the trajectory of a particle moving from one side of the circle to the other in an inertial frame is shown, and on the right the trajectory in the rotating frame (The details don’t correspond exactly to the motion about the Lagrange point, but it suffices to demonstrate qualitatively what’s going on). Note that the particle follows a small curved path in the rotating frame, with the particle returning to its starting point. This effect only occurs for particles moving in the rotating frame: if a particle were fixed (say, at a boundary between light and dark on the edge of the circle) it would not experience such a force.

Now we can piece together the motion of a particle close to L4. If initially at rest, it rolls “downhill” from L4 under combined gravitational and centrifugal forces. However, before it gets too far, the Coriolis force forces it to curve round, back towards L4. As it approaches, it slows, the Coriolis force weakens, and gravitational and centrifugal forces force the particle away from L4 again. The process repeats, with the particle moving towards and away from the Lagrange point. Qualitatively similar behaviour can be seen in the following animation from the discoverers of 2010 TK7, showing the asteroid’s orbit (although note that the large size of the oscillations makes the actual motion rather more complicated):

You have probably noticed that there are actually two components to the motion: an annual epicyclic oscillation, and a long-term libration which slowly varies the centre of the epicyclic oscillation. The large amplitudes of both components mean that 2010 TK7 is only weakly attached to the L4 point. Indeed, the discoverers integrated the asteroid’s orbit backwards in time and found that before AD 500 it was actually librating about the L5 point on the opposite side of Earth, but the particle’s high libration amplitude enabled it to cross the L3 point to enter the L4 point’s sphere of influence.

What of future evolution? Due to the effects of chaos–small errors in the asteroid’s exact position blowing up exponentially–it’s impossible to exactly predict the orbit more than a few thousand years in advance. Nevertheless, it appears that the object will continue transitioning between the Lagrange points, although precisely what will happen is unknown.

Could there be more such asteroids? Since the L4 and L5 points are located only 60 degrees from the Sun as seen from Earth, detecting faint objects there is challenging. 2010 TK7 was detected by the satellite WISE, and then followed up from the ground. The large libration amplitude and epicyclic oscillations, and the fact that the asteroid was discovered at the near-Earth end of its libration, carry it further from the Sun, and hence make it easier to detect. Trojans bound closely to the Lagrange points may well have escaped detection, and it’s intriuguing to think that more may be waiting to be discovered in this region of space so close to us.

Further reading:
  • The paper published in Nature
  • The discoverers’ website, with more visualisations.
  • Murray & Dermott, Solar System Mechanics, CUP, 1999. Not for the mathematophobic!