The strange dynamic of Pluto’s chaotic family
That’s Maths: The New Horizons probe will pass the dwarf planet this month and is likely to find more tiny moons of Pluto
We already know about four tiny moons that orbit Pluto (top of illustration) and its large moon Charon in a chaotic fashion. They follow roughly circular paths but wobble and tumble erratically as they pass close to the two larger bodies. Illustration: Nasa/SETI Institute via the New York Times
An astrodynamical miracle is happening in the sky above. Our ability to launch a space probe from the revolving Earth to reach a moving target billions of kilometres away 10 years later, with pinpoint accuracy, is astounding. The New Horizons mission promises to enhance our knowledge of the solar system and it may help us to understand our own planet too.
Until recently, Pluto was counted as the ninth planet. In 2006 the International Astronomical Union reclassified it as a dwarf planet. We knew that Pluto had a moon and, like the Earth and its moon, Pluto and Charon revolved around their common centre of mass in an orderly and predictable manner.
The Hubble Space Telescope images have shown up four tiny moons in addition to Charon, which have been named Styx, Nix, Kerberos and Hydra. Their orbits around the two larger bodies show signs of chaotic behaviour. They follow roughly circular paths but wobble and tumble erratically as they pass close to Pluto or Charon.
Pluto, about six billion kilometres from Earth, has not previously been observed close up. But on July 14th the New Horizons probe, launched by Nasa in 2006, will pass close to the dwarf planet. It seems likely that more moons of Pluto will be discovered. After passing Pluto, New Horizons will follow the earlier Voyager probes into deep space, never to return to Earth.
The regular elliptic motion of the planets was observed by Johannes Kepler and explained in terms of the attraction of gravity by Newton. Laplace, sometimes styled the Newton of France, expressed the idea that, for an intelligent being having complete knowledge of the present state of the universe and of the laws of classical mechanics, “nothing would be uncertain, and the future, just as the past, would be present before its eyes”.
Developments in thermodynamics in the 19th century showed how there is an arrow of time: physical processes are inherently irreversible and the past history cannot be deduced from present conditions. Then Henri Poincaré showed that, even for a system as basic as three bodies orbiting each other, chaotic behaviour is found and the future motion cannot be predicted with certainty. Of the intricate solutions he found, he wrote: “One will be struck by the complexity of this picture, which I will not even attempt to draw.”
Poincaré’s ideas on chaotic motion go some way towards explaining why long-range weather forecasting is problematic. Tiny errors in the initial state grow rapidly, ultimately spoiling the forecast. Likewise, for chaotic planetary motions, uncertainties in the current position and movement make it impossible to predict future motion with confidence. If the Earth’s orbit were chaotic, the lengths of days and years would vary, the seasons would be erratic and the climate would oscillate wildly. Probably, intelligent life could not have evolved in such conditions.
Thousands of “exoplanets” orbiting stars other than the sun have been found. Some of these revolve around binary stars, and their dynamics are complex. Since Pluto and Charon act like a binary system, the observations of the New Horizons probe may help us understand such complex dynamics more fully, and to estimate the conditions on these exoplanets.