Stability of the Solar System
The stability of the Solar System is a subject of much inquiry in
For this reason (among others), the Solar System is chaotic in the technical sense defined by mathematical chaos theory,[1] and that chaotic behavior degrades even the most precise long-term numerical or analytic models for the orbital motion in the Solar System, so they cannot be valid beyond more than a few tens of millions of years into the past or future – about 1% its present age.[2]
The Solar System is stable on the time-scale of the existence of humans, and far beyond, given that it is unlikely any of the planets will collide with each other or be ejected from the system in the next few billion years,[3] and that Earth's orbit will be relatively stable.[4]
Since
Overview and challenges
The orbits of the planets are open to long-term variations. Modeling the Solar System is a case of the n-body problem of physics, which is generally unsolvable except by numerical simulation. Because of the chaotic behavior embedded in the mathematics, long-term predictions can only be statistical, rather than certain.
Resonance
An orbital resonance happens when the periods of any two objects have a simple numerical ratio. The most fundamental period for an object in the Solar System is its orbital period, and orbital resonances pervade the Solar System. In 1867, the American astronomer Daniel Kirkwood noticed that asteroids in the main belt are not randomly distributed.[6] There were distinct gaps in the belt at locations that corresponded to resonances with Jupiter. For example, there were no asteroids at the 3:1 resonance — a distance of 2.5 AU (370 million km; 230 million mi) — or at the 2:1 resonance, at 3.3 AU (490 million km; 310 million mi). These are now known as the Kirkwood gaps. Some asteroids were later discovered to orbit in these gaps, but when closely analyzed their orbits were determined to be unstable and they will eventually break out of the resonance due to close encounters with a major planet.[citation needed]
Another common form of resonance in the Solar System is spin–orbit resonance, where the
Predictability
The planets' orbits are chaotic over longer time scales, in such a way that the whole Solar System possesses a Lyapunov time in the range of 2~230 million years.[3] In all cases, this means that the positions of individual planets along their orbits ultimately become impossible to predict with any certainty. In some cases, the orbits themselves may change dramatically. Such chaos manifests most strongly as changes in eccentricity, with some planets' orbits becoming significantly more – or less – elliptical.[7][a]
In calculation, the unknowns include
Scenarios
Neptune–Pluto resonance
The Neptune–Pluto system lies in a 3:2 orbital resonance. C.J. Cohen and E.C. Hubbard at the Naval Surface Warfare Center Dahlgren Division discovered this in 1965. Although the resonance itself will remain stable in the short term, it becomes impossible to predict the position of Pluto with any degree of accuracy, as the uncertainty in the position grows by a factor e with each Lyapunov time, which for Pluto is 10–20 million years.[9] Thus, on a time scale of hundreds of millions of years Pluto's orbital phase becomes impossible to determine, even if Pluto's orbit appears to be perfectly stable on 10
Mercury–Jupiter 1:1 perihelion-precession resonance
The planet
Mercury's perihelion-precession rate is dominated by planet–planet interactions, but about 7.5% of Mercury's perihelion precession rate comes from the effects described by general relativity.[11] The work by Laskar and Gastineau (described below) showed the importance of general relativity (G.R.) in long-term Solar System stability. Specifically, without G.R. the instability rate of Mercury would be 60 times higher than with G.R.[12] By modelling the instability time of Mercury as a one-dimensional Fokker–Planck diffusion process, the relationship between the instability time of Mercury and the Mercury–Jupiter 1:1 perihelion-precession resonance can be investigated statistically.[13] This diffusion model shows that G.R. not only distances Mercury and Jupiter from falling into a 1:1 resonance, but also decreases the rate at which Mercury diffuses through phase space.[14] Thus, not only does G.R. decrease the likelihood of Mercury's instability, but also extends the time at which it is likely to occur.
Galilean moon resonance
Jupiter's
Chaos from geological processes
Another example is Earth's axial tilt, which, due to friction raised within Earth's mantle by tidal interactions with the Moon, will be rendered chaotic between 1.5 and 4.5 billion years from now.[16][b]
External influences
Objects coming from outside the Solar System can also affect it. Though they are not technically part of the Solar System for the purposes of studying the system's intrinsic stability, they nevertheless can change it. Unfortunately, predicting the potential influences of these
Recent studies
LonGStOP, 1982
Project LonGStOP (LOng-term Gravitational Study of the Outer Planets) was a 1982 international consortium of Solar System dynamicists led by A.E. Roy. It involved creation of a model on a supercomputer, integrating the orbits of (only) the outer planets. Its results revealed several curious exchanges of energy between the outer planets, but no signs of gross instability.[20]
Digital Orrery, 1988
Another project involved constructing the
If Pluto's orbit is chaotic, then technically the whole Solar System is chaotic. This might be more than a technicality, since even a Solar System body as small as Pluto might affect the others to a perceptible extent through cumulative
Laskar, 1989
In 1989, Jacques Laskar of the Bureau des Longitudes in Paris published the results of his numerical integration of the Solar System over 200 million years. These were not the full equations of motion, but rather averaged equations along the lines of those used by Laplace. Laskar's work showed that the Earth's orbit is chaotic (as are the orbits of all the inner planets) and that an error as small as 15 metres in measuring the position of the Earth today would make it impossible to predict where the Earth would be in its orbit in just over 100 million years' time.
Laskar and Gastineau, 2009
Jacques Laskar and his colleague Mickaël Gastineau in 2008 took a more thorough approach by directly simulating 2,501 possible futures. Each of the 2,501 cases has slightly different initial conditions: Mercury's position varies by about 1 metre (3.3 feet) between one simulation and the next.[22] In 20 cases, Mercury goes into a dangerous orbit and often ends up colliding with Venus or plunging into the Sun. Moving in such a warped orbit, Mercury's gravity is more likely to shake other planets out of their settled paths: In one simulated case, Mercury's perturbations sent Mars heading toward Earth.[12]
Batygin and Laughlin, 2008
Independently of Laskar and Gastineau, Batygin and Laughlin were also directly simulating the Solar System 20 billion years into the future.[b] Their results reached the same basic conclusions as did Laskar and Gastineau, while additionally providing a lower bound of a billion years on the dynamical lifespan of the Solar System.[23]
Brown and Rein, 2020
In 2020, Garett Brown and Hanno Rein of the University of Toronto published the results of their numerical integration of the Solar System over 5 billion years.[b] Their work showed that the Mercury's orbit is highly chaotic and that an error as small as 0.38 millimeters (0.015 inches) in measuring the position of Mercury today would make it impossible to predict the eccentricity of its orbit in just over 200 million years' time.[24]
Footnotes
- ^
The effect of orders of magnitudemore slowly than its edge vibrates.
- ^ a b c d
The dynamical modelling of the Solar System beyond approximately 4 billion years into the future is greatly complicated by the giant phase: The Sun will lose mass at an uncertain rate, heat up, and greatly expand, all of which will change the dynamics of planetary orbits.
See also
References
- ^ a b
Bibcode:1994A&A...287L...9L.
- ^ .
- ^ a b
Hayes, Wayne B. (2007). "Is the outer Solar system chaotic?". S2CID 18705038.
- ^ Gribbin, John (2004). Deep Simplicity. Random House.
- ^
Bibcode:2000eaa..bookE2198L.
- ^
Hall, Nina (September 1994). Exploring Chaos. W.W. Norton & Company. p. 110. ISBN 9780393312263– via Google books.
- ^
Stewart, Ian (1997). Does God Play Dice? (2nd ed.). ISBN 978-0-14-025602-4.
- ^ Shina (17 September 2012). The stability of the Solar system. SlideServe (slides & captions). Retrieved 26 October 2017. — Includes source citations.
- ^ a b
Sussman, Gerald Jay; S2CID 1398095– via groups.csail.mit.edu.
- ^ Shiga, David (23 April 2008). "The Solar system could go haywire before the Sun dies". News service. New Scientist. Archived from the original on 31 December 2014. Retrieved 31 March 2015.
- ^
Park, Ryan S.; Folkner, William M.; Konopliv, Alexander S.; Williams, James G.; Smith, David E.; Zuber, Maria T. (22 February 2017). "Precession of Mercury's perihelion from ranging to the Messenger spacecraft". S2CID 125439949.
- ^ a b
Laskar, J.; Gastineau, M. (2009). "Existence of collisional trajectories of Mercury, Mars, and Venus with the Earth". S2CID 4416436.
- ^
Mogavero, Federico; S2CID 239651491.
- ^
Brown, Garett; Rein, Hanno (10 March 2023). "General relativistic precession and the long-term stability of the solar system". ISSN 0035-8711.
- ^
Lari, Giacomo; Saillenfest, Melaine; Fenucci, Marco (July 2020). "Long-term evolution of the Galilean satellites: The capture of Callisto into resonance". S2CID 209862163.
- ^
de Surgy, O. Neron; Bibcode:1997A&A...318..975N.
- ^
Bailer-Jones, C.A.L.; Rybizki, J; Andrae, R.; Fouesnea, M. (2018). "New stellar encounters discovered in the second Gaia data release". Astronomy & Astrophysics. 616: A37. S2CID 56269929.
- ^ Dodgson, Lindsay (8 January 2017). "A star is hurtling towards our Solar system and could knock millions of comets straight towards Earth". Business Insider.
- ^ Brown, Garett; Rein, Hanno (30 June 2022). "On the long-term stability of the Solar system in the presence of weak perturbations from stellar flybys". . Retrieved 8 July 2022.
- ^ Roy, A.E.; Walker, I.W.; Macdonald, A.J.; Williams, I.P.; Fox, K.; Murray, C.D.; et al. (1988). "Project LonGStOP". .
- ^ "Is the Solar system stable?". fortunecity.com. Archived from the original on 25 June 2008.
- ^ Battersby, Stephen (10 June 2009). "Solar system's planets could spin out of control". New Scientist. Retrieved 11 June 2009.
- ^
S2CID 5999697.
- ^
Brown, Garett; Rein, Hanno (2020). "A repository of vanilla long-term integrations of the Solar system". S2CID 228063964.
External links
- Laskar, Jacques (2009). "Stability of the Solar System". Scholarpedia. Retrieved 18 December 2009.
- "Long shot: Planet could hit Earth in distant future". Space.com.
- "Project LonGStOP - long-term gravitational study of the outer planets" (article abstract) – via adsabs.harvard.edu.