The stability of the Solar System is a subject of much inquiry in astronomy. Though the planets have historically been stable as observed, and will be in the "short" term, their weak gravitational effects on one another can add up in ways that are not predictable by any simple means.
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 Newton's law of gravitation (1687), mathematicians and astronomers (such as Laplace, Lagrange, Gauss, Poincaré, Kolmogorov, V. Arnold, and J. Moser) have searched for evidence for the stability of the planetary motions, and this quest has led to many mathematical developments and several successive "proofs" of stability of the Solar System. [5]
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.
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 rotation period (the time it takes the planet or moon to rotate once about its axis) has a simple numerical relationship with its orbital period. An example is the Moon, which is in a 1:1 spin–orbit resonance that keeps its far side away from Earth. (This feature is also known as tidal locking .) Another example is Mercury, which is in a 3:2 spin–orbit resonance with the Sun.
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] [lower-alpha 1]
In calculation, the unknowns include asteroids, the solar quadrupole moment, mass loss from the Sun through radiation and the solar wind, drag of the solar wind on planetary magnetospheres, galactic tidal forces, and effects from passing stars. [8]
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 myr time scales (Ito & Tanikawa 2002 MNRAS).
The planet Mercury is especially susceptible to Jupiter's influence because of a small celestial coincidence: Mercury's perihelion, the point where it gets closest to the Sun, precesses at a rate of about 1.5 degrees every 1,000 years, and Jupiter's perihelion precesses only a little slower. At one point, the two may fall into sync, at which time Jupiter's constant gravitational tugs could accumulate and pull Mercury off course, with 1–2% probability, 3–4 billion years into the future. This could eject it from the Solar System altogether [1] or send it on a collision course with Venus, the Sun, or Earth. [10]
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.
Jupiter's Galilean moons experience strong tidal dissipation and mutual interactions due to their size and proximity to Jupiter. Currently, Io, Europa, and Ganymede are in a 4:2:1 Laplace resonance with each other, with each inner moon completing two orbits for every orbit of the next moon out. In around 1.5 billion years, outward migration of these moons will trap the fourth and outermost moon, Callisto, into another 2:1 resonance with Ganymede. This 8:4:2:1 resonance will cause Callisto to migrate outward, and it may remain stable with approximately 56% probability, or become disrupted with Io usually exiting the chain. [15]
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] [lower-alpha 2]
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 extrasolar objects is even more difficult than predicting the influences of objects within the system simply because of the sheer distances involved. Among the known objects with a potential to significantly affect the Solar System is the star Gliese 710, which is expected to pass near the system in approximately 1.281 million years. [17] Though the star is not expected to substantially affect the orbits of the major planets, it could substantially disrupt the Oort cloud, potentially causing major comet activity throughout the Solar System. There are at least a dozen other stars that have a potential to make a close approach in the next few million years. [18] In 2022, Garett Brown and Hanno Rein of the University of Toronto published a study exploring the long-term stability of the Solar System in the presence of weak perturbations from stellar flybys. They determined that if a passing star altered the semi-major axis of Neptune by at least 0.03 AU (4.49 million km; 2.79 million miles) it would increase the chance of instability by 10 times over the subsequent 5 billion years. [lower-alpha 2] They also estimated that a flyby of this magnitude is not likely to occur for 100 billion years. [19]
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]
Another project involved constructing the Digital Orrery by G. Sussman and his MIT group in 1988. The group used a special-purpose computer whose multiprocessor architecture was optimized for integrating the orbits of the outer planets. It was used to integrate out to 845 million years – some 20% of the age of the Solar System. In 1988, Sussman and Wisdom found data using the Orrery that revealed that Pluto's orbit shows signs of chaos, due in part to its peculiar resonance with Neptune. [9]
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 gravitational perturbations. [21]
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.
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]
Independently of Laskar and Gastineau, Batygin and Laughlin were also directly simulating the Solar System 20 billion years into the future. [lower-alpha 2] 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]
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. [lower-alpha 2] Their work showed that 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]
Mercury is the first planet from the Sun and the smallest in the Solar System. In English, it is named after the ancient Roman god Mercurius (Mercury), god of commerce and communication, and the messenger of the gods. Mercury is classified as a terrestrial planet, with roughly the same surface gravity as Mars. The surface of Mercury is heavily cratered, as a result of countless impact events that have accumulated over billions of years. Its largest crater, Caloris Planitia, has a diameter of 1,550 km (960 mi) and one-third the diameter of the planet. Similarly to the Earth's Moon, Mercury's surface displays an expansive rupes system generated from thrust faults and bright ray systems formed by impact event remnants.
In celestial mechanics, orbital resonance occurs when orbiting bodies exert regular, periodic gravitational influence on each other, usually because their orbital periods are related by a ratio of small integers. Most commonly, this relationship is found between a pair of objects. The physical principle behind orbital resonance is similar in concept to pushing a child on a swing, whereby the orbit and the swing both have a natural frequency, and the body doing the "pushing" will act in periodic repetition to have a cumulative effect on the motion. Orbital resonances greatly enhance the mutual gravitational influence of the bodies. In most cases, this results in an unstable interaction, in which the bodies exchange momentum and shift orbits until the resonance no longer exists. Under some circumstances, a resonant system can be self-correcting and thus stable. Examples are the 1:2:4 resonance of Jupiter's moons Ganymede, Europa and Io, and the 2:3 resonance between Neptune and Pluto. Unstable resonances with Saturn's inner moons give rise to gaps in the rings of Saturn. The special case of 1:1 resonance between bodies with similar orbital radii causes large planetary system bodies to eject most other bodies sharing their orbits; this is part of the much more extensive process of clearing the neighbourhood, an effect that is used in the current definition of a planet.
Following the discovery of the planet Neptune in 1846, there was considerable speculation that another planet might exist beyond its orbit. The search began in the mid-19th century and continued at the start of the 20th with Percival Lowell's quest for Planet X. Lowell proposed the Planet X hypothesis to explain apparent discrepancies in the orbits of the giant planets, particularly Uranus and Neptune, speculating that the gravity of a large unseen ninth planet could have perturbed Uranus enough to account for the irregularities.
The Solar System is the gravitationally bound system of the Sun and the objects that orbit it. It was formed about 4.6 billion years ago when a dense region of a molecular cloud collapsed, forming the Sun and a protoplanetary disc. The Sun is a typical star that maintains a balanced equilibrium by the fusion of hydrogen into helium at its core, releasing this energy from its outer photosphere. Astronomers classify it as a G-type main-sequence star.
Pluto is a dwarf planet in the Kuiper belt, a ring of bodies beyond the orbit of Neptune. It is the ninth-largest and tenth-most-massive known object to directly orbit the Sun. It is the largest known trans-Neptunian object by volume, by a small margin, but is less massive than Eris. Like other Kuiper belt objects, Pluto is made primarily of ice and rock and is much smaller than the inner planets. Pluto has roughly one-sixth the mass of the Moon, and one-third its volume.
Tidal locking between a pair of co-orbiting astronomical bodies occurs when one of the objects reaches a state where there is no longer any net change in its rotation rate over the course of a complete orbit. In the case where a tidally locked body possesses synchronous rotation, the object takes just as long to rotate around its own axis as it does to revolve around its partner. For example, the same side of the Moon always faces Earth, although there is some variability because the Moon's orbit is not perfectly circular. Usually, only the satellite is tidally locked to the larger body. However, if both the difference in mass between the two bodies and the distance between them are relatively small, each may be tidally locked to the other; this is the case for Pluto and Charon, as well as for Eris and Dysnomia. Alternative names for the tidal locking process are gravitational locking, captured rotation, and spin–orbit locking.
In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination.
Milankovitch cycles describe the collective effects of changes in the Earth's movements on its climate over thousands of years. The term was coined and named after the Serbian geophysicist and astronomer Milutin Milanković. In the 1920s, he hypothesized that variations in eccentricity, axial tilt, and precession combined to result in cyclical variations in the intra-annual and latitudinal distribution of solar radiation at the Earth's surface, and that this orbital forcing strongly influenced the Earth's climatic patterns.
Earth orbits the Sun at an average distance of 149.60 million km (92.96 million mi), or 8.317 light-minutes, in a counterclockwise direction as viewed from above the Northern Hemisphere. One complete orbit takes 365.256 days, during which time Earth has traveled 940 million km (584 million mi). Ignoring the influence of other Solar System bodies, Earth's orbit, also called Earth's revolution, is an ellipse with the Earth–Sun barycenter as one focus with a current eccentricity of 0.0167. Since this value is close to zero, the center of the orbit is relatively close to the center of the Sun.
Planetary migration occurs when a planet or other body in orbit around a star interacts with a disk of gas or planetesimals, resulting in the alteration of its orbital parameters, especially its semi-major axis. Planetary migration is the most likely explanation for hot Jupiters. The generally accepted theory of planet formation from a protoplanetary disk predicts that such planets cannot form so close to their stars, as there is insufficient mass at such small radii and the temperature is too high to allow the formation of rocky or icy planetesimals.
There is evidence that the formation of the Solar System began about 4.6 billion years ago with the gravitational collapse of a small part of a giant molecular cloud. Most of the collapsing mass collected in the center, forming the Sun, while the rest flattened into a protoplanetary disk out of which the planets, moons, asteroids, and other small Solar System bodies formed.
The semi-analytic planetary theory VSOP is a mathematical model describing long-term changes in the orbits of the planets Mercury to Neptune. The earliest modern scientific model considered only the gravitational attraction between the Sun and each planet, with the resulting orbits being unvarying Keplerian ellipses. In reality, all the planets exert slight forces on each other, causing slow changes in the shape and orientation of these ellipses. Increasingly complex analytical models have been made of these deviations, as well as efficient and accurate numerical approximation methods.
Detached objects are a dynamical class of minor planets in the outer reaches of the Solar System and belong to the broader family of trans-Neptunian objects (TNOs). These objects have orbits whose points of closest approach to the Sun (perihelion) are sufficiently distant from the gravitational influence of Neptune that they are only moderately affected by Neptune and the other known planets: This makes them appear to be "detached" from the rest of the Solar System, except for their attraction to the Sun.
Retrograde motion in astronomy is, in general, orbital or rotational motion of an object in the direction opposite the rotation of its primary, that is, the central object. It may also describe other motions such as precession or nutation of an object's rotational axis. Prograde or direct motion is more normal motion in the same direction as the primary rotates. However, "retrograde" and "prograde" can also refer to an object other than the primary if so described. The direction of rotation is determined by an inertial frame of reference, such as distant fixed stars.
Jacques Laskar is a French astronomer. He is a research director at the French National Centre for Scientific Research (CNRS), and a member of Astronomy and dynamical systems of the Institute of Celestial Mechanics and Computation of Ephemerides of the Paris Observatory. He received the CNRS Silver Medal in 1994 and the Milutin Milankovic Medal in 2019. Since 2003, he is a member of the French Academy of Sciences.
A satellite system is a set of gravitationally bound objects in orbit around a planetary mass object or minor planet, or its barycenter. Generally speaking, it is a set of natural satellites (moons), although such systems may also consist of bodies such as circumplanetary disks, ring systems, moonlets, minor-planet moons and artificial satellites any of which may themselves have satellite systems of their own. Some bodies also possess quasi-satellites that have orbits gravitationally influenced by their primary, but are generally not considered to be part of a satellite system. Satellite systems can have complex interactions including magnetic, tidal, atmospheric and orbital interactions such as orbital resonances and libration. Individually major satellite objects are designated in Roman numerals. Satellite systems are referred to either by the possessive adjectives of their primary, or less commonly by the name of their primary. Where only one satellite is known, or it is a binary with a common centre of gravity, it may be referred to using the hyphenated names of the primary and major satellite.
Planet Nine is a hypothetical ninth planet in the outer region of the Solar System. Its gravitational effects could explain the peculiar clustering of orbits for a group of extreme trans-Neptunian objects (ETNOs), bodies beyond Neptune that orbit the Sun at distances averaging more than 250 times that of the Earth. These ETNOs tend to make their closest approaches to the Sun in one sector, and their orbits are similarly tilted. These alignments suggest that an undiscovered planet may be shepherding the orbits of the most distant known Solar System objects. Nonetheless, some astronomers question this conclusion and instead assert that the clustering of the ETNOs' orbits is due to observational biases, resulting from the difficulty of discovering and tracking these objects during much of the year.
514107 Kaʻepaokaʻāwela, provisionally designated 2015 BZ509 and nicknamed Bee-Zed, is a small asteroid, approximately 3 km (2 mi) in diameter, in a resonant, co-orbital motion with Jupiter. It is an unusual minor planet in that its orbit is retrograde, which is opposite to the direction of most other bodies in the Solar System. It was discovered on 26 November 2014, by astronomers of the Pan-STARRS survey at Haleakala Observatory on the island of Maui, United States. Kaʻepaokaʻāwela is the first example of an asteroid in a 1:–1 resonance with any of the planets. This type of resonance had only been studied a few years before the object's discovery. One study suggests that it was an interstellar asteroid captured 4.5 billion years ago into an orbit around the Sun.
The hypothetical Planet Nine would modify the orbits of extreme trans-Neptunian objects via a combination of effects. On very long timescales exchanges of angular momentum with Planet Nine cause the perihelia of anti-aligned objects to rise until their precession reverses direction, maintaining their anti-alignment, and later fall, returning them to their original orbits. On shorter timescales mean-motion resonances with Planet Nine provides phase protection, which stabilizes their orbits by slightly altering the objects' semi-major axes, keeping their orbits synchronized with Planet Nine's and preventing close approaches. The inclination of Planet Nine's orbit weakens this protection, resulting in a chaotic variation of semi-major axes as objects hop between resonances. The orbital poles of the objects circle that of the Solar System's Laplace plane, which at large semi-major axes is warped toward the plane of Planet Nine's orbit, causing their poles to be clustered toward one side.