Molecular machines are a class of molecules typically
described as an assembly of a discrete number of molecular components
intended to produce mechanical movements in response to specific
stimuli, mimicking macromolecular devices such as switches and motors. Naturally occurring or biological molecular machines are responsible for vital living processes such as DNA replication and ATP synthesis. Kinesins and ribosomes are examples of molecular machines, and they often take the form of multi-protein complexes.
For the last several decades, scientists have attempted, with varying
degrees of success, to miniaturize machines found in the macroscopic
world. The first example of an artificial molecular machine (AMM) was
reported in 1994, featuring a rotaxane with a ring and two different possible binding sites. In 2016 the Nobel Prize in Chemistry was awarded to Jean-Pierre Sauvage, Sir J. Fraser Stoddart, and Bernard L. Feringa for the design and synthesis of molecular machines.
AMMs have diversified rapidly over the past few decades and their design principles, properties, and characterization
methods have been outlined better. A major starting point for the
design of AMMs is to exploit the existing modes of motion in molecules,
such as rotation about single bonds or cis-trans isomerization. Different AMMs are produced by introducing various functionalities, such as the introduction of bistability
to create switches. A broad range of AMMs has been designed, featuring
different properties and applications; some of these include molecular motors, switches, and logic gates. A wide range of applications have been demonstrated for AMMs, including those integrated into polymeric, liquid crystal, and crystalline systems for varied functions (such as materials research, homogenous catalysis and surface chemistry).
Terminology
Several
definitions describe a "molecular machine" as a class of molecules
typically described as an assembly of a discrete number of molecular
components intended to produce mechanical movements in response to
specific stimuli. The expression is often more generally applied to
molecules that simply mimic functions that occur at the macroscopic
level.
A few prime requirements for a molecule to be considered a "molecular
machine" are: the presence of moving parts, the ability to consume
energy, and the ability to perform a task. Molecular machines differ from other stimuli-responsive compounds that can produce motion (such as cis-trans isomers) in their relatively larger amplitude of movement (potentially due to chemical reactions) and the presence of a clear external stimulus to regulate the movements (as compared to random thermal motion). Piezoelectric, magnetostrictive,
and other materials that produce a movement due to external stimuli on a
macro-scale are generally not included, since despite the molecular
origin of the motion the effects are not useable on the molecular scale.
This definition generally applies to synthetic molecular
machines, which have historically gained inspiration from the naturally
occurring biological molecular machines (also referred to as
"nanomachines"). Biological machines are considered to be nanoscale
devices (such as molecular proteins) in a living system that convert various forms of energy to mechanical work in order to drive crucial biological processes such as intracellular transport, muscle contractions, ATP generation and cell division.
History
What
would be the utility of such machines? Who knows? I cannot see exactly
what would happen, but I can hardly doubt that when we have some control
of the arrangement of things on a molecular scale we will get an
enormously greater range of possible properties that substances can
have, and of the different things we can do.
Biological molecular machines have been known and studied for years
given their vital role in sustaining life, and have served as
inspiration for synthetically designed systems with similar useful
functionality. The advent of conformational analysis, or the study of conformers
to analyze complex chemical structures, in the 1950s gave rise to the
idea of understanding and controlling relative motion within molecular
components for further applications. This led to the design of
"proto-molecular machines" featuring conformational changes such as
cog-wheeling of the aromatic rings in triptycenes.
By 1980, scientists could achieve desired conformations using external
stimuli and utilize this for different applications. A major example is
the design of a photoresponsive crown ether containing an azobenzene unit, which could switch between cis and trans isomers on exposure to light and hence tune the cation-binding properties of the ether. In his seminal 1959 lecture There's Plenty of Room at the Bottom, Richard Feynman alluded to the idea and applications of molecular devices designed artificially by manipulating matter at the atomic level. This was further substantiated by Eric Drexler during the 1970s, who developed ideas based on molecular nanotechnology such as nanoscale "assemblers", though their feasibility was disputed.
The
first example of an artificial molecular machine (a switchable
molecular shuttle). The positively charged ring (blue) is initially
positioned over the benzidine unit (green), but shifts to the biphenol unit (red) when the benzidine gets protonated (purple) as a result of electrochemicaloxidation or lowering of the pH.
Though these events served as inspiration for the field, the actual
breakthrough in practical approaches to synthesize artificial molecular
machines (AMMs) took place in 1991 with the invention of a "molecular
shuttle" by Sir Fraser Stoddart. Building upon the assembly of mechanically linked molecules such as catenanes and rotaxanes as developed by Jean-Pierre Sauvage in the early 1980s, this shuttle features a rotaxane with a ring that can move across an "axle" between two ends or possible binding sites (hydroquinone units). This design realized the well-defined motion of a molecular unit across the length of the molecule for the first time. In 1994, an improved design allowed control over the motion of the ring by pH variation or electrochemical methods, making it the first example of an AMM. Here the two binding sites are a benzidine and a biphenol
unit; the cationic ring typically prefers staying over the benzidine
ring, but moves over to the biphenol group when the benzidine gets
protonated at low pH or if it gets electrochemically oxidized. In 1998, a study could capture the rotary motion of a decacyclene molecule on a copper-base metallic surface using a scanning tunneling microscope. Over the following decade, a broad variety of AMMs responding to various stimuli were invented for different applications. In 2016, the Nobel Prize in Chemistry was awarded to Sauvage, Stoddart, and Bernard L. Feringa for the design and synthesis of molecular machines.
Over the past few decades, AMMs have diversified rapidly and their design principles, properties, and characterization methods
have been outlined more clearly. A major starting point for the design
of AMMs is to exploit the existing modes of motion in molecules. For instance, single bonds can be visualized as axes of rotation, as can be metallocene complexes. Bending or V-like shapes can be achieved by incorporating double bonds, that can undergo cis-trans isomerization in response to certain stimuli (typically irradiation with a suitable wavelength), as seen in numerous designs consisting of stilbene and azobenzene units. Similarly, ring-opening and -closing reactions such as those seen for spiropyran and diarylethene can also produce curved shapes.
Another common mode of movement is the circumrotation of rings relative
to one another as observed in mechanically interlocked molecules
(primarily catenanes). While this type of rotation can not be accessed
beyond the molecule itself (because the rings are confined within one
another), rotaxanes can overcome this as the rings can undergo
translational movements along a dumbbell-like axis. Another line of AMMs consists of biomolecules such as DNA and proteins as part of their design, making use of phenomena like protein folding and unfolding.
Some
common types of motion seen in some simple components of artificial
molecular machines. a) Rotation around single bonds and in sandwich-like
metallocenes. b) Bending due to cis-trans
isomerization. c) Translational motion of a ring (blue) between two
possible binding sites (red) along the dumbbell-like rotaxane axis
(purple). d) Rotation of interlocked rings (depicted as blue and red
rectangles) in a catenane.
AMM designs have diversified significantly since the early days of the field. A major route is the introduction of bistability
to produce molecular switches, featuring two distinct configurations
for the molecule to convert between. This has been perceived as a step
forward from the original molecular shuttle which consisted of two
identical sites for the ring to move between without any preference, in a
manner analogous to the ring flip in an unsubstituted cyclohexane. If these two sites are different from each other in terms of features like electron density, this can give rise to weak or strong recognition sites as in biological systems — such AMMs have found applications in catalysis and drug delivery.
This switching behavior has been further optimized to acquire useful
work that gets lost when a typical switch returns to its original state.
Inspired by the use of kinetic control to produce work in natural processes, molecular motors are designed to have a continuous energy influx to keep them away from equilibrium to deliver work.
Various energy sources are employed to drive molecular machines
today, but this was not the case during the early years of AMM
development. Though the movements in AMMs were regulated relative to the
random thermal motion generally seen in molecules, they could not be
controlled or manipulated as desired. This led to the addition of
stimuli-responsive moieties in AMM design, so that externally applied
non-thermal sources of energy could drive molecular motion and hence
allow control over the properties. Chemical energy (or "chemical fuels")
was an attractive option at the beginning, given the broad array of reversible chemical reactions (heavily based on acid-base chemistry) to switch molecules between different states.
However, this comes with the issue of practically regulating the
delivery of the chemical fuel and the removal of waste generated to
maintain the efficiency of the machine as in biological systems. Though
some AMMs have found ways to circumvent this, more recently waste-free reactions such based on electron transfers or isomerization have gained attention (such as redox-responsive viologens). Eventually, several different forms of energy (electric, magnetic, optical
and so on) have become the primary energy sources used to power AMMs,
even producing autonomous systems such as light-driven motors.
Types
Various AMMs are tabulated below along with indicative images:
Type
Details
Image
Molecular balance
A molecule that can interconvert between two or more conformational
or configurational states in response to the dynamic of multiple intra-
and intermolecular driving forces,such as hydrogen bonding, solvophobic or hydrophobic effects, π interactions, and steric and dispersion interactions.
The distinct conformers of a molecular balance can show different
interactions with the same molecule, such that analyzing the ratio of
the conformers and the energies for these interactions can enable
quantification of different properties (such as CH-π or arene-arene
interactions, see image).
Molecular hinge
A molecular hinge is a molecule that can typically rotate in a crank-like motion around a rigid axis, such as a double bond or aromatic ring, to switch between reversible configurations. Such configurations must have distinguishable geometries; for instance, azobenzene groups in a linear molecule may undergo cis-trans isomerization when irradiated with ultraviolet light, triggering a reversible transition to a bent or V-shaped conformation (see image). Molecular hinges have been adapted for applications such as nucleobase recognition, peptide modifications, and visualizing molecular motion.
A molecule that performs a logical operation on one or more logic inputs and produces a single logic output. Modelled on logic gates,
these molecules have slowly replaced the conventional silicon-based
machinery. Several applications have come forth, such as water quality
examination, food safety examination, metal ion detection, and pharmaceutical studies.
The first example of a molecular logic gate was reported in 1993,
featuring a receptor (see image) where the emission intensity could be
treated as a tunable output if the concentrations of protons and sodium
ions were to be considered as inputs.
A molecule that is capable of directional rotary motion around a
single or double bond and produce useful work as a result (as depicted
in the image).Carbon nanotube nanomotors have also been produced. Single bond rotary motors are generally activated by chemical reactions whereas double bond rotary motors are generally fueled by light. The rotation speed of the motor can also be tuned by careful molecular design.
Molecular necklace
A class of mechanically interlocked molecules derived from catenanes
where a large macrocycle backbone connects at least three small rings
in the shape of a necklace (see image for example). A molecular necklace
consisting of a large macrocycle threaded by n-1 rings (hence comprising n rings) is represented as [n]MN. The first molecular necklace was synthesized in 1992, featuring several α-cyclodextrins on a single polyethylene glycol
chain backbone; the authors connected this to the idea of a "molecular
abacus" proposed by Stoddart and coworkers around the same time. Several interesting applications have emerged for these molecules, such as antibacterial activity, desulfurization of fuels, and piezoelectricity.
A molecule that can propel fluids when rotated, due to its special
shape that is designed in analogy to macroscopic propellers (see
schematic image on right). It has several molecular-scale blades
attached at a certain pitch angle around the circumference of a
nanoscale shaft.
Propellers have been shown to have interesting properties, such as
variations in pumping rates for hydrophilic and hydrophobic fluids.
A molecule capable of shuttling molecules or ions from one location
to another. This is schematically depicted in the image on the right,
where a ring (in green) can bind to either one of the yellow sites on
the blue macrocyclic backbone.
A common molecular shuttle consists of a rotaxane where the macrocycle
can move between two sites or stations along the dumbbell backbone;
controlling the properties of either site and by regulating conditions
like pH can enable control over which site is selected for binding. This
has led to novel applications in catalysis and drug delivery.
A molecule that can be reversibly shifted between two or more stable
states in response to certain stimuli. This change of states influences
the properties of the molecule according to the state it occupies at
the moment. Unlike a molecular motor, any mechanical work done due to
the motion in a switch is generally undone once the molecule returns to
its original state unless it is part of a larger motor-like system. The
image on the right shows a hydrazone-based switch that switches in response to pH changes.
Host molecules capable of holding items between their two arms.
The open cavity of the molecular tweezers binds items using
non-covalent bonding including hydrogen bonding, metal coordination,
hydrophobic forces, van der Waals forces, π interactions, or electrostatic effects. For instance, the image on the right depicts tweezers formed by corannulene pincers clasping a C60 fullerene molecule, termed "buckycatcher". Examples of molecular tweezers have been reported that are constructed from DNA and are considered DNA machines.
Single-molecule vehicles that resemble macroscopic automobiles and
are important for understanding how to control molecular diffusion on
surfaces. The image on the right shows an example with wheels made of
fullerene molecules. The first nanocars were synthesized by James M. Tour in 2005. They had an H-shaped chassis and 4 molecular wheels (fullerenes) attached to the four corners.
In 2011, Feringa and co-workers synthesized the first motorized nanocar
which had molecular motors attached to the chassis as rotating wheels.
The authors were able to demonstrate directional motion of the nanocar
on a copper surface by providing energy from a scanning tunneling
microscope tip. Later, in 2017, the world's first-ever nanocar race took place in Toulouse.
A ribosome performing the elongation and membrane targeting stages of protein translation. The ribosome is green and yellow, the tRNAs are dark blue, and the other proteins involved are light blue. The produced peptide is released into the endoplasmic reticulum.
Many macromolecular machines are found within cells, often in the form of multi-protein complexes. Examples of biological machines include motor proteins such as myosin, which is responsible for muscle contraction, kinesin, which moves cargo inside cells away from the nucleus along microtubules, and dynein, which moves cargo inside cells towards the nucleus and produces the axonemal beating of motile cilia and flagella.
"[I]n effect, the [motile cilium] is a nanomachine composed of perhaps
over 600 proteins in molecular complexes, many of which also function
independently as nanomachines ... Flexible linkers allow the mobile protein domains connected by them to recruit their binding partners and induce long-range allostery via protein domain dynamics." Other biological machines are responsible for energy production, for example ATP synthase which harnesses energy from proton gradients across membranes to drive a turbine-like motion used to synthesise ATP, the energy currency of a cell. Still other machines are responsible for gene expression, including DNA polymerases for replicating DNA, RNA polymerases for producing mRNA, the spliceosome for removing introns, and the ribosome for synthesising proteins. These machines and their nanoscale dynamics are far more complex than any molecular machines that have yet been artificially constructed.
Biological machines have potential applications in nanomedicine. For example, they could be used to identify and destroy cancer cells. Molecular nanotechnology is a speculative subfield of nanotechnology regarding the possibility of engineering molecular assemblers, biological machines which could re-order matter at a molecular or atomic scale.Nanomedicine would make use of these nanorobots,
introduced into the body, to repair or detect damages and infections,
but these are considered to be far beyond current capabilities.
Research and applications
Advances in this area are inhibited by the lack of synthetic methods. In this context, theoretical modeling has emerged as a pivotal tool to understand the self-assembly or -disassembly processes in these systems.
Possible applications have been demonstrated for AMMs, including those integrated into polymeric, liquid crystal, and crystalline systems for varied functions. Homogenous catalysis is a prominent example, especially in areas like asymmetric synthesis, utilizing noncovalent interactions and biomimetic allosteric catalysis.
AMMs have been pivotal in the design of several stimuli-responsive
smart materials, such as 2D and 3D self-assembled materials and nanoparticle-based systems, for versatile applications ranging from 3D printing to drug delivery.
AMMs are gradually moving from the conventional solution-phase
chemistry to surfaces and interfaces. For instance, AMM-immobilized
surfaces (AMMISs) are a novel class of functional materials consisting
of AMMs attached to inorganic surfaces forming features like
self-assembled monolayers; this gives rise to tunable properties such as
fluorescence, aggregation and drug-release activity.
Most of these "applications" remain at the proof-of-concept
level. Challenges in streamlining macroscale applications include
autonomous operation, the complexity of the machines, stability in the
synthesis of the machines and the working conditions.
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.
Clyde Tombaugh's discovery of Pluto
in 1930 appeared to validate Lowell's hypothesis, and Pluto was
officially named the ninth planet. In 1978, Pluto was conclusively
determined to be too small for its gravity to affect the giant planets,
resulting in a brief search for a tenth planet. The search was largely
abandoned in the early 1990s, when a study of measurements made by the Voyager 2 spacecraft found that the irregularities observed in Uranus's orbit were due to a slight overestimation of Neptune's mass.
After 1992, the discovery of numerous small icy objects with similar or
even wider orbits than Pluto led to a debate over whether Pluto should
remain a planet, or whether it and its neighbours should, like the asteroids, be given their own separate classification. Although a number of the larger members of this group were initially described as planets, in 2006 the International Astronomical Union (IAU) reclassified Pluto and its largest neighbours as dwarf planets, leaving Neptune the farthest known planet in the Solar System.
While the astronomical community widely agrees that Planet X, as
originally envisioned, does not exist, the concept of an
as-yet-unobserved planet has been revived by a number of astronomers to
explain other anomalies observed in the outer Solar System. As of March 2014, observations with the WISE telescope have ruled out the possibility of a Saturn-sized object (95 Earth masses) out to 10,000 AU, and a Jupiter-sized (≈318 Earth masses) or larger object out to 26,000 AU.
In 2014, based on similarities of the orbits of a group of recently discovered extreme trans-Neptunian objects,
astronomers hypothesized the existence of a super-Earth or ice giant
planet, 2 to 15 times the mass of the Earth and beyond 200 AU with
possibly a highly inclined orbit at some 1,500 AU.
In 2016, further work showed this unknown distant planet is likely to
be on an inclined, eccentric orbit that goes no closer than about 200 AU
and no farther than about 1,200 AU from the Sun. The orbit is predicted
to be anti-aligned to the clustered extreme trans-Neptunian objects. Because Pluto is no longer considered a planet by the IAU, this new hypothetical object has become known as Planet Nine.
Jacques Babinet, an early proponent of a trans-Neptunian planet
In the 1840s, the French mathematician Urbain Le Verrier used Newtonian mechanics
to analyse perturbations in the orbit of Uranus, and hypothesised that
they were caused by the gravitational pull of a yet-undiscovered planet.
Le Verrier predicted the position of this new planet and sent his
calculations to German astronomer Johann Gottfried Galle. On 23 September 1846, the night following his receipt of the letter, Galle and his student Heinrich d'Arrest discovered Neptune, exactly where Le Verrier had predicted. There remained some slight discrepancies in the giant planets' orbits. These were taken to indicate the existence of yet another planet orbiting beyond Neptune.
Even before Neptune's discovery, some speculated that one planet
alone was not enough to explain the discrepancy. On 17 November 1834,
the British amateur astronomer the Reverend Thomas John Hussey reported a conversation he had had with French astronomer Alexis Bouvard to George Biddell Airy,
the British Astronomer Royal. Hussey reported that when he suggested to
Bouvard that the unusual motion of Uranus might be due to the
gravitational influence of an undiscovered planet, Bouvard replied that
the idea had occurred to him, and that he had corresponded with Peter Andreas Hansen, director of the Seeberg Observatory in Gotha,
about the subject. Hansen's opinion was that a single body could not
adequately explain the motion of Uranus, and postulated that two planets
lay beyond Uranus.
In 1848, Jacques Babinet
raised an objection to Le Verrier's calculations, claiming that
Neptune's observed mass was smaller and its orbit larger than Le Verrier
had initially predicted. He postulated, based largely on simple
subtraction from Le Verrier's calculations, that another planet of
roughly 12 Earth masses, which he named "Hyperion", must exist beyond
Neptune.
Le Verrier denounced Babinet's hypothesis, saying, "[There is]
absolutely nothing by which one could determine the position of another
planet, barring hypotheses in which imagination played too large a
part."
In 1850 James Ferguson, Assistant Astronomer at the United States Naval Observatory,
noted that he had "lost" a star he had observed, GR1719k, which Lt.
Matthew Maury, the superintendent of the Observatory, claimed was
evidence that it must be a new planet. Subsequent searches failed to
recover the "planet" in a different position, and in 1878, CHF Peters, director of the Hamilton College Observatory in New York, showed that the star had not in fact vanished, and that the previous results had been due to human error.
In 1879, Camille Flammarion noted that the comets 1862 III and 1889 III had aphelia of 47 and 49 AU,
respectively, suggesting that they might mark the orbital radius of an
unknown planet that had dragged them into an elliptical orbit. Astronomer George Forbes
concluded on the basis of this evidence that two planets must exist
beyond Neptune. He calculated, based on the fact that four comets
possessed aphelia at around 100 AU and a further six with aphelia
clustered at around 300 AU, the orbital elements of a pair of
hypothetical trans-Neptunian planets. These elements accorded
suggestively with those made independently by another astronomer named David Peck Todd, suggesting to many that they might be valid. However, sceptics argued that the orbits of the comets involved were still too uncertain to produce meaningful results. Some have considered Forbes's hypothesis a precursor to Planet Nine.
In 1900 and 1901, Harvard College Observatory director William Henry Pickering led two searches for trans-Neptunian planets. The first was begun by Danish astronomer Hans Emil Lau
who, after studying the data on the orbit of Uranus from 1690 to 1895,
concluded that one trans-Neptunian planet alone could not account for
the discrepancies in its orbit, and postulated the positions of two
planets he believed were responsible. The second was launched when
Gabriel Dallet suggested that a single trans-Neptunian planet lying at
47 AU could account for the motion of Uranus. Pickering agreed to
examine plates for any suspected planets. In neither case were any
found.
In 1902, after observing the orbits of comets with aphelia beyond Neptune, Theodor Grigull of Münster,
Germany proclaimed the existence of a Uranus-sized planet at 50 AU with
a 360-year period, which he named Hades, cross-checking with the
deviations in the orbit of Uranus. In 1921, Grigull revised his orbital
period to 310–330 years, to better fit the observed deviations.
In 1909, Thomas Jefferson Jackson See,
an astronomer with a reputation as an egocentric contrarian, opined
"there is certainly one, most likely two and possibly three planets
beyond Neptune".
Tentatively naming the first planet "Oceanus", he placed their
respective distances at 42, 56 and 72 AU from the Sun. He gave no
indication as to how he determined their existence, and no known
searches were mounted to locate them.
In 1911, Indian astronomer Venkatesh P. Ketakar suggested the existence of two trans-Neptunian planets, which he named after the Hindu gods Brahma and Vishnu, by reworking the patterns observed by Pierre-Simon Laplace in the planetary satellites of Jupiter and applying them to the outer planets. The three inner Galilean moons of Jupiter, Io, Europa and Ganymede, are locked in a complicated 1:2:4 resonance called a Laplace resonance.
Ketakar suggested that Uranus, Neptune and his hypothetical
trans-Neptunian planets were also locked in Laplace-like resonances.
This is incorrect; Uranus and Neptune, while in a near-2:1 resonance,
are not in full resonance.
His calculations predicted a mean distance for Brahma of 38.95 AU and
an orbital period of 242.28 Earth years (3:4 resonance with Neptune).
When Pluto was discovered 19 years later, its mean distance of 39.48 AU
and orbital period of 248 Earth years were close to Ketakar's prediction
(Pluto in fact has a 2:3 resonance with Neptune).
Ketakar made no predictions for the orbital elements other than mean
distance and period. It is not clear how Ketakar arrived at these
figures, and his second planet, Vishnu, was never located.
In 1894, with the help of William Pickering, Percival Lowell (a wealthy Bostonian) founded the Lowell Observatory in Flagstaff, Arizona.
In 1906, convinced he could resolve the conundrum of Uranus's orbit, he
began an extensive project to search for a trans-Neptunian planet, which he named Planet X, a name previously used by Gabriel Dallet. The X in the name represents an unknown and is pronounced as the letter, as opposed to the Roman numeral
for 10 (at the time, Planet X would have been the ninth planet).
Lowell's hope in tracking down Planet X was to establish his scientific
credibility, which had eluded him due to his widely derided belief that
channel-like features visible on the surface of Mars were canals constructed by an intelligent civilization.
Lowell's first search focused on the ecliptic, the plane encompassed by the zodiac
where the other planets in the Solar System lie. Using a 5-inch
photographic camera, he manually examined over 200 three-hour exposures
with a magnifying glass, and found no planets. At that time Pluto was
too far above the ecliptic to be imaged by the survey. After revising his predicted possible locations, Lowell conducted a second search from 1914 to 1916. In 1915, he published his Memoir of a Trans-Neptunian Planet, in which he concluded that Planet X had a mass roughly seven times that of Earth—about half that of Neptune—and a mean distance from the Sun of 43 AU. He assumed Planet X would be a large, low-density object with a high albedo, like the giant planets. As a result, it would show a disc with diameter of about one arcsecond and an apparent magnitude between 12 and 13—bright enough to be spotted.
Separately, in 1908,
Pickering announced that, by analysing irregularities in Uranus's orbit,
he had found evidence for a ninth planet. His hypothetical planet,
which he termed "Planet O" (because it came after "N", i.e. Neptune), possessed a mean orbital radius of 51.9 AU and an orbital period of 373.5 years. Plates taken at his observatory in Arequipa, Peru, showed no evidence for the predicted planet, and British astronomer P. H. Cowell
showed that the irregularities observed in Uranus's orbit virtually
disappeared once the planet's displacement of longitude was taken into
account.
Lowell himself, despite his close association with Pickering, dismissed
Planet O out of hand, saying, "This planet is very properly designated
"O", [for it] is nothing at all."
Unbeknownst to Pickering, four of the photographic plates taken in the
search for "Planet O" by astronomers at the Mount Wilson Observatory in
1919 captured images of Pluto, though this was only recognised years later.[25] Pickering went on to suggest many other possible trans-Neptunian planets up to the year 1932, which he named P, Q, R, S, T, and U; none were ever detected.
Lowell's sudden death in 1916 temporarily halted the search for
Planet X. Failing to find the planet, according to one friend,
"virtually killed him".
Lowell's widow, Constance, engaged in a legal battle with the
observatory over Lowell's legacy which halted the search for Planet X
for several years.
In 1925, the observatory obtained glass discs for a new 13 in (33 cm)
wide-field telescope to continue the search, constructed with funds from
Abbott Lawrence Lowell, Percival's brother. In 1929 the observatory's director, Vesto Melvin Slipher, summarily handed the job of locating the planet to Clyde Tombaugh,
a 22-year-old Kansas farm boy who had only just arrived at the Lowell
Observatory after Slipher had been impressed by a sample of his
astronomical drawings.
Tombaugh's task was to systematically capture sections of the
night sky in pairs of images. Each image in a pair was taken two weeks
apart. He then placed both images of each section in a machine called a blink comparator, which by exchanging images quickly created a time lapse
illusion of the movement of any planetary body. To reduce the chances
that a faster-moving (and thus closer) object be mistaken for the new
planet, Tombaugh imaged each region near its opposition point, 180
degrees from the Sun, where the apparent retrograde motion
for objects beyond Earth's orbit is at its strongest. He also took a
third image as a control to eliminate any false results caused by
defects in an individual plate. Tombaugh decided to image the entire
zodiac, rather than focus on those regions suggested by Lowell.
Discovery photographs of Pluto
By the beginning of 1930, Tombaugh's search had reached the
constellation of Gemini. On 18 February 1930, after searching for nearly
a year and examining nearly 2 million stars, Tombaugh discovered a
moving object on photographic plates taken on 23 January and 29 January
of that year. A lesser-quality photograph taken on January 21 confirmed the movement. Upon confirmation, Tombaugh walked into Slipher's office and declared, "Doctor Slipher, I have found your Planet X."
The object was just six degrees from one of two locations for Planet X
Lowell had suggested; thus it seemed he had at last been vindicated. After the observatory obtained further confirmatory photographs, news of the discovery was telegraphed to the Harvard College Observatory on March 13, 1930. The new object was later precovered on photographs dating back to 19 March 1915. The decision to name the object Pluto was intended in part to honour Percival Lowell, as his initials made up the word's first two letters. After discovering Pluto, Tombaugh continued to search the ecliptic for other distant objects. He found hundreds of variable stars and asteroids, as well as two comets, but no further planets.
To the observatory's disappointment and surprise, Pluto showed no
visible disc; it appeared as a point, no different from a star, and, at
only 15th magnitude, was six times dimmer than Lowell had predicted,
which meant it was either very small, or very dark. Because of Lowell's predictions, astronomers thought that Pluto would be massive enough to perturb planets. This led them to assume that its albedo
could be no less than 0.07 (meaning that, at minimum, it would reflect
7% of the light that hit it), which would have made Pluto about as dark
as asphalt, and similar in reflectivity to the least reflective planet,
which is Mercury. This would have given Pluto an estimated mass of no more than 70% that of Earth. Observations also revealed that Pluto's orbit was very elliptical, far more than that of any other planet.
Almost immediately, some astronomers questioned Pluto's status as
a planet. Barely a month after its discovery was announced, on April
14, 1930, in an article in The New York Times, Armin O. Leuschner
suggested that Pluto's dimness and high orbital eccentricity made it
more similar to an asteroid or comet: "The Lowell result confirms the
possible high eccentricity announced by us on April 5. Among the
possibilities are a large asteroid greatly disturbed in its orbit by
close approach to a major planet such as Jupiter, or it may be one of
many long-period planetary objects yet to be discovered, or a bright
cometary object." In that same article, Harvard Observatory director Harlow Shapley
wrote that Pluto was a "member of the Solar System not comparable with
known asteroids and comets, and perhaps of greater importance to
cosmogony than would be another major planet beyond Neptune." In 1931, after examining the structure of the residuals of Uranus' longitude using a trigonometric formula, Ernest W. Brown asserted (in agreement with E. C. Bower)
that the presumed irregularities in the orbit of Uranus could not be
due to the gravitational effect of a more distant planet, and thus that
Lowell's supposed prediction was "purely accidental".
Throughout the mid-20th century, estimates of Pluto's mass were
revised downward. In 1931, Nicholson and Mayall calculated its mass,
based on its supposed effect on the giant planets, as roughly that of
Earth; a value somewhat in accord with the 0.91 Earth mass calculated in 1942 by Lloyd R. Wylie at the US Naval Observatory, using the same assumptions. In 1949, Gerard Kuiper's measurements of Pluto's diameter with the 200-inch telescope at Mount Palomar Observatory
led him to the conclusion that it was midway in size between Mercury
and Mars and that its mass was most probably about 0.1 Earth mass.
In 1973, based on the similarities in the periodicity and amplitude of brightness variation with Triton,
Dennis Rawlins conjectured Pluto's mass must be similar to Triton's. In
retrospect, the conjecture turns out to have been correct; it had been
argued by astronomers Walter Baade and E.C. Bower as early as 1934.
However, because Triton's mass was then believed to be roughly 2.5% of
the Earth–Moon system (more than ten times its actual value), Rawlins's
determination for Pluto's mass was similarly incorrect. It was
nonetheless a meagre enough value for him to conclude Pluto was not
Planet X. In 1976, Dale Cruikshank, Carl Pilcher, and David Morrison of the University of Hawaii analysed spectra from Pluto's surface and determined that it must contain methaneice,
which is highly reflective. This meant that Pluto, far from being dark,
was in fact exceptionally bright, and thus was probably no more than 1⁄100 Earth mass.
Mass estimates for Pluto
Year
Mass
Notes
1931
1 Earth
Nicholson & Mayall
1942
0.91 Earth
Wylie
1948
0.1 (1/10 Earth)
Kuiper
1973
0.025 (1/40 Earth)
Rawlins
1976
0.01 (1/100 Earth)
Cruikshank, Pilcher, & Morrison
1978
0.002 (1/500 Earth)
Christy & Harrington
2006
0.00218 (1/459 Earth)
Buie et al.
Pluto's size was finally determined conclusively in 1978, when American astronomer James W. Christy discovered its moon Charon. This enabled him, together with Robert Sutton Harrington
of the U.S. Naval Observatory, to measure the mass of the Pluto–Charon
system directly by observing the moon's orbital motion around Pluto. They determined Pluto's mass to be 1.31×1022 kg;
roughly one five-hundredth that of Earth or one-sixth that of the Moon,
and far too small to account for the observed discrepancies in the
orbits of the outer planets. Lowell's prediction had been a coincidence:
If there was a Planet X, it was not Pluto.
Further searches for Planet X
After
1978, a number of astronomers kept up the search for Lowell's Planet X,
convinced that, because Pluto was no longer a viable candidate, an
unseen tenth planet must have been perturbing the outer planets.
In the 1980s and 1990s, Robert Harrington led a search to determine the real cause of the apparent irregularities.
He calculated that any Planet X would be at roughly three times the
distance of Neptune from the Sun; its orbit would be highly eccentric, and strongly inclined to the ecliptic—the planet's orbit would be at roughly a 32-degree angle from the orbital plane of the other known planets. This hypothesis was met with a mixed reception. Noted Planet X skeptic Brian G. Marsden of the Minor Planet Center
pointed out that these discrepancies were a hundredth the size of those
noticed by Le Verrier, and could easily be due to observational error.
In 1972, Joseph Brady of the Lawrence Livermore National Laboratory studied irregularities in the motion of Halley's Comet. Brady claimed that they could have been caused by a Jupiter-sized planet beyond Neptune at 59 AU that is in a retrograde orbit around the Sun. However, both Marsden and Planet X proponent P. Kenneth Seidelmann
attacked the hypothesis, showing that Halley's Comet randomly and
irregularly ejects jets of material, causing changes to its own orbital
trajectory, and that such a massive object as Brady's Planet X would
have severely affected the orbits of known outer planets.
Although its mission did not involve a search for Planet X, the IRAS
space observatory made headlines briefly in 1983 due to an "unknown
object" that was at first described as "possibly as large as the giant
planet Jupiter and possibly so close to Earth that it would be part of
this Solar System". Further analysis revealed that of several unidentified objects, nine were distant galaxies and the tenth was "interstellar cirrus"; none were found to be Solar System bodies.
In 1988, A. A. Jackson and R. M. Killen studied the stability of
Pluto's resonance with Neptune by placing test "Planet X-es" with
various masses and at various distances from Pluto. Pluto and Neptune's
orbits are in a 3:2 resonance, which prevents their collision or even
any close approaches, regardless of their separation in the z axis.
It was found that the hypothetical object's mass had to exceed 5 Earth
masses to break the resonance, and the parameter space is quite large
and a large variety of objects could have existed beyond Pluto without
disturbing the resonance. Four test orbits of a trans-Plutonian planet
have been integrated forward for four million years in order to
determine the effects of such a body on the stability of the
Neptune–Pluto 3:2 resonance. Planets beyond Pluto with masses of 0.1 and
1.0 Earth masses in orbits at 48.3 and 75.5 AU, respectively, do not
disturb the 3:2 resonance. Test planets of 5 Earth masses with
semi-major axes of 52.5 and 62.5 AU disrupt the four-million-year
libration of Pluto's argument of perihelion.
Planet X disproved
Harrington died in January 1993, without having found Planet X. Six months before, E. Myles Standish had used data from Voyager 2's 1989 flyby of Neptune, which had revised the planet's total mass downward by 0.5%—an amount comparable to the mass of Mars—to recalculate its gravitational effect on Uranus. When Neptune's newly determined mass was used in the Jet Propulsion Laboratory Developmental Ephemeris (JPL DE), the supposed discrepancies in the Uranian orbit, and with them the need for a Planet X, vanished. There are no discrepancies in the trajectories of any space probes such as Pioneer 10, Pioneer 11, Voyager 1, and Voyager 2 that can be attributed to the gravitational pull of a large undiscovered object in the outer Solar System. Today, most astronomers agree that Planet X, as Lowell defined it, does not exist.
After the discovery of Pluto and Charon, no more trans-Neptunian objects (TNOs) were found until 15760 Albion in 1992. Since then, thousands of such objects have been discovered. Most are now recognized as part of the Kuiper belt, a swarm of icy bodies left over from the Solar System's formation that orbit near the ecliptic plane just beyond Neptune. Though none were as large as Pluto, some of these distant trans-Neptunian objects, such as Sedna, were initially described in the media as "new planets".
In 2005, astronomer Mike Brown and his team announced the discovery of 2003 UB313 (later named Eris after the Greek goddess of discord and strife), a trans-Neptunian object then thought to be just barely larger than Pluto. Soon afterwards, a NASA Jet Propulsion Laboratory press release described the object as the "tenth planet".
Eris was never officially classified as a planet, and the 2006 definition of planet defined both Eris and Pluto not as planets but as dwarf planets because they have not cleared their neighbourhoods.
They do not orbit the Sun alone, but as part of a population of
similarly sized objects. Pluto itself is now recognized as being a
member of the Kuiper belt and the largest dwarf planet, larger than the
more massive Eris.
A number of astronomers, most notably Alan Stern, the head of NASA's New Horizons
mission to Pluto, contend that the IAU's definition is flawed, and that
Pluto and Eris, and all large trans-Neptunian objects, such as Makemake, Sedna, Quaoar, Gonggong and Haumea, should be considered planets in their own right.
However, the discovery of Eris did not rehabilitate the Planet X theory
because it is far too small to have significant effects on the outer
planets' orbits.
Subsequently proposed trans-Neptunian planets
Although
most astronomers accept that Lowell's Planet X does not exist, a number
have revived the idea that a large unseen planet could create
observable gravitational effects in the outer Solar System. These
hypothetical objects are often referred to as "Planet X", although the
conception of these objects may differ considerably from that proposed
by Lowell.
The
orbit of Sedna (red) set against the orbits of Jupiter (orange), Saturn
(yellow), Uranus (green), Neptune (blue), and Pluto (purple)
Sedna's orbit
When Sedna
was discovered, its extreme orbit raised questions about its origin.
Its perihelion is so distant (approximately 76 AU (11.4 billion km;
7.1 billion mi)) that no currently observed mechanism can explain
Sedna's eccentric distant orbit. It is too far from the planets to have
been affected by the gravity of Neptune or the other giant planets and
too bound to the Sun to be affected by outside forces such as the galactic tides. Hypotheses to explain its orbit include that it was affected by a passing star, that it was captured from another planetary system, or that it was tugged into its current position by a trans-Neptunian planet.
The most obvious solution to determining Sedna's peculiar orbit would
be to locate a number of objects in a similar region, whose various
orbital configurations would provide an indication as to their history.
If Sedna had been pulled into its orbit by a trans-Neptunian planet, any
other objects found in its region would have a similar perihelion to
Sedna (around 80 AU (12 billion km; 7.4 billion mi)).
Excitement of Kuiper belt orbits
In
2008, Tadashi Mukai and Patryk Sofia Lykawka suggested a distant Mars-
or Earth-sized planet, currently in a highly eccentric orbit between 100
and 200 AU
and orbital period of 1000 years with an inclination of 20° to 40°, was
responsible for the structure of the Kuiper belt. They proposed that
the perturbations of this planet excited the eccentricities and
inclinations of the trans-Neptunian objects, truncated the planetesimal disk at 48 AU, and detached the orbits of objects like Sedna from Neptune. During Neptune's migration
this planet is posited to have been captured in an outer resonance of
Neptune and to have evolved into a higher perihelion orbit due to the Kozai mechanism leaving the remaining trans-Neptunian objects on stable orbits.
Elongated orbits of group of Kuiper belt objects
In
2012, Rodney Gomes modelled the orbits of 92 Kuiper belt objects and
found that six of those orbits were far more elongated than the model
predicted. He concluded that the simplest explanation was the
gravitational pull of a distant planetary companion, such as a
Neptune-sized object at 1,500 AU. This Neptune-sized object would cause
the perihelia of objects with semi-major axes greater than 300 AU to
oscillate, delivering them into planet-crossing orbits like those of (308933) 2006 SQ372 and (87269) 2000 OO67 or detached orbits like Sedna's.
Prediction of hypothetical Planet Nine's orbit based on unique clustering
In 2014, astronomers announced the discovery of 2012 VP113, a large object with a Sedna-like 4,200-year orbit and a perihelion of roughly 80 AU, which led them to suggest that it offered evidence of a potential trans-Neptunian planet. Trujillo and Sheppard argued that the orbital clustering of arguments of perihelia for 2012 VP113 and other extremely distant TNOs suggests the existence of a "super-Earth" of between 2 and 15 Earth masses beyond 200 AU and possibly on an inclined orbit at 1,500 AU.
In 2014 astronomers at the Universidad Complutense in Madrid suggested that the available data actually indicates more than one trans-Neptunian planet;
subsequent work further suggests that the evidence is robust enough but
rather than connected with the longitudes of the ascending nodes and
the arguments of perihelia, semi-major axes and nodal distances could be
the signposts.
Additional work based on improved orbits of 39 objects still indicates
that more than one perturber could be present and that one of them could
orbit the Sun at 300-400 AU.
On January 20, 2016, Brown and Konstantin Batygin published an article corroborating Trujillo and Sheppard's initial findings; proposing a super-Earth (dubbed Planet Nine) based on a statistical clustering of the arguments of perihelia (noted before) near zero and also ascending nodes near 113° of six distant trans-Neptunian objects. They estimated it to be ten times the mass of Earth (about 60% the mass of Neptune) with a semimajor axis of approximately 400–1500 AU.
Probability
Even
without gravitational evidence, Mike Brown, the discoverer of Sedna,
has argued that Sedna's 12,000-year orbit means that probability alone
suggests that an Earth-sized object exists beyond Neptune. Sedna's orbit
is so eccentric that it spends only a small fraction of its orbital
period near the Sun, where it can be easily observed. This means that
unless its discovery was a freak accident, there is probably a
substantial population of objects roughly Sedna's diameter yet to be
observed in its orbital region. Mike Brown noted that
Sedna is about three-quarters the
size of Pluto. If there are sixty objects three-quarters the size of
Pluto [out there] then there are probably forty objects the size of
Pluto ... If there are forty objects the size of Pluto, then there are
probably ten that are twice the size of Pluto. There are probably three
or four that are three times the size of Pluto, and the biggest of these
objects ... is probably the size of Mars or the size of the Earth.
However, Brown notes that even though it might approach or exceed
Earth in size, should such an object be found it would still be a "dwarf
planet" by the current definition, because it would not have cleared
its neighbourhood sufficiently.
Kuiper cliff and "Planet Ten"
Additionally, speculation of a possible trans-Neptunian planet has revolved around the so-called "Kuiper cliff".
The Kuiper belt terminates suddenly at a distance of 48 AU
(7.2 billion km; 4.5 billion mi) from the Sun. Brunini and Melita have
speculated that this sudden drop-off may be attributed to the presence
of an object with a mass between those of Mars and Earth located beyond
48 AU.
The presence of an object with a mass similar to that of Mars in a
circular orbit at 60 AU (9.0 billion km; 5.6 billion mi) leads to a
trans-Neptunian object population incompatible with observations. For
instance, it would severely deplete the plutino population.
Astronomers have not excluded the possibility of an object with a mass
similar to that of Earth located farther than 100 AU (15 billion km;
9.3 billion mi) with an eccentric and inclined orbit. Computer simulations by Patryk Lykawka of Kobe University have suggested that an object with a mass between 0.3~0.7ME,
ejected outward by Neptune early in the Solar System's formation and
currently in an elongated orbit between 101 and 200 AU (15.1 and
29.9 billion km; 9.4 and 18.6 billion mi) from the Sun, could explain
the Kuiper cliff and the peculiar detached objects such as Sedna and 2012 VP113.
Although some astronomers, such as Renu Malhotra and David
Jewitt, have cautiously supported these claims, others, such as
Alessandro Morbidelli, have dismissed them as "contrived". Malhotra & Volk (2017)
argued that an unexpected variance in inclination for KBOs farther than
the cliff at 50 AU (7.5 billion km; 4.6 billion mi) provided evidence
of a possible Mars-sized planet, possibly up to 2.4ME, residing at the edge of the Solar System, which many news sources began referring to as "Planet Ten". Shortly after it was proposed, Lorenzo Iorio showed that the hypothetical planet's existence cannot be ruled out by Cassini ranging data.
Starting in 2018, several surveys have discovered multiple
objects located beyond the Kuiper Cliff. Some of these new discoveries
are close to the heliopause (120 AU) or well beyond it (2018 VG18, 2018 AG37, 2020 BE102, 2020 MK53).
An analysis of the TNO data available prior to September 2023 shows
that there is a gap at about 72 AU, far from any mean-motion resonances
with Neptune. Such a gap may have been induced by a massive perturber located further away.
Other proposed planets
Tyche was a hypothetical gas giant proposed to be located in the Solar System's Oort cloud. It was first proposed in 1999 by astrophysicists John Matese, Patrick Whitman and Daniel Whitmire of the University of Louisiana at Lafayette. They argued that evidence of Tyche's existence could be seen in a supposed bias in the points of origin for long-period comets. In 2013, Matese and Whitmire
re-evaluated the comet data and noted that Tyche, if it existed, would
be detectable in the archive of data that was collected by NASA's Wide-field Infrared Survey Explorer (WISE) telescope.
In 2014, NASA announced that the WISE survey had ruled out any object
with Tyche's characteristics, indicating that Tyche as hypothesized by
Matese, Whitman, and Whitmire does not exist.
Conversely, in 1999, British astronomer John Murray theorized the
existence of a Jupiter-sized planet similar to Tyche 32,000
astronomical units away from the Sun in a retrograde orbit. Murray
estimates that the planet would be located in the constellation of Delphinus.
These parameters, also based on the orbits of various long-period
comets, are different from those originally hypothesized by Matese,
Whitman, and Whitmire for Tyche, and hence signify a different object. Unlike Tyche, this putative planet lies outside the 26,000 AU limit set by mid-infrared observations by the WISE telescope, but this limit can be as high as 82,000 AU based on albedo. A brown dwarf, for instance, would have a smaller albedo than a Jupiter analog.
The oligarch theory of planet formation
states that there were hundreds of planet-sized objects, known as
oligarchs, in the early stages of the Solar System's evolution. In 2005,
astronomer Eugene Chiang speculated that although some of these
oligarchs became the planets we know today, most would have been flung
outward by gravitational interactions. Some may have escaped the Solar
System altogether to become free-floating planets,
whereas others would be orbiting in a halo around the Solar System,
with orbital periods of millions of years. This halo would lie at
between 1,000 and 10,000 AU (150 and 1,500 billion km; 93 and
930 billion mi) from the Sun, or between a third and a thirtieth the
distance to the Oort cloud.
In December 2015, astronomers at the Atacama Large Millimeter Array
(ALMA) detected a brief series of 350 GHz pulses that they concluded
must either be a series of independent sources, or a single, fast moving
source. Deciding that the latter was the most likely, they calculated
based on its speed that, were it bound to the Sun, the object, which
they named "Gna" after a fast-moving messenger goddess in Norse mythology, would be about 12–25 AU distant and have a dwarf planet-sized diameter of 220 to 880 km. However, if it were a rogue planet not gravitationally bound to the Sun, and as far away as 4000 AU, it could be much larger. The paper was never formally accepted, and has been withdrawn until the detection is confirmed.
Scientists' reactions to the notice were largely sceptical; Mike Brown
commented that, "If it is true that ALMA accidentally discovered a
massive outer Solar System object in its tiny, tiny, tiny, field of
view, that would suggest that there are something like 200,000
Earth-sized planets in the outer Solar System ... Even better, I just
realized that this many Earth-sized planets existing would destabilize
the entire Solar System and we would all die."
Constraints on additional planets
As of 2023 the following observations severely constrain the mass and distance of any possible additional Solar System planet:
An analysis of mid-infrared observations with the WISE telescope have ruled out the possibility of a Saturn-sized object (95 Earth masses) out to 10,000 AU, and a Jupiter-sized or larger object out to 26,000 AU. WISE
has continued to take more data since then, and NASA has invited the
public to help search this data for evidence of planets beyond these
limits, via the Backyard Worlds: Planet 9 citizen science project.
Using modern data on the anomalous precession
of the perihelia of Saturn, Earth, and Mars, Lorenzo Iorio concluded
that any unknown planet with a mass of 0.7 times that of Earth must be
farther than 350–400 AU; one with a mass of 2 times that of Earth,
farther than 496–570 AU; and finally one with a mass of 15 times that of
Earth, farther than 970–1,111 AU.
Moreover, Iorio stated that the modern ephemerides of the Solar System
outer planets has provided even tighter constraints: no celestial body
with a mass of 15 times that of Earth can exist closer than
1,100–1,300 AU.
However, work by another group of astronomers using a more
comprehensive model of the Solar System found that Iorio's conclusion
was only partially correct. Their analysis of Cassini
data on Saturn's orbital residuals found that observations were
inconsistent with a planetary body with the orbit and mass similar to
those of Batygin and Brown's Planet Nine having a true anomaly
of −130° to −110°, or −65° to 85°. Furthermore, the analysis found that
Saturn's orbit is slightly better explained if such a body is located
at a true anomaly of 117.8°+11° −10°. At this location, it would be approximately 630 AU from the Sun.
Using public data on the orbits of the extreme trans-Neptunian objects,
it has been confirmed that a statistically significant (62σ) asymmetry
between the shortest mutual ascending and descending nodal distances
does exist; in addition, multiple highly improbably (p < 0.0002)
correlated pairs of orbits with mutual nodal distances as low as 0.2 AU
at 152 AU from the Solar System's barycentre or 1.3 AU at 339 AU have
been found.
Both findings suggest that massive perturbers may exist at hundreds of
AUs from the Sun and are difficult to explain within the context of a
uniform distribution of orbital orientations in the outermost Solar
System.
