Clearing the Neighbourhood: Definition of 'Orbital Region'?

Clearing the Neighbourhood: Definition of 'Orbital Region'?





Is there a formal way to define the 'neighbourhood'?




Margot's $Pi$ uses $2sqrt 3$ times the Hill radius.





Planets in deep space

Well, we just became aware that there are likely thousands of planet sized objects in wide orbits around the sun. There could be thousands more planet sized objects ejected from orbit.

We can measure the mass of the galaxy by the orbital speed of the objects in it. Not easy because they are so big, but doable for many.

There are many ways planets can end up in deep space. Interactions with other planets (especially early in the solar system's life-cycle when there are dozens of large objects forming, colliding, and affecting each other), gravitational interactions from passing stars and black holes in which a planet gets caught in the crossfire and expelled from its solar system (more common in star clusters and closer in towards the center of the galaxy), being "released" from a solar system due reduced gravity of a parent sun when it goes through the red giant phase and expels most of its mass in fierce solar winds (a future possibility for Earth), or even due to supernovae. All of these are possible and even likely throughout the galaxy. Raw guesses on numbers are not really possible, but billions of interstellar wanderers may be plausible from what I have read. And over the vast eons of time, almost any interaction that can occur, will occur, throughout the galaxy and universe. Not only that, many of these wandering "dark" planets may have internal sources of heat, sub-glacial oceans, and primitive life. So the answer to your question is most definitely "yes", but actual data is hard to come by because we can't see these objects at all.

As for your question relating to overall mass of the galaxy, I would guess the contribution from a few billion interstellar planets would be negligible in a galaxy with hundreds of billions of stars, considering that stars can be millions of times the mass of a single planet, and super-massive black holes billions of times more massive than the stars.

Types of resonance

In general, an orbital resonance may

  • involve one or any combination of the orbit parameters (e.g. eccentricity versus semimajor axis, or eccentricity versus orbital inclination).
  • act on any time scale from short term, commensurable with the orbit periods, to secular, measured in 10 4 to 10 6 years.









The perihelion secular resonance between asteroids and Saturn (ν6 = g -g6) helps shape the asteroid belt. Asteroids which approach it have their eccentricity slowly increased until they become Mars-crossers, at which point they are usually ejected from the asteroid belt by a close pass to Mars. This resonance forms the inner and "side" boundaries of the asteroid belt around 2 AU, and at inclinations of about 20°.

Numerical simulations have suggested that the eventual formation of a perihelion secular resonance between Mercury and Jupiter (g1=g5) has the potential to greatly increase Mercury's eccentricity and possibly destabilize the inner Solar System several billion years from now. [ 6 ] [ 7 ]

The Titan Ringlet within Saturn's C Ring represents another type of resonance in which the rate of apsidal precession of one orbit exactly matches the speed of revolution of another. The outer end of this eccentric ringlet always points towards Saturn's major moon Titan.


In an example of another type of resonance involving orbital eccentricity, the eccentricities of Ganymede and Callisto vary with a common period of 181 years, although with opposite phases. [ 8 ]


Astronomical observations of distant stars tell us that many have planets orbiting them, and that some are of a size and density and orbital distance such that temperatures suitable for life are theoretically possible.

Scientists can search for exoplanets only within a limited range of orbital distances.


There’s protection from micrometeorites based on a similar design for the current orbital EMUs.

Such conjunctions recur every two decades owing to their orbital periods.






But, because of it's great mass, our orbital velocity is something terrific!

Our orbital velocity is seven hundred thousand kilometers per second!

At the orbital velocity of the ship, focussing on the star was indeed a difficult thing to do.

The rotations of the planets and the sun are in the same direction as the orbital motions and nearly in the same plane.

Is there any connection between their orbital distances, or between their orbits and the times of describing them?

Part 2

In order to understand where the fuel for the solar nebula came from, it is important to examine the stages of the life cycle of a star, which results in the formation of the heavier elements that we find in our solar system. This “stardust” is thought to have been a part of our solar system since the beginning, when it was a diffuse nebula.

-Nebula: a cloud of gas and dust in space.

– Interstellar medium: gas and dust found in the spaces between stars.

  • Interstellar dust: microscopic grains of dust, composed of elements like carbon, silicon, oxygen and iron.
  • Molecular cloud: when a gas cloud cools sufficiently, the atoms can form into molecules creating a molecular cloud (not all elements can form molecules).

– Thermal pressure: pressure in a gas arising from the motions of its
particles in relation to the object’s temperature.

-Protostar: A forming star which has not yet reached temperatures and pressures required for sustained fusion to occur in its core.

-Protostellar disk: A disk of material surrounding a protostar. Sometimes
these disks coalesce into planetary solar systems.

-Convection: the energy transport process in which warm material expands.

rises while cooler material contracts and falls to the centre.

-Self -Sustaining Fusion: Fusion which occurs where the energy being created in the fusion process is radiated away at the same rate, effectively halting gravitational contraction, and bringing the star in equilibrium.

Stardust as “Fuel” for Solar Nebula

With the exception of hydrogen and helium, many of the elements found in our solar system were not formed during the Big Bang, but were instead formed during the various stages of the life cycle of a star. By analyzing the processes by which these elements are formed, it possible to achieve a greater understanding of how solar nebula are formed, and how our solar system was formed as a result.

In order to understand how stardust becomes fuel for solar nebula, it is important to examine the stages of the life cycle of a star that result the formation of the elements that we find in our solar system.

Formation of Solar Nebula

To understand the formation of the solar nebula, we need to understand the life cycle of a star. Stars are born in an area of high density Nebula, by condensing into a large globule of gas and dust that contracts under its own gravity. Specifically, they begin forming in cold and dense regions of the interstellar medium known as molecular clouds. The temperature of these clouds is between 10K and 30K (Kelvin) and have an average density of 300 molecules per cubic centimetre, which is almost a million trillion times less dense than the Earth’s atmosphere. Although this doesn’t seem dense enough to form into anything, it is far denser than empty space. These clouds consist mostly of molecular hydrogen (i.e. H2) since helium atoms do not combine with other atoms to form molecules, but there are also elements like carbon, silicon, oxygen and iron present in the form of interstellar dust, which will be discussed below.

By overcoming the thermal pressure of the gas cloud, gravity causes the densest regions (often referred to as “clumps”) of these clouds to contract, coalescing into increasingly dense regions of interstellar gas and dust. The contraction also eventually results in the fragmentation of the clump from the gas cloud, caused by the dense regions of the cloud contracting (overcoming the thermal pressure) to the point that they break away. The contraction converts some of the clouds gravitational potential energy into thermal energy. Due to the opaqueness of the aforementioned interstellar dust within the cloud, this heat cannot be radiated away as fast as the heat is created by gravitational contraction. The object that results is an increasingly hot and dense molecular mass called a protostar.

Protostar to Main Sequence Star

The protostar stage is the first stage in a star’s life cycle, occurring after the initial gravitational collapse of the nebula, but before the star begins fusing hydrogen to create heavier elements. The stages leading up to this “hydrogen fusion” stage are summarised in Table 1.1. [v]

Convective contraction The protostar surface temperature remains near 3000K while convection is the dominant form of energy transport. Gravitational contraction continues increasing the core temperature. The reason the core temperature rises while the surface temperature stays constant is that the energy at the core rises until it reaches the layer at which the photons can escape to space. This layer is 3000K because at higher temperatures, the collisions that occur can strip electrons from hydrogen atoms creating positively charged hydrogen ions, which absorb light photons better than neutral charged hydrogen atoms (which occurs at 3000K).
Radiative contraction The primary energy transport moves from convective to radiative diffusion. This is done as the contracting protostar’s core becomes hot enough to strip almost all of its atom’s electrons, making it easier for radiation to flow freely through the star’s interior. Surface temperature begins to increase, up to about 5000K. During this stage, the protostar releases about half of the thermal energy it gains from contraction. If this did not occur the thermal pressure would balance out the gravitational contraction before nuclear ignition could occur. Hydrogen nuclei begin to fuse into helium nuclei, but the amount of energy released by the process is small compared to the amount radiated away. Thus, fusion is non self-sustaining at this point.
Self-sustaining fusion Gravitational contraction continues, increasing the core temperature to between 10 and 15 million K. At this point there is sufficient temperature and pressure to achieve a fusion rate that balances with the rate which energy is radiated away. Equilibrium is achieved as the thermal pressure matches gravity. The result is a self-sustaining fusion process. At this point, the protostar becomes a star. Once a star begins the self-sustaining fusion process, the energy it generates balances the energy it radiates into space, and the internal pressure of the star becomes stable. Once equilibrium is achieved it is called a Main Sequence Star.

Heavy Elements in Solar Nebula

Mass plays an important role in the life cycle of each main sequence star. A star with a higher mass comes into equilibrium at a much higher temperature than a lower mass star thus, fusion energy is released at a much higher rate. Because of this a higher mass main sequence star will consume hydrogen at a much higher rate, resulting in a shorter life despite having a greater amount of hydrogen to fuse. A star with 8 solar masses or more, is considered a high-mass star. Stars of this mass behave in a similar fashion to a low mass star in the early stages of life, with the exception of a much faster rate of fusion. Once the core hydrogen is spent, the paths of a high-mass and low-mass star diverge, as a high mass star continues to fuse heavier elements in its core due to higher core pressures and temperatures which result from higher mass. The life cycle of a high-mass star continues as summarized in table 1.2.

Red Super Giant After the core hydrogen is exhausted, the core shrinks and temperature rises. Hydrogen begins to fuse in a shell around the helium core (helium is the result of hydrogen core fusion), pushing the outer layers of the star out due to increased thermal energy.
Helium- core fusing supergiant Once the core temperature becomes hot enough to fuse helium into carbon, helium core fusion begins. The core expands, hydrogen shell fusion slows and the star’s outer layers shrink.
Multiple shell fusion super-giant As the process continues the star begins to fuse many different elements in shells around an iron core.
Supernova Iron cannot provide fusion energy, so as the heaviest element in the process, it accumulates in the core until fusion ceases. Once this happens, outward thermal pressure ceases. Gravity becomes the dominant force, allowing the outer layers of the star to collapse inward, starting a chain reaction creating the rest of the elements. The collapse halts once the outer layers reach the central core of neutrons and violently bounce back, sending the elements created in the fusion process out into space to become the ingredients for the birth of next generation stars.

The aftermath: The birth, life and death of a high-mass first generation star (a star formed from hydrogen and helium only) injects the interstellar medium with elements formed in the fusion process, which are heavier than hydrogen and helium. Together, all of these elements combine, cool and coalesce into molecular gas clouds. Through gravitational contraction, these clouds form clumps, which continue to contract and eventually break away from the larger cloud and form a protostar. As the cloud surrounding a protostar contracts, the gas begins to rotate. This rotational speed increases (due to the physical law of conservation of angular momentum), which prevents gas from raining directly down into the protostar, instead settling into a protostellar disks. Once the processes of star ignition described above take place, these protostellar disks become solar nebula, which consist mostly of hydrogen, helium, carbon, silicon, oxygen and iron, and the rest of the elements on the periodic table that result from the final chain reaction of a dying high-mass star. This is how the stardust that results from the life and death of high-mass stars (along with hydrogen and helium already present from the big bang) becomes fuel for a solar nebula. [vii]

Pluto and the Kuiper Belt

















“Pluto Through Time”. Copyright 2016 Christopher Altrogge.

  • 1992: David Jewitt and Jane Luu successfully detect the first object in the Kuiper Belt since Pluto, QB1. 8
  • 2006: NASA’s New Horizons satellite is launched. 7
  • 2006: IAU ratifies a resolution that defines Planets and Dwarf Planets Pluto is classified as a dwarf planet. 10
  • 2015: New Horizons arrives at Pluto. 4


Facts on the Kuiper Belt.














The Kuiper Belt. Courtesy of NASA/JHUAPL/SwRI.










The IAU has officially designated five objects as dwarf planets: Pluto, Eris, Makemake, Haumea, and Ceres. This is only a small fraction of the hundreds of other probable candidates. But what is a dwarf planet?


In other words, a dwarf planet:



  1. Orbits the sun
  2. Needs to be large enough to have its own gravity which makes it mostly round











  1. a coherentstatement or set of ideas that explainsobservedfacts or phenomena, or which sets out the laws and principles of something known or observed a hypothesis confirmed by observation, experiment etc.
  3. a field of study attempting to exhaustivelydescribe a particular class of constructs
  4. a hypothesis or conjecture


The overall theory of astronomy consists of three fundamental parts:

  1. the derivation of logical laws,








1.a: an "independent, separate, or self-contained existence", 1.b: "the existence of a thing as contrasted with its attributes", or 2. "something that has separate and distinct existence and objective or conceptual reality",

1.a: "something that is or is capable of being seen, touched, or otherwise sensed", 1.b: "something physical or mental of which a subject is cognitively aware", 2. "something that arouses an emotion in an observer", or 3. "a thing that forms an element of or constitutes the subject matter of an investigation or science"

1.a: "a mass of matter distinct from other masses" or 2.b: "something that embodies or gives concrete reality to a thing [specifically] : a sensible object in physical space"

1.a: "a separate and distinct individual quality, fact, idea, or [usually] entity", 1.b: "the concrete entity as distinguished from its appearances", 1.c: "a spatial entity", or 1.d: "an inanimate object distinguished from a living being"

1: "an observable fact or event", 2.a: "an object or aspect known through the senses rather than by though or intuition", 2.b: "an object of experience in space and time as distinguished from a thing-in-itself", or 2.c: "a fact or event of scientific interest susceptible of scientific description and explanation"

is called a phenomenon. [2]










1.a: an "independent, separate, or self-contained [astronomical] existence", 1.b: "the [astronomical] existence of a [person, place, or] thing as contrasted with its attributes", or 2. "some [astronomical] thing that has separate and distinct existence and objective or conceptual reality", [2]

is called an astronomical entity.


What are some astronomical entities?




"Astronomical named entities":

  1. "Names of telescopes and other measurement instruments,"
  2. "Names of celestial objects,"
  3. "Types of objects," and




Types of entities for Natural Language Processing (NLP):

  1. names - person, location, organization
  2. temporal expressions - date, time
  3. numeric expressions - money, percent
  4. instrument name
  5. source name
  6. source type
  7. spectral feature and
  8. text and scientific databases. [10]



Dominant groups Edit


Genera differentia for "dominant group" [4]
“superior” 36 SUPERIORITY "arrangement" 60 ARRANGEMENT
“influential” 171 INFLUENCE "class" 61 CLASSIFICATION
“musical note” 462 HARMONICS "assembly" 74 ASSEMBLAGE
“most important” 670 IMPORTANCE "size" 194 SIZE







A celestial source is any astronomical source except the Earth.





The science of astronomy consists of three fundamental parts:






Star by dictionary Edit

For the object, "star", a dictionary definition is

1.a: "any natural luminous body visible in the sky [especially] at night", 1.b: "a self-luminous gaseous celestial body of great mass whose shape is [usually] spheroidal and whose size may be as small as the earth or larger than the earth's orbit". [2]




Atmospheres Edit



Interplanetary medium Edit



Interstellar medium Edit


Intergalactic medium Edit


Ions Edit


Materials Edit




Meteorites Edit


Shelters Edit






Def. the art of describing or delineating the stars a description or mapping of the heavens is called astrography.















Electrical Sun Edit


"[A] variety of geophysical and astrophysical phenomena can be explained by a net charge on the Sun of -1.5 x 10 28 e.s.u." [39] This figure was later reduced by a factor of five. [40]


Milky Way Edit


Coronal clouds Edit




Zodiacal lights Edit





Orbital theory Edit






Eccentricities Edit

"Mercury's orbit eccentricity [e] varies between about 0.11 and 0.24 with the shortest time lapse between the extremes being about 4 x 10 5 yr". [47] "Smaller amplitude variations occur with about a 10 5 yr period." [47]

Inclinations Edit

"The orbital inclination [i] [of Mercury] varies between 5° and 10° with a 10 6 yr period with smaller amplitude variations with a period of about 10 5 yr." [47]

Obliquities Edit



Precessions Edit


Orbital poles Edit


Resonances Edit


Orbital decays Edit





Astronomical units Edit










Auroras Edit


Fluctuating visible source Edit





Luminosity Edit

The luminosity of stars is measured in two forms: apparent (visible light only) and bolometric (total radiant energy). (A bolometer is an instrument that measures radiant energy over a wide band by absorption and measurement of heating.) When not qualified, "luminosity" means bolometric luminosity, which is measured either in the SI units, watts or in terms of solar luminosities, L ⊙ > , that is, how many times as much energy the object radiates as the Sun.




mstar is the apparent magnitude of the star (a pure number) msun is the apparent magnitude of the Sun (also a pure number) Lstar is the visible luminosity of the star L ⊙ > is the solar visible luminosity dstar is the distance to the star dsun is the distance to the Sun

Nucleosynthesis Edit




3 He + 4 He → 7 Be + γ (429 keV)

and the associated reaction chains

generate 14% and 0.1% of the α-particles, respectively, and 10.7% of the present-epoch luminosity of the Sun. [56] Usually, the 7 Be produced is assumed to be deep within the core of the Sun however, such 7 Be would not escape to reach the leading edge of the LDEF.

Stars Edit


Starspots Edit



Weak equivalence principle Edit








Planets Edit

Def. "a celestial body that

(a) is in orbit around the Sun,




Def. "a celestial body that

(a) is in orbit around the Sun,






From a theoretical planetary physics perspective: "The shape of objects with mass above 5 x 10 20 kg and diameter greater than 800 km would normally be determined by self-gravity, but all borderline cases would have to be established by observation." [67]

Def. a celestial body "formed by accumulation of a rocky core, on a much longer timescale, ≳ 10 7 yr, with subsequent acquisition of a gaseous envelope if the circumstances allow this, and with an initially fractionated elemental composition" is called a planet. [57]









A= 14.713 deg/day (± 0.0491) B= –2.396 deg/day (± 0.188) C= –1.787 deg/day (± 0.253)

"[B]y assuming a harmonic variation having a period of 11.13 years . the phases of such a variation [in polar diameter minus equatorial diameter of the Sun] coincide to within one-fifth of a year with the phases of the sun-spot fluctuations that, at times corresponding to minimum of sun-spottedness, the polar diameter is relatively larger that, at times of maximum sun-spottedness, the equatorial diameter is relatively larger. The amplitude of the variation is extremely small, but its reality would seem to be established. [This] at least renders the existence of such periodic fluctuations in the shape of the sun more probable than their non-existence." [72]

"Solar oblateness, the difference between the equatorial and polar diameters, reflects certain fundamental properties of the Sun. . the oblateness reflects properties of the Sun's interior, . [There is] a time varying, excess equatorial brightness [producing] a difference between the equatorial and polar limb darkening functions . at times when the excess brightness is reduced, the intrinsic visual oblateness can be obtained from the observations without detailed knowledge of the excess brightness. A period of reduced excess brightness occurred in 1973 September." [73] The period of reduced excess equatorial brightness occurred between solar cycle maximum around 1970 and minimum around 1975. Considering excess equatorial brightness and seeking to perform measurements at opportunities of reduced excess equatorial brightness has the effect of reducing solar oblateness from some 86.6 ± 6.6 milli-arcsec to 18.4 ± 12.5 milli-arcsec. [73]






Galaxy formation is hypothesized to occur, from structure formation theories, as a result of tiny quantum fluctuations in the aftermath of the Big Bang. The simplest model for this that is in general agreement with observed phenomena is the Λ Cold Dark Matter cosmology that is to say that clustering and merging is how galaxies gain in mass, and can also determine their shape and structure.

Topics similar to or like Commensurability (astronomy)

Time a given astronomical object takes to complete one orbit around another object, and applies in astronomy usually to planets or asteroids orbiting the Sun, moons orbiting planets, exoplanets orbiting other stars, or binary stars. Often referred to as the sidereal period, determined by a 360° revolution of one celestial body around another, e.g. the Earth orbiting the Sun. Wikipedia

Object in the direction opposite the rotation of its primary, that is, the central object . Object's rotational axis. Wikipedia

Set of gravitationally bound objects in orbit around a planetary mass object or minor planet, or its barycenter. Set of natural satellites , 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. Wikipedia

Measure of the mass of a planet-like object. Solar mass, the mass of the Sun. Wikipedia

Orbiting astronomical body always has the same face toward the object it is orbiting. Known as synchronous rotation: the tidally locked body takes just as long to rotate around its own axis as it does to revolve around its partner. Wikipedia

List of types of orbits: Less commonly used Wikipedia


"Clearing the neighbourhood" around a celestial body's orbit describes the body becoming gravitationally dominant that there are no other bodies of comparable size other than its natural satellites or those otherwise under its gravitational influence. One of three necessary criteria for a celestial body to be considered a planet in the Solar System, according to the definition adopted in 2006 by the International Astronomical Union . Wikipedia

Either point at the ends of an imaginary line segment that runs through the center of an orbit and is perpendicular to the orbital plane. Projected onto the celestial sphere, orbital poles are similar in concept to celestial poles, but are based on the body's orbit instead of its equator. Wikipedia

Recent variation of the Nice model that begins with five giant planets, the four plus an additional ice giant in a chain of mean-motion resonances. Broken, the five giant planets undergo a period of planetesimal-driven migration, followed by an instability with gravitational encounters between planets similar to that in the original Nice model. Wikipedia

Astronomical body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and – according to the International Astronomical Union but not all planetary scientists – has cleared its neighbouring region of planetesimals. Ancient, with ties to history, astrology, science, mythology, and religion. Wikipedia

Astronomical body or object is the speed at which it orbits around either the barycenter or, if one object is much more more massive than the other bodies in the system, its speed relative to the center of mass of the most massive body.. Entire orbit, or its instantaneous speed at a particular point in its orbit. Wikipedia


Torus-shaped region in the Solar System, located roughly between the orbits of the planets Jupiter and Mars, that is occupied by a great many solid, irregularly shaped bodies, of many sizes but much smaller than planets, called asteroids or minor planets. Also called the main asteroid belt or main belt to distinguish it from other asteroid populations in the Solar System such as near-Earth asteroids and trojan asteroids. Wikipedia

Angle between an object's rotational axis and its orbital axis, or, equivalently, the angle between its equatorial plane and orbital plane. It differs from orbital inclination. Wikipedia



There continues to be criticism regarding the wording of the final draft of the definition. Notably, the lead scientist on NASA's robotic mission to Pluto, Alan Stern, contends that, like Pluto, Earth, Mars, Jupiter and Neptune have not fully cleared their orbital zones either. Earth orbits with 10,000 near-Earth asteroids. Jupiter, meanwhile, is accompanied by 100,000 Trojan asteroids on its orbital path. "If Neptune had cleared its zone, Pluto wouldn't be there," he added. However, his own earlier work on neighborhood clearing supported the distinction between the largest eight planets and the rest of the solar system. There is a substantial difference in the extent to which the neighborhood has been cleared between Pluto and the eight planets. Also, Pluto's position is due to the gravitational effects of Neptune as they are in orbital resonance.

The debates have clarified that "clearing its orbit" refers to the process that happened during the formation of the planets. It does not talk about the presence of bodies that later strayed into the orbit after the accretions took place.

The definition may be difficult to apply outside our solar system. Techniques for identifying extrasolar objects generally cannot determine if an object has "cleared its orbit," except indirectly via Stern and Levison's Λ parameter, and provide limited information about when the objects were formed. The wording of the new definition is heliocentric in its use of the word Sun instead of star or stars, and is thus not applicable to the numerous objects that have been identified in orbit around other stars.


The final vote has come under criticism because of the relatively small percentage of the 9000-strong membership who participated. Besides the fact that most members do not attend the General Assemblies, this lack was also due to the timing of the vote: the final vote was taken on the last day of the 10-day event, after many participants had left or were preparing to leave. Of over 2,700 astronomers attending the conference, about 800 were present on the day for the significant resolutions on a vote on a subsidiary resolution, the first that required a count, only 424 votes were cast.There is also the issue of the many astronomers who were unable or who chose not to make the trip to Prague and, thus, cast a vote. Astronomer Marla Geha has clarified that not all members of the Union were needed to vote on the classification issue: only those whose work is directly related to planetary studies.


Some astrologers have chosen not to follow the new definiton.

Petition for a "better definition"

Within five days of the new IAU Planet Definition over 300 scientists signed a petition that opposes the new definition. The full text of the petition says: “We, as planetary scientists and astronomers, do not agree with the IAU's definition of a planet, nor will we use it. A better definition is needed.” The petition does not list any specific complaint with the definition, so it is unknown whether all the signatories opposed it for the same reasons.

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