Pseudorapidity

Template:TNO In astronomy, a resonant trans-Neptunian object is a trans-Neptunian object (TNO) in mean motion orbital resonance with Neptune. The orbital periods of the resonant objects are in a simple integer relations with the period of Neptune e.g. 1:2, 2:3 etc. Resonant TNOs can be either part of the main Kuiper belt population, or the more distant scattered disc population.

Distribution

Distribution of trans-Neptunian objects. Resonant objects are in red.

The diagram illustrates the distribution of the known trans-Neptunian objects (up to 70 AU) in relation to the orbits of the planets together with centaurs for reference. Resonant objects are plotted in red. Orbital resonances with Neptune are marked with vertical bars; 1:1 marks the position of Neptune’s orbit (and its trojans), 2:3 marks the orbit of Pluto and plutinos, and 1:2, 2:5 etc. mark a number of smaller families.

The designation 2:3 or 3:2 refer both to the same resonance for TNOs. There’s no confusion possible as TNOs, by definition, have periods longer than Neptune. The usage depends on the author and the field of research. The statement "Pluto is in 2:3 resonance to Neptune" appears better to capture the meaning: Pluto completes 2 orbits for every 3 orbits of Neptune.

Origin

28 year-old Painting Investments Worker Truman from Regina, usually spends time with pastimes for instance interior design, property developers in new launch ec Singapore and writing. Last month just traveled to City of the Renaissance. Detailed analytical and numerical studies of Neptune’s resonances have shown that they are quite "narrow" (i.e. the objects must have a relatively precise range of energy). If the object semi-major axis is outside these narrow ranges, the orbit becomes chaotic, with widely changing orbital elements.

As TNOs were discovered, a substantial (more than 10%) proportion were found to be in 2:3 resonances, far from a random distribution. It is now believed that the objects have been collected from wider distances by sweeping resonances during the migration of Neptune.

Well before the discovery of the first TNO, it was suggested that interaction between giant planets and a massive disk of small particles would, via momentum transfer, make Jupiter migrate inwards while Saturn, Uranus and especially Neptune would migrate outwards. During this relatively short period of time, Neptune’s resonances would be sweeping the space, trapping objects on initially-varying heliocentric orbits into resonance.

Known populations

2:3 resonance ("plutinos", period ~250 years)

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The motion of Orcus in a rotating frame with a period equal to Neptune's orbital period. (Neptune is held stationary.)

Pluto and its moons (top) compared in size, albedo and colour with Orcus and Ixion.

The 2:3 resonance at 39.4 AU is by far the dominant category among the resonant objects, with 92 confirmed and 104 possible member bodies. The objects following orbits in this resonance are named plutinos after Pluto, the first such body discovered. Large, numbered plutinos include:

• 90482 Orcus
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• 28978 Ixion
• 38628 Huya

3:5 resonance (period ~275 years)

A population of 10 objects at 42.3 AU as of October, 2008, including:

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4:7 resonance (period ~290 years)

Another important population of objects (20 identified as of October 2008) is orbiting the Sun at 43.7 AU (in the midst of the classical objects). The objects are rather small (with a single exception, H>6) and most of them follow orbits close to the ecliptic. Objects with well established orbits include:

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1:2 resonance ("twotinos", period ~330 years)

This resonance at 47.8 AU is often considered as the outer "edge" of the Kuiper belt and the objects in this resonance are sometimes referred to as twotinos. Twotinos have inclinations less than 15 degrees and generally moderate eccentricities (0.1 < e < 0.3). An unknown number of the 2:1 resonants likely did not originate in a planetesimal disk that was swept by the resonance during Neptune's migration.

There are far fewer objects in this resonance (a total of 14 as of October, 2008) than plutinos. Long-term orbital integration shows that the 1:2 resonance is less stable than 2:3 resonance; only 15% of the objects in 1:2 resonance were found to survive 4 Gyr as compared with 28% of the plutinos. Consequently it might be that twotinos were originally as numerous as plutinos, but their population has dropped significantly below that of plutinos since.

Objects with well established orbits include (in order of the absolute magnitude):

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Selected resonant objects (in red).

2:5 resonance (period ~410 years)

Objects with well established orbits at 55.4 AU include:

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In total, the orbits of 11 objects are classified as 2:5 as of October, 2008.

Other resonances

The nominal 7:12 libration of Haumea in a rotating frame. Where red turns to green is where it crosses the ecliptic.

So called higher-order resonances are known for a limited number of objects, including the following numbered objects

• 4:5 (35 AU, ~205 years) Template:Mpl+
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• 5:9 (44.5 AU, ~295 years) Advertising Manager Courtney from Regina, spends time with pastimes for instance frisbee golf (frolf), property developers in singapore and bee keeping. These days has paid a visit to Historical Monuments at Makli.
  
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• 4:9 (52 AU, ~370 years) Template:Mpl+, Advertising Manager Courtney from Regina, spends time with pastimes for instance frisbee golf (frolf), property developers in singapore and bee keeping. These days has paid a visit to Historical Monuments at Makli.
  
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• 3:7 (53 AU, ~385 years) Template:Mpl+, Template:Mpl+, Advertising Manager Courtney from Regina, spends time with pastimes for instance frisbee golf (frolf), property developers in singapore and bee keeping. These days has paid a visit to Historical Monuments at Makli.
  
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• 5:12 (55 AU, ~395 years) Template:Mpl+, Advertising Manager Courtney from Regina, spends time with pastimes for instance frisbee golf (frolf), property developers in singapore and bee keeping. These days has paid a visit to Historical Monuments at Makli.
  
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• 3:8 (57 AU, ~440 years) Template:Mpl+ (84% probability according to Emel’yanenko)
• 3:10 (67 AU, ~549 years) Template:Mpl+
• 2:7 (70 AU, ~580 years) Advertising Manager Courtney from Regina, spends time with pastimes for instance frisbee golf (frolf), property developers in singapore and bee keeping. These days has paid a visit to Historical Monuments at Makli.
  
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A few objects are known on simple, distant resonances

• 1:3 (62.5 AU, ~495 years) Template:Mpl+
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Some notable unproven (they could be coincidental) dwarf planet resonances include:

• 7:12 (43 AU, ~283 years) Haumea (nominal orbit very likely in resonance)
• 6:11 (45 AU, ~302 years) Makemake (Systems Analyst Kepp from Lloydminster, loves bird watching, property developers in singapore and fossils. Advocates that you simply journey to Gulf of Porto: Calanche of Piana.
  
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• 5:17 (67 AU, ~560 years) Eris (Systems Analyst Kepp from Lloydminster, loves bird watching, property developers in singapore and fossils. Advocates that you simply journey to Gulf of Porto: Calanche of Piana.
  
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1:1 resonance (Neptune trojans, period ~165 years)

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Only the last three objects are near Neptune's Template:L5 Lagrangian point; the others are located in Neptune's Template:L4 region.

Coincidental versus true resonances

One of the concerns is that weak resonances may exist and would be difficult to prove due to the current lack of accuracy in the orbits of these distant objects. Many objects have orbital periods of more than 300 years and most have only been observed over a short observation arc of a couple years. Due to their great distance and slow movement against background stars, it may be decades before many of these distant orbits are determined well enough to confidently confirm whether a resonance is true or merely coincidental. A true resonance will smoothly oscillate while a coincidental near resonance will circulate. (See Toward a formal definition)

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The orbital period of 2001 XT₂₅₄ around the 7:3 (2.333) resonance of Neptune.

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The orbital period of 1995 TL₈ missing the 7:3 (2.333) resonance of Neptune.

Toward a formal definition

The classes of TNO have no universally agreed precise definitions, the boundaries are often unclear and the notion of resonance is not defined precisely. The Deep Ecliptic Survey introduced formally defined dynamical classes based on long-term forward integration of orbits under the combined perturbations from all four giant planets. (see also formal definition of classical KBO)

In general, the mean motion resonance may involve not only orbital periods of the form

${\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}}}}}$

where p and q are small integers, λ and λ_N are respectively the mean longitudes of the object and Neptune, but can also involve the longitude of the perihelion and the longitudes of the nodes (see orbital resonance, for elementary examples)

An object is a Resonant if for some small integers p,q,n,m,r,s, the argument (angle) defined below is librating (i.e. is bounded)

$\phi ={\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}-{\rm {m\cdot \varpi -{\rm {n\cdot \Omega -{\rm {r\cdot \varpi _{\rm {N}}-{\rm {s\cdot \Omega _{\rm {N}}}}}}}}}}}}}}$

where the $\varpi$ are the longitudes of perihelia and the $\Omega$ are the longitudes of the ascending nodes, for Neptune (with subscripts "N") and the resonant object (no subscripts).

The term libration denotes here periodic oscillation of the angle around some value and is opposed to circulation where the angle can take all values from 0 to 360°. For example, in the case of Pluto, the resonant angle $\phi$ librates around 180° with an amplitude of around 82° degrees, i.e. the angle changes periodically from 180°-82° to 180°+82°.

All new plutinos discovered during the Deep Ecliptic Survey proved to be of the type

$\phi ={\rm {3\cdot \lambda -{\rm {2\cdot \lambda _{\rm {N}}-\varpi }}}}$

similar to Pluto's mean motion resonance.

More generally, this 2:3 resonance is an example of the resonances p:(p+1) (example 1:2, 2:3, 3:4 etc.) that have proved to lead to stable orbits. Their resonant angle is

$\phi ={\rm {p\cdot \lambda -{\rm {q\cdot \lambda _{\rm {N}}-({\rm {p-{\rm {q)\cdot \varpi }}}}}}}}$

In this case, the importance of the resonant angle $\phi \,$ can be understood by noting that when the object is at perihelion, i.e. $\lambda =\varpi$, then

$\phi =q\cdot (\varpi -\lambda _{\rm {N}})$

i.e. $\phi \,$ gives a measure of the distance of the object's perihelion from Neptune. The object is protected from the perturbation by keeping its perihelion far from Neptune provided $\phi \,$ librates around an angle far from 0°.

Classification methods

As the orbital elements are known with a limited precision, the uncertainties may lead to false positives (i.e. classification as resonant of an orbit which is not).

A recent approach considers not only the current best-fit orbit but also two additional orbits corresponding to the uncertainties of the observational data. In simple terms, the algorithm determines whether the object would be still classified as resonant if its actual orbit differed from the best fit orbit, as the result of the errors in the observations.

The three orbits are numerically integrated over a period of 10 million years. If all three orbits remain resonant (i.e. the argument of the resonance is librating, see formal definion), the classification as a resonant object is considered secure.

If only two out of the three orbits are librating the object is classified as probably in resonance. Finally, if only one orbit passes the test, the vicinity of the resonance is noted to encourage further observations to improve the data.

The two extreme values of the semi-major axis used in the algorithm are determined to correspond to uncertainties of the data of at most 3 standard deviations. Such range of semi-axis values should, with a number of assumptions, reduce the probability that the actual orbit is beyond this range to less than 0.3%.

The method is applicable to objects with observations spanning at least 3 oppositions.

References

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Further reading

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  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
• One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting
  
  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang (as HTML)

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