View source for Uncertainty parameter

{{Short description|Parameter introduced by the Minor Planet Center}}{{For|the quantification of uncertainty in general|Measurement uncertainty}}[[File:NEA-sizes-vs-uncertainties-compact.PNG|thumb|upright=1.25| The orbits of kilometre class [[Near-Earth asteroid|NEAs]] are generally well known, though a few have been [[Lost minor planet|lost]]. However, large numbers of smaller NEAs have highly uncertain orbits.<ref name="MPC-NEA"/>]]

The '''uncertainty parameter''' ''U'' is introduced by the [[Minor Planet Center]] (MPC) to quantify the uncertainty of a [[Perturbation (astronomy)|perturbed]] orbital solution for a [[minor planet]].<ref name="MPC-Uncertainty"/><ref name="User-Guide"/> The parameter is a [[logarithmic scale]] from 0 to 9 that measures the anticipated longitudinal uncertainty<ref name="MPC-24597"/> in the minor planet's [[mean anomaly]] after 10 years.<ref name="MPC-Uncertainty"/><ref name="User-Guide"/><ref name="Strategic-Implications"/> The larger the number, the larger the uncertainty. The uncertainty parameter is also known as '''condition code''' in JPL's [[JPL Small-Body Database|Small-Body Database Browser]].<ref name="User-Guide"/><ref name="Strategic-Implications"/><ref name="conditioncode"/> The ''U'' value should not be used as a predictor for the uncertainty in the future motion of [[near-Earth object]]s.<ref name="MPC-Uncertainty"/>
== Orbital uncertainty ==
{| class="wikitable floatright" style="text-align:center; font-size:0.9em;"
|+ [[Classical Kuiper belt object]]s 40–50 AU from the Sun
|- style="align:center;vertical-align:bottom;"
| [[JPL SBDB]]<br/>'''Uncertainty<br/>parameter'''<br/> &nbsp;
| [[JPL Horizons On-Line Ephemeris System|Horizons]]<br/>January 2018<br/>'''Uncertainty in<br/>distance from the Sun'''<br/>(millions of kilometers)
| '''Object'''<br/> &nbsp;
| '''Reference<br/>Ephemeris'''<br/>Location: @sun<br/>Table setting: 39
|-
! 0
| ±0.01
|align=left| [[Pluto|(134340) Pluto]]
| [https://www.minorplanetcenter.net/db_search/show_object?object_id=134340 E2022-J69]
|-
|-
! 1
| ±0.04
|align=left| {{mpl|2013 BL|76}}
| {{JPL|2013+BL76}}
|-
! 2
| ±0.14
|align=left| [[20000 Varuna]]
| {{JPL|20000}}
|-
! 3
| ±0.84
|align=left| [[19521 Chaos]]
| {{JPL|19521}}
|-
! 4
|  ±1.4 
|align=left| {{mpl|(15807) 1994 GV|9}}
| {{JPL|15807}}
|-
! 5
| ±8.2
|align=left| {{mp|(160256) 2002 PD|149}}
| {{JPL|160256}}
|-
! 6
| ±70
|align=left| {{mp|1999 DH|8}}
| {{JPL|1999+DH8}}
|-
! 7
| ±190
|align=left| {{mp|1999 CQ|153}}
| {{JPL|1999+CQ153}}
|-
! 8 <!-- corrected: formerly was '9' -->
| ±590
|align=left|{{mp|1995 KJ|1}}
| {{JPL|1995+KJ1}}
|-
! 9
| ±1,600
|align=left| [[1995 GJ]]
| {{JPL|1995+GJ}}
|-
! ‘D’
|colspan="3;" align=left| &nbsp; '''D'''ata insufficient for orbit determination.
|-
! ‘E’
|colspan="3;" align=left| &nbsp; '''E'''ccentricity was guessed instead of determined.<ref name="ExportFormat"/>

|-
! ‘F’
|colspan="3;" align=left| &nbsp; Both ‘D’ and ‘E’ apply.<ref name="ExportFormat"/>
|}
Orbital uncertainty is related to several parameters used in the [[orbit determination]] process including the number of [[observation]]s (measurements), the time spanned by those observations ([[observation arc]]), the quality of the observations (e.g. [[Radar astronomy|radar]] vs. optical), and the geometry of the observations. Of these parameters, the time spanned by the observations generally has the greatest effect on the orbital uncertainty.<ref name="NASA-uncertainty"/>

Occasionally, the Minor Planet Center substitutes a letter-code (‘D’, ‘E’, ‘F’) for the uncertainty parameter. 
:{|
|- style="vertical-align: top;"
! D &nbsp; &nbsp;
| Objects with a ‘D’ have only been observed for a single opposition, and have been assigned two (or more) different designations ("double").
|- style="vertical-align: top;"
! E
| Objects such as {{mp|2003 UU|291}} with a condition code ‘E’<ref name=IAU-MPC-2003-UU-291/> in the place of a numeric uncertainty parameter denotes orbits for which the listed [[Orbital eccentricity|'''e'''ccentricity]] was assumed, rather than determined.<ref name="ExportFormat"/> Objects with assumed eccentricities are generally considered [[Lost asteroid|lost]] if they have not recently been observed because their orbits are not well constrained.{{citation needed|date=April 2020|reason="Lost" not found in Export Format reference}}
|- style="vertical-align: top;"
! F
|Objects with an ‘F’ fall in both categories ‘D’ and ‘E’.<ref name="ExportFormat"/>
|}

== Calculation ==
The ''U'' parameter is calculated in two steps.<ref name="MPC-Uncertainty"/><ref name="StatisticalAnalysis"/> First the in-orbit longitude runoff <math>r</math> in [[Minute and second of arc|seconds of arc]] per decade is calculated, (i.e. the discrepancy between the observed and calculated position extrapolated over ten years):

:<math>r=\left(\Delta\tau\cdot e + 10\cdot\frac{\;\Delta P\;}{P}\right) \cdot 3600 \cdot 3 \cdot \frac{\;k_\text{o}\;}{P}</math>

with
:{| 
|-
| <math>\Delta\tau</math>|| uncertainty in the [[perihelion]] time in days
|-
| <math>e</math>|| [[Orbital eccentricity|eccentricity]] of the determined orbit
|-
| <math>P</math>|| [[orbital period]] in years
|-
| <math>\Delta P</math> || uncertainty in the orbital period in days 
|-
| <math>k_\text{o}</math> || <math>0.01720209895\cdot\frac{180^\circ}{\pi}</math>, [[Gaussian gravitational constant]], converted to degrees
|}

Then, the obtained in-orbit longitude runoff is converted to the "uncertainty parameter" {{mvar|U}}, which is an integer between 0 and 9. The calculated number can be less than 0 or more than 9, but in those cases either 0 or 9 is used instead. The formula for cutting off the calculated value of {{mvar|U}} is

:<math>U=\min \left\{ ~9, ~ \max \Bigl\{ \; 0, \; \left\lfloor 9\cdot\frac{\log r}{\;\log 648{,}000\;} \right\rfloor + 1 \; \Bigr\} ~ \right\} </math>

For instance: As of 10&nbsp;September 2016, [[Ceres (dwarf planet)|Ceres]] technically has an uncertainty of around &minus;2.6, but is instead displayed as the minimal 0.

The result is the same regardless of the choice of [[logarithm|base]] for the logarithm, so long as the same logarithm is used throughout the formula; e.g. for "{{math|log}}" = {{math|log{{sub|10}}}}, {{math|log{{sub|''e''}}}}, {{math|ln}}, or {{math|log{{sub|2}}}} the calculated value of {{mvar|U}} remains the same if the logarithm is the same in both places in the formula.

[[File:Mpc-uncertainty-parameter.svg|frame|right|Function graph U(r)]]
{| class="wikitable alternance centre" style="font-size:0.9em;"
 |+ 
 |-
 ! scope="col" | {{mvar|U}}
 ! scope="col" | Runoff<br/>Longitude runoff per decade
 |-
 | 0
 | <&nbsp;1.0&nbsp;arc second
 |-
 | 1
 | 1.0&ndash;4.4&nbsp;arc seconds
 |-
 | 2
 | 4.4&ndash;19.6&nbsp;arc seconds
 |-
 | 3
 | 19.6&nbsp;arc seconds  &ndash;  1.4&nbsp;arc minutes
 |-
 | 4
 | 1.4&ndash;6.4&nbsp;arc minutes
 |-
 | 5
 | 6.4&ndash;28&nbsp;arc minutes
 |-
 | 6
 | 28&nbsp;arc minutes &ndash; 2.1° 
 |-
 | 7
 | 2.1°&ndash;9.2°
 |-
 | 8
 | 9.2°&ndash;41°
 |-
 | 9
 | >&nbsp;41°
|}

648&thinsp;000 is the number of arc seconds in a half circle, so a value greater than 9 would be meaningless as we would have no idea where the object will be in 10 years within the orbit.
{{clear}}

== References ==
{{reflist|25em|refs=

<ref name="MPC-NEA">
{{cite web
  |title=Orbits for Near Earth Asteroids (NEAs)
  |department=[[Minor Planet Center]]
  |publisher=[[International Astronomical Union]]
  |url=https://www.minorplanetcenter.net/iau/MPCORB/NEA.txt
  |access-date=25 June 2020
  |place=
}} via
{{cite web
  |title=M.P. Orbit Format
  |department=[[Minor Planet Center]]
  |publisher=[[International Astronomical Union]]
  |url=https://www.minorplanetcenter.net/iau/info/MPOrbitFormat.html
}}
</ref>

<ref name=IAU-MPC-2003-UU-291>
{{cite web
 |title=2003 UU{{sub|291}}
 |department=[[Minor Planet Center]]
 |publisher=[[International Astronomical Union]]
 |url=http://www.minorplanetcenter.net/db_search/show_object?object_id=2003+UU291
}}
</ref>

<ref name="MPC-Uncertainty">
{{cite web
  |title=Uncertainty parameter 'U'
  |department=[[Minor Planet Center]]
  |publisher=[[International Astronomical Union]]
  |url=http://www.minorplanetcenter.org/iau/info/UValue.html
  |access-date=2011-11-15 |df=dmy-all
}}
</ref>

<ref name="ExportFormat">
{{cite web
  |title=Export format for minor-planet orbits
  |department=[[Minor Planet Center]]
  |publisher=[[International Astronomical Union]]
  |url=http://www.minorplanetcenter.net/iau/info/MPOrbitFormat.html
  |access-date=2016-03-03 |df=dmy-all
}}
</ref>

<ref name="Strategic-Implications">
{{cite report
  |last=Drake |first=Bret G.
  |date=2011 
  |title=Strategic implications of human exploration of near-Earth asteroids
  |series=NASA Technical Reports 
  |publisher=[[NASA]] 
  |id=2011-0020788
  |url=https://ntrs.nasa.gov/search.jsp?R=20110020788
  |access-date=2016-03-03 |df=dmy-all
}}
</ref>

<ref name="User-Guide">
{{cite web
  |title=Trajectory Browser User Guide
  |series=Mission Design Center Trajectory Browser
  |publisher=[[NASA]] 
  |department=[[Ames Research Center]]
  |url=http://trajbrowser.arc.nasa.gov/user_guide.php
  |access-date=2016-03-03 |df=dmy-all
}}
</ref>

<ref name="conditioncode">
{{cite web
  |title=Definition / description for SBDB parameter / field: condition code
  |department=JPL Solar System Dynamics
  |url=http://ssd.jpl.nasa.gov/sbdb_help.cgi?name=condition_code
  |access-date=2011-11-15 |df=dmy-all
}}
</ref>

<ref name="NASA-uncertainty">{{cite web
  |date=31 Aug 2005
  |title=Near-Earth objects close-approach uncertainties
  |publisher=[[NASA]] / [[JPL]] 
  |department=JPL Near-Earth Object Program Office
  |url=http://neo.jpl.nasa.gov/ca/neo_ca_info.html
  |url-status=dead  |access-date=2011-11-15
  |archive-url=https://web.archive.org/web/20040324140637/http://neo.jpl.nasa.gov/ca/neo_ca_info.html
  |archive-date=24 March 2004 |df=dmy-all
}}
</ref>

<ref name="MPC-24597">
{{cite report
  |title=Editorial Notice
  |series=The Minor Planet Circulars / Minor Planets and Comets
  |date=1995-02-15
  |id=MPC 24597–24780
  |pages=24597
  |url=http://www.minorplanetcenter.net/iau/ECS/MPCArchive/1995/MPC_19950215.pdf
  |access-date=3 March 2016
}}
</ref>

<ref name="StatisticalAnalysis">
{{cite journal
  |last1=Desmars    |first1=Josselin    |last2=Bancelin |first2=David
  |last3=Hestroffer |first3=Daniel      |last4=Thuillot |first4=William
  |date=Jun 2011
  |title=Statistical analysis on the uncertainty of asteroid ephemerides
  |url=http://hal.upmc.fr/hal-00647644
  |editor1-last=Alecian |editor1-first=G.    |editor2-last=Belkacem     |editor2-first=K.
  |editor3-last=Samadi  |editor3-first=R.    |editor4-last=Valls-Gabaud |editor4-first=D.
  |journal=SF2A 2011: Annual Meeting of the French Society of Astronomy and Astrophysics
  |pages=639–642
  |location=Paris, France
  |bibcode=2011sf2a.conf..639D |access-date=3 March 2016
}}
</ref>

}} <!-- end "refs=" -->

[[Category:Orbits]]
[[Category:Measurement]]