# Uncertainty parameter

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{{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 [NEAs](/source/Near-Earth_asteroid) are generally well known, though a few have been [lost](/source/Lost_minor_planet). 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](/source/Minor_Planet_Center) (MPC) to quantify the uncertainty of a [perturbed](/source/Perturbation_(astronomy)) orbital solution for a [minor planet](/source/minor_planet).<ref name="MPC-Uncertainty"/><ref name="User-Guide"/> The parameter is a [logarithmic scale](/source/logarithmic_scale) from 0 to 9 that measures the anticipated longitudinal uncertainty<ref name="MPC-24597"/> in the minor planet's [mean anomaly](/source/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 [Small-Body Database Browser](/source/JPL_Small-Body_Database).<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](/source/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](/source/Classical_Kuiper_belt_object)s 40–50 AU from the Sun
|- style="align:center;vertical-align:bottom;"
| [JPL SBDB](/source/JPL_SBDB)<br/>'''Uncertainty<br/>parameter'''<br/> &nbsp;
| [Horizons](/source/JPL_Horizons_On-Line_Ephemeris_System)<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
| 0.00
|align=left| [(134340) Pluto](/source/Pluto)
| [https://www.minorplanetcenter.net/db_search/show_object?object_id=134340 E2022-J69]
|-
|-
! 1
| ±0.005
|align=left| [38628 Huya](/source/38628_Huya)
| {{JPL|38628}}
|-
! 2
| ±0.03
|align=left| [19521 Chaos](/source/19521_Chaos)
| {{JPL|19521}}
|-
! 3
| ±0.10
|align=left| [15760 Albion](/source/15760_Albion)
| {{JPL|15760}}
|-
! 4
|  ±1.4 
|align=left| {{mpl|(15807) Goibniu}}
| {{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](/source/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](/source/orbit_determination) process including the number of [observation](/source/observation)s (measurements), the time spanned by those observations ([observation arc](/source/observation_arc)), the quality of the observations (e.g. [radar](/source/Radar_astronomy) 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 ['''e'''ccentricity](/source/Orbital_eccentricity) was assumed, rather than determined.<ref name="ExportFormat"/> Objects with assumed eccentricities are generally considered [lost](/source/Lost_asteroid) 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 [seconds of arc](/source/Minute_and_second_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](/source/perihelion) time in days
|-
| <math>e</math>|| [eccentricity](/source/Orbital_eccentricity) of the determined orbit
|-
| <math>P</math>|| [orbital period](/source/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](/source/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](/source/Ceres_(dwarf_planet)) 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 [base](/source/logarithm) 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.

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](/source/Minor_Planet_Center)
  |publisher=[International Astronomical Union](/source/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](/source/Minor_Planet_Center)
  |publisher=[International Astronomical Union](/source/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](/source/Minor_Planet_Center)
 |publisher=[International Astronomical Union](/source/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](/source/Minor_Planet_Center)
  |publisher=[International Astronomical Union](/source/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](/source/Minor_Planet_Center)
  |publisher=[International Astronomical Union](/source/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](/source/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](/source/NASA) 
  |department=[Ames Research Center](/source/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](/source/NASA) / [JPL](/source/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

---
Adapted from the Wikipedia article [Uncertainty parameter](https://en.wikipedia.org/wiki/Uncertainty_parameter) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Uncertainty_parameter?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.