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Paramètre d'incertitude — Wikipédia
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planètes mineures">Centre des planètes mineures</a> (MPC) pour quantifier de manière concise l'incertitude de la <a href="/wiki/Orbite" title="Orbite">solution orbitale</a> <a href="/wiki/Perturbation_(astronomie)" title="Perturbation (astronomie)">perturbée</a> d'un <a href="/wiki/Plan%C3%A8te_mineure" title="Planète mineure">objet mineur</a>. C'est un entier compris entre 0 et 9, où 0 indique une incertitude très faible et 9 une incertitude extrêmement élevée<sup id="cite_ref-MPC-Uncertainty_1-1" class="reference"><a href="#cite_note-MPC-Uncertainty-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup>. En pratique, U est rarement supérieur à 6<sup id="cite_ref-MPC-Uncertainty_1-2" class="reference"><a href="#cite_note-MPC-Uncertainty-1"><span class="cite_crochet">[</span>1<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Définition"><span id="D.C3.A9finition"></span>Définition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&veaction=edit&section=1" title="Modifier la section : Définition" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&action=edit&section=1" title="Modifier le code source de la section : Définition"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Le paramètre U se calcule de la manière suivante : </p><p>Tout d'abord, il faut calculer le paramètre <i>R</i> (<i>runoff</i>) : </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=({\mathrm {d} }T\cdot e+{\frac {10}{P}}\cdot {\mathrm {d} }P)\cdot {\frac {k_{0}}{P}}\cdot 3600\cdot 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>T</mi> <mo>⋅<!-- ⋅ --></mo> <mi>e</mi> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>10</mn> <mi>P</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> </mrow> <mi>P</mi> <mo stretchy="false">)</mo> <mo>⋅<!-- ⋅ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>P</mi> </mfrac> </mrow> <mo>⋅<!-- ⋅ --></mo> <mn>3600</mn> <mo>⋅<!-- ⋅ --></mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=({\mathrm {d} }T\cdot e+{\frac {10}{P}}\cdot {\mathrm {d} }P)\cdot {\frac {k_{0}}{P}}\cdot 3600\cdot 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e2e53238c0b00b0d932b8e38b2a333a3e6c5c0b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:37.033ex; height:5.343ex;" alt="{\displaystyle R=({\mathrm {d} }T\cdot e+{\frac {10}{P}}\cdot {\mathrm {d} }P)\cdot {\frac {k_{0}}{P}}\cdot 3600\cdot 3}"></span> </p><p>où : </p> <ul><li>d<i>T</i> est l'incertitude sur le <a href="/wiki/Moment_du_p%C3%A9rih%C3%A9lie" class="mw-redirect" title="Moment du périhélie">moment du périhélie</a>, en <a href="/wiki/Jour" title="Jour">jours</a></li> <li><i>e</i> est l'<a href="/wiki/Excentricit%C3%A9_orbitale" title="Excentricité orbitale">excentricité</a></li> <li><i>P</i> est la <a href="/wiki/P%C3%A9riode_de_r%C3%A9volution" title="Période de révolution">période orbitale</a>, en années</li> <li>d<i>P</i> est l'incertitude sur la période orbitale, en jours</li> <li><i>k</i><sub>0</sub> est la <a href="/wiki/Constante_gravitationnelle_de_Gauss" title="Constante gravitationnelle de Gauss">constante gravitationnelle de Gauss</a>, en degrés : <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{0}={\frac {180\mathrm {deg} }{\pi \mathrm {rad} }}\times 0{,}017\,202\,098\,95\;A^{\frac {3}{2}}\;D^{-1}\ S^{-{\frac {1}{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>180</mn> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">g</mi> </mrow> </mrow> <mrow> <mi>π<!-- π --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">d</mi> </mrow> </mrow> </mfrac> </mrow> <mo>×<!-- × --></mo> <mn>0,017</mn> <mspace width="thinmathspace" /> <mn>202</mn> <mspace width="thinmathspace" /> <mn>098</mn> <mspace width="thinmathspace" /> <mn>95</mn> <mspace width="thickmathspace" /> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> </mrow> </msup> <mspace width="thickmathspace" /> <msup> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <mtext> </mtext> <msup> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{0}={\frac {180\mathrm {deg} }{\pi \mathrm {rad} }}\times 0{,}017\,202\,098\,95\;A^{\frac {3}{2}}\;D^{-1}\ S^{-{\frac {1}{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7bfcbca90e30cef43d157dabed29fcb979ea30a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:45.916ex; height:5.509ex;" alt="{\displaystyle k_{0}={\frac {180\mathrm {deg} }{\pi \mathrm {rad} }}\times 0{,}017\,202\,098\,95\;A^{\frac {3}{2}}\;D^{-1}\ S^{-{\frac {1}{2}}}}"></span> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5ebb239b453149a6dedba8f18670ce9a9390c08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle {A}}"></span> l'<a href="/wiki/Unit%C3%A9_astronomique" title="Unité astronomique">unité astronomique</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {D}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>D</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {D}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2b48bdc67a19ddefb0aa409e442e815517a87e7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.924ex; height:2.176ex;" alt="{\displaystyle {D}}"></span> le <a href="/wiki/Temps_solaire" title="Temps solaire">jour solaire moyen</a>,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfd749ff84450814edb04bb695d674c8dd6a2d24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.499ex; height:2.176ex;" alt="{\displaystyle {S}}"></span> la masse solaire (ces trois unités étant celles du <a href="/wiki/Syst%C3%A8me_astronomique_d%27unit%C3%A9s" title="Système astronomique d'unités">système astronomique d'unités</a>).</li></ul></li> <li>3600 est le facteur de conversion des degrés aux <a href="/wiki/Seconde_d%27arc" class="mw-redirect" title="Seconde d'arc">secondes d'arc</a></li> <li>3 est un <a href="/wiki/Empirisme" title="Empirisme">facteur empirique</a> pour que l'erreur formelle calculée soit plus proche de la réalité</li> <li><i>R</i> est le décalage (<i>runoff</i> en anglais) de <a href="/wiki/Longitude" title="Longitude">longitude</a> sur l'orbite, en secondes d'arc par <a href="/wiki/D%C3%A9cennie" title="Décennie">décennie</a>.</li></ul> <p>Le paramètre <i>R</i> est ensuite converti en le « paramètre d'incertitude », noté <i>U</i>, qui est un <a href="/wiki/Entier_naturel" title="Entier naturel">nombre entier</a> compris entre 0 et 9 : </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle U=\mathrm {E} \left({\frac {\mathrm {ln} (R)}{C}}\right)+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>U</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">E</mi> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">l</mi> <mi mathvariant="normal">n</mi> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </mrow> <mi>C</mi> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle U=\mathrm {E} \left({\frac {\mathrm {ln} (R)}{C}}\right)+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d29f7b04d7c41b125de52fc5168b88e0a282ce10" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:20.624ex; height:6.343ex;" alt="{\displaystyle U=\mathrm {E} \left({\frac {\mathrm {ln} (R)}{C}}\right)+1}"></span> </p><p>où : </p> <ul><li>E est la fonction <a href="/wiki/Partie_enti%C3%A8re" class="mw-redirect" title="Partie entière">partie entière</a> : par exemple, E(3,5) = 3 et E(-0,5) = -1.</li> <li>ln est la fonction <a href="/wiki/Logarithme_n%C3%A9p%C3%A9rien" title="Logarithme népérien">logarithme népérien</a></li> <li><i>C</i> est une constante : <i>C</i> = ln(648 000)/9 ≈ 1,49</li></ul> <p>Si le <i>U</i> obtenu est négatif, on prend <i>U</i> = 0 ; si le <i>U</i> obtenu est plus grand que 9, on prend <i>U</i> = 9. </p><p>En résumé, on a : </p> <table class="wikitable alternance centre"> <caption> </caption> <tbody><tr> <th scope="col">U </th> <th scope="col">Runoff <br /> (arcsec/décennie) </th></tr> <tr> <td>0 </td> <td>< 1,0 </td></tr> <tr> <td>1 </td> <td>1,0~4,4 </td></tr> <tr> <td>2 </td> <td>4,4~19,6 </td></tr> <tr> <td>3 </td> <td>19,6~86,5 </td></tr> <tr> <td>4 </td> <td>86,5~382 </td></tr> <tr> <td>5 </td> <td>382~1692 </td></tr> <tr> <td>6 </td> <td>1692~7488 </td></tr> <tr> <td>7 </td> <td>7488~33121 </td></tr> <tr> <td>8 </td> <td>33121~146502 </td></tr> <tr> <td>9 </td> <td>> 146 502 </td></tr></tbody></table> <div class="mw-heading mw-heading2"><h2 id="Utilisation">Utilisation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&veaction=edit&section=2" title="Modifier la section : Utilisation" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&action=edit&section=2" title="Modifier le code source de la section : Utilisation"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>La page web du <a href="/wiki/JPL_Small-Body_Database" title="JPL Small-Body Database">JPL Small-Body Database</a> désigne le "paramètre d'incertitude U" du MPC comme le "code de condition" (en anglais <i>condition code</i>)<sup id="cite_ref-conditioncode_2-0" class="reference"><a href="#cite_note-conditioncode-2"><span class="cite_crochet">[</span>2<span class="cite_crochet">]</span></a></sup>. </p><p>Cette incertitude est liée à plusieurs paramètres entrant dans le processus de détermination des orbites, dont le nombre d'observations (de mesures), la durée couverte (<a href="/wiki/Arc_d%27observation" title="Arc d'observation">arc d'observation</a>), leur qualité (<a href="/wiki/Astronomie_radar" title="Astronomie radar">radar</a> ou optique) et leur géométrie. Parmi ces paramètres, la durée couverte a généralement l'effet le plus important sur l'incertitude de l'orbite<sup id="cite_ref-NASA-uncertainty_3-0" class="reference"><a href="#cite_note-NASA-uncertainty-3"><span class="cite_crochet">[</span>3<span class="cite_crochet">]</span></a></sup>. </p><p>Des objets tels que <span class="nowrap"><a href="/wiki/1995_SN55" class="mw-redirect" title="1995 SN55">1995 SN<sub>55</sub></a></span> ayant un code de condition (paramètre d'incertitude U) <span class="need_ref" title="Ce passage nécessite des précisions supplémentaires." style="cursor:help;">égal à E</span><sup class="need_ref_tag" style="padding-left:2px;"><a href="/wiki/Aide:Pr%C3%A9ciser_un_fait" title="Aide:Préciser un fait">[Quoi ?]</a></sup> sont considérés comme <a href="/wiki/Ast%C3%A9ro%C3%AFde_perdu" class="mw-redirect" title="Astéroïde perdu">perdus</a>. </p><p>L'<a href="/wiki/Ast%C3%A9ro%C3%AFde_ar%C3%A9ocroiseur" title="Astéroïde aréocroiseur">astéroïde aréocroiseur</a> <span class="nowrap"><a href="/w/index.php?title=2004_BX159&action=edit&redlink=1" class="new" title="2004 BX159 (page inexistante)">2004 BX<sub>159</sub></a></span>, qui a une très courte période d'observation (3 jours) et un paramètre d'incertitude de 9, a une grande zone d'incertitude qui donne une probabilité cumulée d'impact d'environ 1 sur 2,1 milliards<sup id="cite_ref-summary-BX159_4-0" class="reference"><a href="#cite_note-summary-BX159-4"><span class="cite_crochet">[</span>4<span class="cite_crochet">]</span></a></sup>. </p><p>L'<a href="/wiki/Ast%C3%A9ro%C3%AFde_Aten" class="mw-redirect" title="Astéroïde Aten">astéroïde Aten</a> <span class="nowrap"><a href="/w/index.php?title=1994_WR12&action=edit&redlink=1" class="new" title="1994 WR12 (page inexistante)">1994 WR<sub>12</sub></a></span> a un paramètre d'incertitude de 8 et la prochaine période favorable pour l'observer ne surviendra pas avant <time class="nowrap" datetime="2044-11" data-sort-value="2044-11">novembre 2044</time> ; l'incertitude de son orbite le conduira à passer quelque part entre 0,03 et 0,19 <a href="/wiki/Unit%C3%A9_astronomique" title="Unité astronomique">unité astronomique</a> de la Terre<sup id="cite_ref-close-WR12_5-0" class="reference"><a href="#cite_note-close-WR12-5"><span class="cite_crochet">[</span>5<span class="cite_crochet">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Références"><span id="R.C3.A9f.C3.A9rences"></span>Références</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&veaction=edit&section=3" title="Modifier la section : Références" class="mw-editsection-visualeditor"><span>modifier</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Param%C3%A8tre_d%27incertitude&action=edit&section=3" title="Modifier le code source de la section : Références"><span>modifier le code</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="references-small decimal" style=""><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-MPC-Uncertainty-1"><span class="mw-cite-backlink noprint">↑ <sup><a href="#cite_ref-MPC-Uncertainty_1-0">a</a> <a href="#cite_ref-MPC-Uncertainty_1-1">b</a> et <a href="#cite_ref-MPC-Uncertainty_1-2">c</a></sup> </span><span class="reference-text"> <span class="ouvrage"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="http://www.minorplanetcenter.org/iau/info/UValue.html"><cite style="font-style:normal;" lang="en">Uncertainty Parameter U</cite></a> », <a href="/wiki/Centre_des_plan%C3%A8tes_mineures" title="Centre des planètes mineures">Centre des planètes mineures</a> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2011-11-15" data-sort-value="2011-11-15">15 novembre 2011</time>)</small></span></span> </li> <li id="cite_note-conditioncode-2"><span class="mw-cite-backlink noprint"><a href="#cite_ref-conditioncode_2-0">↑</a> </span><span class="reference-text"><span class="ouvrage"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/sbdb_help.cgi?name=condition_code"><cite style="font-style:normal;" lang="en">Definition/Description for SBDB Parameter/Field: condition code</cite></a> », JPL Solar System Dynamics <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2011-11-15" data-sort-value="2011-11-15">15 novembre 2011</time>)</small></span></span> </li> <li id="cite_note-NASA-uncertainty-3"><span class="mw-cite-backlink noprint"><a href="#cite_ref-NASA-uncertainty_3-0">↑</a> </span><span class="reference-text"><span class="ouvrage" id="2005"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="https://neo.jpl.nasa.gov/ca/neo_ca_info.html"><cite style="font-style:normal;" lang="en">Near Earth Objects Close-Approach Uncertainties</cite></a> », NASA/JPL Near-Earth Object Program Office, <time class="nowrap" datetime="2005-08-31" data-sort-value="2005-08-31">31 août 2005</time> <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2011-11-15" data-sort-value="2011-11-15">15 novembre 2011</time>)</small></span></span> </li> <li id="cite_note-summary-BX159-4"><span class="mw-cite-backlink noprint"><a href="#cite_ref-summary-BX159_4-0">↑</a> </span><span class="reference-text"><span class="ouvrage"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="https://neo.jpl.nasa.gov/risk/2004bx159.html"><cite style="font-style:normal;" lang="en">Earth Impact Risk Summary: 2004 BX159</cite></a> », NASA/JPL Near-Earth Object Program Office <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2011-11-16" data-sort-value="2011-11-16">16 novembre 2011</time>)</small></span></span> </li> <li id="cite_note-close-WR12-5"><span class="mw-cite-backlink noprint"><a href="#cite_ref-close-WR12_5-0">↑</a> </span><span class="reference-text"><span class="ouvrage" id="1994"><abbr class="abbr indicateur-langue" title="Langue : anglais">(en)</abbr> « <a rel="nofollow" class="external text" href="https://ssd.jpl.nasa.gov/sbdb.cgi?sstr=1994WR12;cad=1#cad"><cite style="font-style:normal;" lang="en">JPL Close-Approach Data: (1994 WR12)</cite></a> », 1994-12-31 last obs (arc=35 days) <small style="line-height:1em;">(consulté le <time class="nowrap" datetime="2011-04-07" data-sort-value="2011-04-07">7 avril 2011</time>)</small></span></span> </li> </ol></div> </div> <ul id="bandeau-portail" class="bandeau-portail"><li><span class="bandeau-portail-element"><span class="bandeau-portail-icone"><span class="noviewer skin-invert-image" typeof="mw:File"><a 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