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-		<p>Comet C/2013 A1 (siding Spring) will experience a high velocity encounter with Mars on <measure type="value"><date when="2014-10-19">October 19, 2014</date></measure> at a distance of <measure type="interval"><num type="base">135,000</num><measure type="LENGTH" unit="km">km</measure> &#xB1; <num type="range">5000</num><measure type="LENGTH" unit="km">km</measure></measure> from the planet center. We present a comprehensive analysis of the trajectory of both the comet nucleus and the dust tail. The nucleus of C/2013 A1 cannot impact on Mars even in the case of unexpectedly large nongravitational perturbations. Furthermore, we compute the required ejection velocities for the dust grains of the tail to reach Mars as a function of particle radius and density and heliocentric distance of the ejection. A comparison between our results and the most current modeling of the ejection velocities suggests that impacts are possible only for millimeter to centimeter size particles released more than <measure type="interval"><num atLeast="13">13</num> <measure type="LENGTH" unit="au">au</measure></measure> from the Sun. However, this level of cometary activity that far from the Sun is considered extremely unlikely. The arrival time of these particles spans a <measure type="interval"><num type="range">20</num>-<measure type="TIME" unit="minute">minute</measure> time interval centered at <date type="base" when="2014-10-19T20:09">October 19, 2014 at 20:09 TDB</date></measure>, i.e., around the time that Mars crosses the orbital plane of C/2013 A1. Ejection velocities larger than currently estimated by a factor <measure type="interval">&gt; <num atMost="2">2</num></measure> would allow impacts for smaller particles ejected as close as <measure type="value"><num>3</num> <measure type="LENGTH" unit="au">au</measure></measure> from the Sun. These particles would reach Mars from <measure type="interval"><num atLeast="43">43</num> to <num atMost="130">130</num> <measure type="TIME" unit="min">min</measure></measure> after the nominal close approach epoch of the purely gravitational trajectory of the nucleus.</p>
+		<p>Comet C/2013 A1 (siding Spring) will experience a high velocity encounter with Mars on <measure type="value"><date when="2014-10-19">October 19, 2014</date></measure> at a distance of <measure type="value"><num>135,000</num><measure type="LENGTH" unit="km">km</measure></measure> &#xB1; <measure type="value"><num>5000</num><measure type="LENGTH" unit="km">km</measure></measure> from the planet center. We present a comprehensive analysis of the trajectory of both the comet nucleus and the dust tail. The nucleus of C/2013 A1 cannot impact on Mars even in the case of unexpectedly large nongravitational perturbations. Furthermore, we compute the required ejection velocities for the dust grains of the tail to reach Mars as a function of particle radius and density and heliocentric distance of the ejection. A comparison between our results and the most current modeling of the ejection velocities suggests that impacts are possible only for millimeter to centimeter size particles released more than <measure type="interval"><num atLeast="13">13</num> <measure type="LENGTH" unit="au">au</measure></measure> from the Sun. However, this level of cometary activity that far from the Sun is considered extremely unlikely. The arrival time of these particles spans a <!-- 1) to check par rapport à la doc où pas d'attribut type="base" dans la balise de date><measure type="interval"><num type="range">20</num>-<measure type="TIME" unit="minute">minute</measure> time interval centered at <date type="base" when="2014-10-19T20:09">October 19, 2014 at 20:09 TDB</date></measure><-->, i.e., around the time that Mars crosses the orbital plane of C/2013 A1. Ejection velocities larger than currently estimated by a factor <!-- 2) inclure le > dans la balise measure ? --><measure type="interval">&gt; <num atLeast="2">2</num></measure> would allow impacts for smaller particles ejected as close as <measure type="value"><num>3</num> <measure type="LENGTH" unit="au">au</measure></measure> from the Sun. These particles would reach Mars from <measure type="interval"><num atLeast="43">43</num> to <num atMost="130">130</num> <measure type="TIME" unit="min">min</measure></measure> after the nominal close approach epoch of the purely gravitational trajectory of the nucleus.</p>
 		<p>Comet C/2013 A1 (Siding Spring) was discovered on <measure type="value"><date when="2013-01">January 2013</date></measure> at the Siding Spring observatory (McNaught et al. 2013). Shortly after discovery it was clear that C/2013 A1 was headed for a close encounter with Mars on <measure type="value"><date when="2014-10-19">October 19, 2014</date></measure>. C/2013 A1 is on a near parabolic retrograde orbit and will have a high relative velocity with respect to Mars of about <measure type="value"><num>56</num><measure type="VELOCITY" unit="km/s">km/s</measure></measure> during the close approach. If the comet has no significant nongravitational perturbations, the trajectory of the nucleus consistent with the present set of astrometric observations rules out an impact on Mars. However, comet orbits are generally difficult to predict. As the comet gets closer to the Sun cometary activity can result in significant nongravitational perturbations (Marsden et al. 1973) that in turn can lead to significant deviations from the purely gravitational ( " ballistic " ) trajectory. In the case of C/2013 A1, cometary activity was already visible in the discovery observations, when the comet was at more than <measure type="interval"><num atLeast="7">7</num> <measure type="LENGTH" unit="au">au</measure></measure> from the Sun.</p>
 		<p>Beside the effect of nongravitational perturbations, dust grains in the tail of the comet could reach Mars and possibly damage spacecrafts orbiting Mars, i.e., NASA's Mars Reconnaissance Orbiter , NASA's Mars Odyssey, ESA's Mars Express, NASA's MAVEN, and ISRO's MOM. Vaubaillon et al. (2014) and Moorhead et al. (2014) show that dust grains can reach Mars if they are ejected from the nucleus with a sufficiently high velocity. The modeling of the ejection velocity is in continuous evolution. As the comet gets closer to the inner solar system we have additional observation that provide constraints to the ejection velocities of dust grains. In particular, by making use of observations from HST/WFC3, Swift/UVOT, and WISE, Farnham et al. (2014) and Tricarico et al. (2014) find ejection velocities lower than those derived by Vaubaillon et al. (2014) and Moorhead et al. (2014), thus significantly reducing the hazard due to dust grains in the comet tail.</p>
 		<p>In this paper we study the trajectory of C/2013 A1's nucleus, including the contribution of nongravitational perturbations. We also present an analysis of the required ejection velocities for the dust grains to reach Mars. This analysis can be used as a reference as the understanding and the modeling of the dust grain ejection velocities evolve.</p>
-		<p>We examined all available ground-based optical astrometry (Right Ascension and Declination angular pairs) as of <measure type="value"><date when="2014-03-15">March 15, 2014</date></measure>. To remove biased contributions from individual observatories we conservatively excluded from the orbital fit batches of more than <measure type="interval"><num atLeast="4">four</num></measure> observations in the same night with mean residual larger than <measure type="interval"><num atLeast="0.5">0.5</num><measure type="ANGLE" unit="arcsecond">&#x2032;&#x2032;</measure></measure>, and batches of <measure type="list"><num>three</num> or <num>four</num></measure> observations showing mean residual larger than <measure type="interval"><num atLeast="1">1</num> <measure type="ANGLE" unit="arcsecond">&#x2032;&#x2032;</measure></measure>. We also adopted the outlier rejection scheme of Carpino et al. (2003) with &#x3C7; rej = 2. To the remaining <measure type="value"><num>597</num></measure> optical observations we applied the standard one arcsecond data-weights used for comet astrometry. Figure 1 shows the residuals of C/2013 A1's observations against our new orbit solution (JPL solution 46). [Figure 1 about here.] Our force model included solar and planetary perturbations based on JPL's planetary ephemerides DE431 1 , the gravitational attraction due to the <measure type="value"><num>16</num></measure> most massive bodies in the main asteroid belt, and the Sun relativistic term. No significant nongravitational forces were evident in the astrometric data and so the corresponding JPL orbit solution is ballistic, identified as number 46. Table 1 contains the orbital elements of the computed solution.</p>
+		<p>We examined all available ground-based optical astrometry (Right Ascension and Declination angular pairs) as of <measure type="value"><date when="2014-03-15">March 15, 2014</date></measure>. To remove biased contributions from individual observatories we conservatively excluded from the orbital fit batches of more than <measure type="interval"><num atLeast="4">four</num></measure> observations in the same night with mean residual larger than <measure type="interval"><num atLeast="0.5">0.5</num><measure type="ANGLE" unit="arcsecond">&#x2032;&#x2032;</measure></measure>, and batches of <measure type="list"><num>three</num> or <num>four</num></measure> observations showing mean residual larger than <measure type="interval"><num atLeast="1">1</num> <measure type="ANGLE" unit="arcsecond">&#x2032;&#x2032;</measure></measure>. We also adopted the outlier rejection scheme of Carpino et al. (2003) with <!-- ?? TODO -->&#x3C7; rej = 2. To the remaining <measure type="value"><num>597</num></measure> optical observations we applied the standard one arcsecond data-weights used for comet astrometry. Figure 1 shows the residuals of C/2013 A1's observations against our new orbit solution (JPL solution 46). [Figure 1 about here.] Our force model included solar and planetary perturbations based on JPL's planetary ephemerides DE431 1 , the gravitational attraction due to the <measure type="value"><num>16</num></measure> most massive bodies in the main asteroid belt, and the Sun relativistic term. No significant nongravitational forces were evident in the astrometric data and so the corresponding JPL orbit solution is ballistic, identified as number 46. Table 1 contains the orbital elements of the computed solution.</p>
 		<p>Table 2 provides information on the close encounter between C/2013 A1 and Mars. C/2013 A1 passes through the orbital plane of Mars <measure type="value"><num>69</num><measure type="TIME" unit="minute">minutes</measure></measure> before the close approach epoch, while Mars passes through the orbital plane of C/2013 A1 <measure type="value"><num>99</num><measure type="TIME" unit="minute">minutes</measure></measure> after the close approach. The Minimum Orbit Intersection Distance (MOID) is the minimum distance between the orbit of the comet and the orbit of Mars (MOID, Gronchi et al. 2007). The MOID points on the <measure type="value"><num>two</num></measure> orbits are not on the line of nodes. Mars arrives at the minimum distance point <measure type="value"><num>101</num><measure type="TIME" unit="min">min</measure></measure> after the close approach epoch, while C/2013 A1 arrives at the minimum distance point <measure type="value"><num>70</num><measure type="TIME" unit="minute">min</measure></measure> before the close approach, which means that the comet is <measure type="value"><num>171</num><measure type="TIME" unit="minute">min</measure></measure> early for the minimum distance encounter. [Table 2 about here.] A standard tool to analyze planetary encounters is the b-plane (Kizner 1961; Valsecchi et al. 2003 ), defined as the plane passing through the center of mass of the planet and normal to the inbound hyperbolic approach asymptote. The coordinates on the b-plane described in Valsecchi et al. (2003) are oriented such that the projected heliocentric velocity of the planet is along &#x2212;&#x3B6;. Therefore , &#x3B6; varies with the time of arrival, i.e., a positive &#x3B6; means that the comet arrives late at the encounter while a negative &#x3B6; means that the comet arrives early. On the other hand &#x3BE; is related to the MOID. The b-plane is used on a daily basis for asteroid close approaches to the Earth and computing the corresponding impact probabilities (Milani et al. 2005). Figure 2 shows the projection of the 3&#x3C3; uncertainty ellipsoid of JPL solution 46 on the b-plane. The projection of the velocity of Mars on this plane is oriented as &#x2212;&#x3B6;, while the Mars-to-Sun vector projection is on the left side, at a counterclockwise angle of <measure type="value"><num>186</num> <measure type="ANGLE" unit="degree">°</measure></measure> with respect to the &#x3BE; axis. The negative &#x3B6; coordinate of the center of the ellipse corresponds to the <measure type="value"><num>171</num><measure type="TIME" unit="minute">min</measure></measure> time shift between Mars and C/2013 A1. [Figure 2 about here.]</p>
 		<p>Comet trajectories can be significantly affected by nongravitational perturbations due to cometary outgassing. We use the Marsden et al. (1973) comet nongravitational model:</p>
 		<p>where g(r) is a known function of the heliocentric distance r, and A i are free parameters that give the nongravitational acceleration at 1 au in the radial-transverse-normal reference frame defined by&#x2C6;rby&#x2C6;by&#x2C6;r, &#x2C6; t, &#x2C6; n.</p>