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ebenaissa committed Sep 4, 2017
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<p>Although the nucleus of comet C/2013 A1 (Siding Spring) will safely pass Mars in <measure type="value"><date when="2014-10">October 2014</date></measure>, the dust in the coma and tail will more closely approach the planet. Using a dynamical model of comet dust, we estimate the impact fluence. Based on our nominal model no impacts are expected at Mars. Relaxing our nominal model's parameters, the fluence is no greater than ∼ <measure type="interval"><num atMost="10^-7">10 −7</num> <measure type="DENSITY" unit="grain.m^-2">grains m −2</measure></measure> for grain radii larger than <measure type="interval"><num atLeast="10">10</num> <measure type="LENGTH" unit="µm">µm</measure></measure>. Mars orbiting spacecraft are unlikely to be impacted by large dust grains, but Mars may receive as many as ∼ <measure type="interval"><num atMost="10^7">10 7</num> <measure type="MASS" unit="grain">grains</measure></measure>, or ∼ <measure type="interval"><num atMost="100">100</num> <measure type="MASS" unit="kg">kg</measure></measure> of total dust. We also estimate the flux of impacting gas molecules commonly observed in comet comae.</p>
<p>Comet C/2013 A1 (Siding Spring) will pass Mars with <!--a close approach distance of 1.35 ± <measure type="value"><num>0.05 × 10 5</num> <measure type="LENGTH" unit="km">km</measure></measure>, and -->a relative speed of <measure type="value"><num>55.96</num> <measure type="VELOCITY" unit="km.s^-1">km s −1</measure></measure> on <measure type="interval"><date type="base" when="2014-10-19T18:29Z">2014 Oct 19 at 18:29</date>±<num type="range">:03</num><measure type="TIME" unit="min"/> UTC</measure></measure> (3-σ uncertainties; Farnocchia et al. 2014). The nucleus will miss the planet, its moons, and orbiting spacecraft. However, given the right combination of ejection velocity, ejection time, and response to radiation pressure, dust grains from the comet can reach the planet. Farnocchia et al. (2014) predict that Mars will miss the comet's orbit by <measure type="value"><num>2.7 × 10 4</num> <measure type="LENGTH" unit="km">km</measure></measure> at <measure type="value"><date when="2014-10-19T20:10Z">20:10 UTC</date></measure>. This second close approach potentially reduces the energy required to place dust grains on impacting orbits. We present models of the dust and gas based on the summary of the comet's activity by Farnham et al. (in preparation) and estimate the impact hazard for Mars and its satellites as well as the comet gas flux at Mars.</p>
<p>Comet C/2013 A1 (Siding Spring) will pass Mars with <!--a close approach distance of 1.35 ± <measure type="value"><num>0.05 × 10 5</num> <measure type="LENGTH" unit="km">km</measure></measure>-->, and a relative speed of <measure type="value"><num>55.96</num> <measure type="VELOCITY" unit="km.s^-1">km s −1</measure></measure> on <measure type="interval"><date type="base" when="2014-10-19T18:29Z">2014 Oct 19 at 18:29</date>±<num type="range">:03</num><measure type="TIME" unit="min"> UTC</measure></measure> (3-σ uncertainties; Farnocchia et al. 2014). The nucleus will miss the planet, its moons, and orbiting spacecraft. However, given the right combination of ejection velocity, ejection time, and response to radiation pressure, dust grains from the comet can reach the planet. Farnocchia et al. (2014) predict that Mars will miss the comet's orbit by <measure type="value"><num>2.7 × 10 4</num> <measure type="LENGTH" unit="km">km</measure></measure> at <measure type="value"><date when="2014-10-19T20:10Z">20:10 UTC</date></measure>. This second close approach potentially reduces the energy required to place dust grains on impacting orbits. We present models of the dust and gas based on the summary of the comet's activity by Farnham et al. (in preparation) and estimate the impact hazard for Mars and its satellites as well as the comet gas flux at Mars.</p>
<p>To assess the impact hazard, we generated <measure type="value"><num>two</num></measure> simulations of <measure type="value"><num>10 9</num></measure> particles each, picked from broad parameter ranges. These raw simulations act as guides to determine which combinations of size, ejection speed, and ejection time may result in impacts. Next, we define more limited parameter sets that are carefully chosen to match known parameters of the comet. We select and weight particles from the raw simulations that match those sets, and use them to estimate the fluence at Mars. Below we describe our dynamical model, the raw simulations, and <measure type="value"><num>four</num></measure> parameter sets used to estimate the impact hazard.</p><p>The circumstances of the encounter are simulated with the dynamical model of Kelley (2006). For this study we msk@astro.umd.edu use the JPL ephemeris solution #46 ( Farnocchia et al. 2014). In order to reduce the required computational time, we modified the model to use the <measure type="value"><num>two</num></measure>-body (Keplerian) propagation functions from NASA's Navigation and Ancillary Information Facility SPICE toolkit. Dust grains are parameterized by β, the ratio of the force from solar radiation pressure to the force from solar gravity: β = 0.57Q pr /ρa, where Q pr is the radiation pressure efficiency, ρ is the grain density in units of g cm −3 , and a is the grain radius in units of µm ( Burns et al. 1979). In the Keplerian solution, the gravitational force from the Sun is reduced by the factor (1 − β).</p>
<p>The magnitude of the error introduced by neglecting planetary perturbations can be estimated by comparing zero-ejection velocity syndynes (lines of constant β with variable ejection times; Finson &amp; Probstein 1968) generated using the Keplerian solution to those generated using the original code. The distances between the syndynes define the error. For grains ejected up to <measure type="interval"><num atMost="4">4</num> <measure type="TIME" unit="year">years</measure></measure> before the closest approach, the error is at most <measure type="interval"><num atMost="300">300</num> <measure type="LENGTH" unit="km">km</measure></measure> for dust found within <measure type="interval"><num atMost="10^6">10 6</num> <measure type="LENGTH" unit="km">km</measure></measure> from the nucleus. We also considered whether the gravitational pull of Mars is significant. Ignoring the atmosphere, particles grazing the surface are displaced &lt; <measure type="interval"><num atMost="100">100</num> <measure type="LENGTH" unit="km">km</measure></measure> at closest approach, and the cross-section enhancement factor from gravitational focusing by Mars is <measure type="value"><num>1.008</num></measure> (Jones &amp; Poole 2007). The Keplerian solution is sufficient for our purposes.</p>
<p>Simulation 1 contains <measure type="value"><num>10 9 particles</num></measure> selected from the following parameters, based on observations of the comet with a generous conservative margin: ages range uniformly from <measure type="interval"><num atLeast="0">0</num> to <num atMost="4">4</num> <measure type="TIME" unit="year">yr</measure></measure> (out to r h = <measure type="value"><num>13</num> <measure type="LENGTH" unit="AU">AU</measure></measure>); expansion speeds range uniformly from <measure type="value"><num>0</num></measure> to v ref (a/1 mm) −0.5 (r h /5 AU) −1 , where v ref = <measure type="value"><num>1.9</num> <measure type="VELOCITY" unit="m.s^-1">m s −1</measure></measure> is the expansion speed of <measure type="value"><num>1</num> <measure type="LENGTH" unit="mm">mm</measure></measure> grains ejected at <measure type="value"><num>5</num> <measure type="LENGTH" unit="AU">AU</measure></measure> from the Sun; ejection velocities are radial and isotropically distributed around the nucleus; and, radii are selected from a distribution uniform in log-space (dn/d log a ∝ 1) ranging from <measure type="interval"><num atLeast="10">10</num> to <num atMost="10^4">10 4</num> <measure type="LENGTH" unit="µm">µm</measure></measure>. The logarithmic distribution ensures our final results will have a statistically uniform representation of each size decade. For the conversion from radius to β we assume a grain density of <measure type="value"><num>1</num> <measure type="DENSITY" unit="g.cm^-3">g cm −3</measure></measure> , and Q pr = <measure type="value"><num>1</num></measure>. J.Y. Li et al. (in preparation) imaged Siding Spring at <measure type="list"><num>4.6</num>, <num>3.8</num>, and <num>3.3</num> <measure type="LENGTH" unit="AU">AU</measure></measure> from the Sun with the Hubble Space Telescope WFC3 instrument. The high spatial resolution of the images (<measure type="value"><num>40</num> <measure type="RESOLUTION" unit="mas.pixel^-1">mas per pixel</measure></measure>, corresponding to ≥ <measure type="interval"><num atLeast="100">100</num> <measure type="RESOLUTION" unit="km.pixel^-1">km per pixel</measure></measure>) resolve the inner coma, and allow investigations of the dust grain expansion velocities. Farnham et al. (in preparation) analyzed those images and found that the dust that comprises the bulk of the coma and tail has speeds best matched by v ref (a/1 mm) −0.6 (r h /5 AU) −1.5 , for v ref = <measure type="value"><num>0.42</num> <measure type="VELOCITY" unit="m.s^-1">m s −1</measure></measure>. Grains with these speeds are a subset of simulation 1.</p>
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