Figure 1 - available from: Nature
This content is subject to copyright. Terms and conditions apply.
| Light curves of the occultation. Light curves in the form of normalized flux versus time (at mid-exposure) were obtained from the different observatories that recorded the occultation (Table 1). The black points and lines represent the light curves extracted from the observations. The blue lines show the best square-well-model fits to the main body and the ring at Konkoly, with square-well models derived from the assumed ring width and opacity (W = 70 km and p′ = 0.5) at other sites. The red points and lines correspond to the optimal synthetic profile deduced from the squarewell model fitted at each data point (see Methods). The rectangular profile in green corresponds to the ring egress event at Skalnate Pleso, which fell in a readout time of the camera (see Fig. 3). The light curves have been shifted in steps of 1 vertically for better viewing. 'Munich' corresponds to the Bavarian Public Observatory. Error bars are 1σ.
Source publication
Haumea-one of the four known trans-Neptunian dwarf planets- is a very elongated and rapidly rotating body1-3. In contrast to other dwarf planets4-6, its size, shape, albedo and density are not well constrained. The Centaur Chariklo was the first body other than a giant planet known to have a ring system7, and the Centaur Chiron was later found to p...
Contexts in source publication
Context 1
... Astrophysical Institute of the Hungarian Academy of Sciences, the 0.65-m telescope at Ondrejov Observatory, operated by the Astronomical Institute of the Czech Academy of Sciences, the 1.5-m telescope at Sierra Nevada Observatory, operated by the Instituto de Astrofisica de Andalucia-CSIC, the that best simultaneously fits the secondary events of Fig. 1. The ring fit provides an opening angle B ring = 13.8° ± 0.5° and a position angle for the apparent minor axis of the ring of P ring = − 74.3° ± 1.3°. This is aligned, to within error bars, with Haumea's apparent minor axis P limb = − 76.3° ± 1.2° (Fig. 2). Moreover, the orbital pole position of Hi'iaka 14 implies a sub-observer ...
Context 2
... Lomb periodogram 30 of the residuals in declination showed its strongest peak at a signifi- cant periodicity of 49.5 ± 0.9 days, which coincides with the known 20 orbital period of Hi'iaka (49.462 ± 0.083 days). A sinusoidal fit to the residuals (Extended Data Fig. 1) using the orbital period of Hi'iaka had a maximum when the theoretical position of Hi'iaka was at its northernmost position with respect to Haumea, and the minimum of the fit corresponded to the southernmost position of the satellite Hi'iaka. Hence we verified that the oscillation was indeed correlated with the the- oretical positions of Hi'iaka. ...
Context 3
... average. The main parameters of the star are shown in Extended Data Table 1. The brightness of the star was similar to that of Haumea, so at the time of the occultation we expected a brightness change of around 50% in the Haumea + star blended source. The resulting light curves (photon flux relative to the average value, versus time) are shown in Fig. ...
Context 4
... we use the best available dataset-the Asiago light curve-to derive Haumea's atmospheric upper limits (Fig. 1). From Haumea's mass of (4.006 ± 0.04) × 10 21 kg (ref. 20) and assuming that the body itself is in hydrostatic equilibrium we derive an average surface gravity of 0.39 m s −2 ...
Context 5
... body, the light curves reveal brief dimmings from most of the sites before and/or after the main event. The timings of these events (see Extended Data Table 2) were extracted by fitting square-well ring profiles to the short events, in the same way as for Chariklo (ref. 7). However, the only resolved profiles come from the Konkoly 1-m telescope ( Fig. 1). At that station, we derive a radial width (in the ring plane) of W ring ≈ 74 km at ingress and W ring ≈ 44 km at egress, with respective apparent opacities (along the line of sight) of p′ = 0.55 and p′ = 0.56. This implies so-called equivalent widths W equiv = W ring p′ of 41 km and 25 km, respectively, a measure of the radially ...
Context 6
... of each event. Consequently, we used a simple model with a uniform ring of width of 70 km and apparent opacity of 0.5 that provides the typical average equivalent width observed at Konkoly. These fits account for the readout times between exposures and eventually provide the timings of the synthetic events. Note that in one case (Skalnate egress; Fig. 1) the ring is not detected because it should occur during a readout time. Note also that at several stations (Lajatico, San Marcello Pistoiese, Asiago and Wendelstein) the egress ring event is not recorded, not as a result of a lack of signal-to-noise ratio, but because our view of the ring is blocked by Haumea's body (Fig. ...
Similar publications
Among the four known transneptunian dwarf planets, Haumea is an exotic, very elongated, and fast rotating body. In contrast to the other dwarf planets, its size, shape, albedo, and density are not well constrained. Here we report results of a multi-chord stellar occultation, observed on 2017 January 21. Secondary events observed around the main bod...
Citations
... It provided an accurate shape for the body, a very elongated triaxial ellipsoid (Ortiz et al 2017 and Table 4), a point discussed later. As for Chariklo, secondary events revealed the presence of a narrow and dense ring of width ≈ 70 km orbiting at 2287 +75 45 km from Haumea's center, see Table 3 and Fig. 13 and details in Ortiz et al (2017). Again this is well outside the synchronous orbit, near 1400 km, and a bit outside the Roche limit (Hedman, 2023). ...
Stellar occultations provide a powerful tool to explore objects of the outer solar system. The Gaia mission now provides milli-arcsec accuracy on the predictions of these events and makes possible observations that were previously unthinkable. Occultations return kilometric accuracies on the three-dimensional shape of bodies irrespective of their geocentric distances, with the potential of detecting topographic features along the limb. From the shape, accurate values of albedo can be derived, and if the mass is known, the bulk density is pinned down, thus constraining the internal structure and equilibrium state of the object. Occultations are also extremely sensitive to tenuous atmospheres, down to the nanobar level. They allowed the monitoring of Pluto's and Triton's atmospheres in the last three decades, constraining their seasonal evolution. They may unveil in the near future atmospheres around other remote bodies of the solar system. Since 2013, occultations have led to the surprising discovery of ring systems around the Centaur object Chariklo, the dwarf planet Haumea and the large trans-Neptunian object Quaoar, while revealing dense material around the Centaur Chiron. This suggests that rings are probably much more common features than previously thought. Meanwhile, they have raised new dynamical questions concerning the confining effect of resonances forced by irregular objects on ring particles. Serendipitous occultations by km-sized trans-Neptunian or Oort objects has the potential to provide the size distribution of a population that suffered few collisions until now, thus constraining the history of primordial planetesimals in the 1-100 km range.
... Stellar occultations by Solar System minor bodies and their ring systems can last less than a second (see e.g. Braga-Ribas et al. 2014;Ortiz et al. 2017;Morgado et al. 2023), such that sub-second time resolution observations can help map kilometer-level features. 1 Pulsars are precise cosmic clocks that show a wide variety of periodicities, from the accretion powered millisecond pulsars (e.g. ...
JWST, despite not being designed to observe astrophysical phenomena that vary on rapid time scales, can be an unparalleled tool for such studies. If timing systematics can be controlled, JWST will be able to open up the sub-second infrared timescale regime. Rapid time-domain studies, such as lag measurements in accreting compact objects and Solar System stellar occultations, require both precise inter-frame timing and knowing when a time series begins to an absolute accuracy significantly below 1s. In this work we present two long-duration observations of the deeply eclipsing double white dwarf system ZTF J153932.16+502738.8, which we use as a natural timing calibrator to measure the absolute timing accuracy of JWST's clock. From our two epochs, we measure an average clock accuracy of s, implying that JWST can be used for sub-second time-resolution studies down to the ms level, a factor improvement upon the pre-launch clock accuracy requirement. We also find an asymmetric eclipse profile in the F322W2 band, which we suggest has a physical origin.
... Recent studies found ring systems around Centaurs and trans-Neptunian objects including Chariklo, Haumea and Quaoar (Braga-Ribas et al. 2014;Ortiz et al. 2017;Morgado et al. 2023;Pereira et al. 2023), suggesting that these rings may be common around outer Solar system bodies, and here we assume that diffuse dust around Makemake may have a similar form. ...
... 3, and green stripe in Fig. 3). If the ring was made exclusively of these very small grains, the optical depth of the ring in the visible range would be τ ≈ 0.1, assuming a thin and narrow disk, and a ring width of 10 km and ring radius of r = 4300 km, corresponding to the 3:1 spinorbit resonance, similarly to those found around other small bodies (Braga-Ribas et al. 2014;Ortiz et al. 2017;Morgado et al. 2023). Note that the optical depth depends on the actual ring width chosen, and smaller for a wider ring. ...
We report on the discovery of a very prominent mid-infrared (18-25 {\mu}m) excess associated with the trans-Neptunian dwarf planet (136472) Makemake. The excess, detected by the MIRI instrument of the James Webb Space Telescope, along with previous measurements from the Spitzer and Herschel space telescopes, indicates the occurrence of temperatures of about 150 K, much higher than what solid surfaces at Makemake's heliocentric distance could reach by solar irradiation. We identify two potential explanations: a continuously visible, currently active region, powered by subsurface upwelling and possibly cryovolcanic activity, covering <1% of Makemake's surface, or an as yet undetected ring containing very small carbonaceous dust grains, which have not been seen before in trans-Neptunian or Centaur rings. Both scenarios point to unprecedented phenomena among trans-Neptunian objects and could greatly impact our understanding of these distant worlds.
... An alternative to the radiometric technique for deriving sizes and albedos is the use of stellar occultations. The observation of stellar occultations by small bodies (asteroids, comets, Centaurs, TNOs, and planetary moons) of the Solar System is an instrumental relatively simple, but powerful, technique for: directly measuring the size and shapes of these objects with (sub)kilometer accuracy, probing the environment around them with the possibility of revealing a binary nature (Leiva et al. 2020); discovering moons (e.g., Gault et al. 2022) and rings (Braga-Ribas et al. 2014;Ortiz et al. 2015Ortiz et al. , 2017; and detecting, measuring, or constraining an atmosphere down to the nanobar pressure level (e.g., Hubbard et al. 1988;Sicardy et al. 2003;Oliveira et al. 2022). In addition, the occultation observation provides an astrometric measurement of the occulting object with (sub)milliarcsecond accuracy within the Gaia reference system (Rommel et al. 2020;Ferreira et al. 2022;Kaminski et al. 2023), which can be used to improve the orbit and therefore also pre-dictions of future occultation events. ...
Context . Trans-Neptunian objects (TNOs) are considered to be among the most primitive objects in our Solar System. Knowledge of their primary physical properties is essential for understanding their origin and the evolution of the outer Solar System. In this context, stellar occultations are a powerful and sensitive technique for studying these distant and faint objects.
Aims . We aim to obtain the size, shape, absolute magnitude, and geometric albedo for TNO (143707) 2003 UY 117 .
Methods . We predicted a stellar occultation by this TNO for 2020 October 23 UT and ran a specific campaign to investigate this event. We derived the projected profile shape and size from the occultation observations by means of an elliptical fit to the occultation chords. We also performed photometric observations of (143707) 2003 UY 117 to obtain the absolute magnitude and the rotational period from the observed rotational light curve. Finally, we combined these results to derive the three-dimensional shape, volume-equivalent diameter, and geometric albedo for this TNO.
Results . From the stellar occultation, we obtained a projected ellipse with axes of (282 ± 18) × (184 ± 32) km. The area-equivalent diameter for this ellipse is D eq,A = 228 ± 21 km. From our photometric R band observations, we derived an absolute magnitude of H V = 5.97 ± 0.07 mag using V − R = 0.46 ± 0.07 mag, which was derived from a V band subset of these data. The rotational light curve has a peak-to-valley amplitude of ∆m = 0.36 ± 0.13 mag. We find the most likely rotation period to be P = 12.376 ± 0.0033 hours. By combining the occultation with the rotational light curve results and assuming a triaxial ellipsoid, we derived axes of a × b × c = (332 ± 24) km × (216 ± 24) km × (180 −24 ⁺²⁸ ) km for this ellipsoid, and therefore a volume-equivalent diameter of D eq,V = 235 ± 25 km. Finally, the values for the absolute magnitude and for the area-equivalent diameter yield a geometric albedo of p V = 0.139 ± 0.027.
... An alternative to the radiometric technique for deriving sizes and albedos is the use of stellar occultations. The observation of stellar occultations by small bodies (asteroids, comets, Centaurs, TNOs, and planetary moons) of the Solar System is an instrumental relatively simple, but powerful, technique for: directly measuring the size and shapes of these objects with (sub)kilometer accuracy, probing the environment around them with the possibility of revealing a binary nature (Leiva et al. 2020); discovering moons (e.g., Gault et al. 2022) and rings (Braga-Ribas et al. 2014;Ortiz et al. 2015Ortiz et al. , 2017; and detecting, measuring, or constraining an atmosphere down to the nanobar pressure level (e.g., Hubbard et al. 1988;Sicardy et al. 2003;Oliveira et al. 2022). In addition, the occultation observation provides an astrometric measurement of the occulting object with (sub)milliarcsecond accuracy within the Gaia reference system (Rommel et al. 2020;Ferreira et al. 2022;Kaminski et al. 2023), which can be used to improve the orbit and therefore also pre-dictions of future occultation events. ...
Trans-Neptunian objects (TNOs) are considered to be among the most primitive objects in our Solar System. Knowledge of their primary physical properties is essential for understanding their origin and the evolution of the outer Solar System. We predicted a stellar occultation by this TNO for 2020 October 23 UT and ran a specific campaign to investigate this event. We derived the projected profile shape and size from the occultation observations by means of an elliptical fit to the occultation chords. We also performed photometric observations of (143707) 2003 UY117 to obtain the absolute magnitude and the rotational period from the observed rotational light curve. Finally, we combined these results to derive the three-dimensional shape, volume-equivalent diameter, and geometric albedo for this TNO. From the stellar occultation, we obtained a projected ellipse with axes of km. The area-equivalent diameter for this ellipse is km. From our photometric R band observations, we derived an absolute magnitude of mag using mag, which was derived from a V band subset of these data. The rotational light curve has a peak-to-valley amplitude of mag. We find the most likely rotation period to be hours. By combining the occultation with the rotational light curve results and assuming a triaxial ellipsoid, we derived axes of km km km for this ellipsoid, and therefore a volume-equivalent diameter of km. Finally, the values for the absolute magnitude and for the area-equivalent diameter yield a geometric albedo of .
... Esta investigação tem rendido frutos, com a descoberta de novos anéis ao redor de (136108) Haumea, em 2017 [18], de (50000) Quaoar, em 2023 [8,19], e, ainda sob análise [20], os possíveis anéis de (2060) Chiron. ...
... O evento ocorreu em 21 de janeiro de 2017 e contou com a participação de 12 observatórios. Além de revelar semi-eixos do Haumea (1161 x 852 x 513 km) com grande precisão, a ocultação também revelou a presença de um anel confinado, com cerca de 70 km de largura, com um raio de de 2287 km[18] (figura 7).O trabalho, que contou com a colaboração de 8 brasileiros, foi liderado pelo espanhol Dr. José-Luis Ortiz e foi publicado na revista Nature, em 2017. Revelou não só os anéis, mas também que estas estruturas são mais comuns do que pensávamos, e que elas podem existir em diferentes tipos de objetos, mesmo a grandes distâncias do Sol. ...
... Em azul vemos as detecções do corpo principal. A seta mostra a direção de deslocamento da sombra[18]. ...
Há cerca de 10 anos anunciamos a descoberta do primeiro sistema de anéis ao redor de um pequeno corpo do Sistema Solar. A técnica de ocultações estelares, que permitiu o feito, vem sendo largamente utilizada para caracterizar objetos do Sistema Solar. Seu alto poder de resolução espacial tem permitido que dimensões e formas venham sendo obtidas, com grande precisão, para muitos objetos, desde aqueles próximos à Terra, até aqueles mais distantes do Sol. Além dos anéis de Chariklo descobertos em 2013, anéis já foram identificados ao redor do planeta-anão Haumea e do objeto transnetuniano Quaoar. Isto mostra que anéis podem ser comuns no Sistema Solar Exterior, já que limites previamente imaginados, como o Limite de Roche, não se aplicam à estes anéis. Os pesquisadores brasileiros e astrônomos cidadãos tem tido papel fundamental nesta pesquisa, a qual, graças ao LSST, deve expandir consideravelmente nos próximos anos.
... Alternatively, this trend could also be produced by the pebble accretion and streaming instability model if accreted pebbles were relatively rich in silicates (Cañas et al. 2024). The large KBOs are generally rock-rich with a canonical rock mass fraction of 70 % (Nimmo et al. 2017;Ortiz et al. 2017;Bierson & Nimmo 2019;Kiss et al. 2019); they have often been referred to as a representative composition of the solid materials in the outer protosolar nebula (McKinnon & Mueller 1988;Simonelli et al. 1989;McKinnon et al. 2017McKinnon et al. , 2021. Furthermore, KBOs that were formed via low-velocity collisions, with impact speeds similar to escape speeds, would make large primary/moon companions similar to Pluto/Charon or Orcus/Vanth, and should retain their primordial compositions (Canup 2005;Barr & Schwamb 2016;Canup et al. 2021;McKinnon et al. 2021). ...
We examine the role of refractory organics as a major C carrier in the outer protosolar nebula and its implications for the compositions of large Kuiper belt objects (KBOs) and CI chondrites. By utilizing Rosetta measurements of refractory organics in comet 67P/Churyumov-Gerasimenko, we show that they would make up a large fraction of the protosolar C inventory in the KBO-forming region based on the current widely adopted solar abundances. However, this would free up too much O to form water ice, producing solid material that is not sufficiently rock-rich to explain the uncompressed density of the Pluto-Charon system and other large KBOs; the former has been argued as the most representative value we have for the bulk composition of large KBOs (Barr & Schawmb 2016, Bierson & Nimmo 2019). This inconsistency further highlights the solar abundances problem - an ongoing challenge in reconciling spectroscopically determined heavy element abundances with helioseismology constraints. By employing a new dataset from solar CNO neutrinos and solar wind measurements of C, N, and O, we show that the uncompressed density of the Pluto-Charon system can be reproduced over a wide range of scenarios. We show that a lack of sulfates in Ryugu and Bennu samples implies a lower amount of water ice initially accreted into CI chondrite parent bodies than previously thought. These data are found to be consistent with the solar C/O ratio implied by the new dataset. Our predictions can be tested by future neutrino, helioseismology, and cosmochemical measurements.
... Rings have also been observed encircling various small objects, including the centaurs Chariklo and Chiron (Braga-Ribas et al. 2014;Ortiz et al. 2015;Wood et al. 2017;Bérard et al. 2017), as well as the trans-Neptunian dwarf planets Haumea and Quaoar (Ortiz et al. 2017;Morgado et al. 2023;Sicardy et al. 2022), through stellar occultations. Nonetheless, neither the rocky planets of the inner Solar System nor the moons of any planet possess planetary rings. ...
Rings are complex structures surrounding giant planets and some minor bodies in the Solar System. While some formation mechanisms could also potentially foster their existence around (regular or irregular) satellites, none of these bodies currently bear these structures. We aim to understand the underlying mechanisms that govern the potential formation, stability, and/or decay of hypothetical circumsatellital rings (CSRs), orbiting the largest moons in the Solar System. This extends to the exploration of short-term morphological features within these rings, providing insights into the ring survival time-scales and the interactions that drive their evolution. To conduct this study, we use numerical N-body simulations under the perturbing influence of the host planet and other moon companions. We found that moons with a lower Roche-to-Hill radius can preserve their rings over extended periods. Moreover, the gravitational environment in which these rings are immersed influences the system's morphological evolution, inducing gaps through the excitation of eccentricity and inclination of constituent particles. Specifically, our results show that Iapetus' and Rhea's rings experience minimal variations in their orbital parameters, enhancing their long-term stability. This agrees with the hypothesis that some of the features of Iapetus and Rhea were produced by ancient ring systems, for example, the huge ridge in Iapetus equator as a result of a decaying ring. From a dynamical perspective, we found that there are no mechanisms that preclude the existence of CSRs and we attribute their current absence to non-gravitational phenomena. Effects such as stellar radiation, magnetic fields, and the influence of magnetospheric plasma can significantly impact the dynamics of constituent particles and trigger their decay, highlighing the importance of future studies on these effects.
... Stellar occultation measurements have led to several major Solar System discoveries such as the discovery of ring systems around the planets Uranus and Neptune (Elliot et al. 1977;Reitsema et al. 1981), and more recently, the centaur (a type of small body inhabiting the region between the orbits of Jupiter and Neptune) (10199) Chariklo, along with numerous other small bodies since then (Braga-Ribas et al. 2014;Ortiz et al. 2017;Pereira et al. 2023). Occultation measurements also revealed the presence of the Neptunian satellite Larissa (Hubbard et al. 1986), its existence later confirmed by Voyager 2 (Smith et al. 1989). ...
Monitoring stellar occultations provides a powerful means to measure the shapes and sizes of small Solar System bodies, but produces large quantities of image data which can be laborious to analyse. An automated Python-based software, occ_find, was written for performing high-speed aperture photometry on spool files packed with large volumes of images from the 1.54m Danish Telescope. occ_find processed 11 spool files at a maximum rate of around 4–6 minutes per spool file, without image reduction. From these files, 3 occultation events were detected. The measured chord lengths are consistent with prior size measurements of these small bodies.
... 在 Ida 的卫星 Dactyl 被发现之前， 碰撞被认为是双小 行星系形成的一种重要机制， 大部分研究都围绕碰撞 碎片相互结合形成大石块以及由于小行星表面坡度 过大或高速撞击导致的旋转破裂等方面展开 [8,9] 。美 国 天 文 学 会 行 星 科 学 部 成 员 Merlin 等 人 [8] 以 及 Richardson 和 Walsh [9] 研究发现， 主星直径大于 20 km 双小行星系统可能是小行星遭受碰撞破碎后， 其碎片 聚集形成的。 对其他双小行星系统形成机制的研究首 先集中在对小行星 Ida 的撞击事件产生的碎片的运动 仿真上 [10,11] 。欧洲航天局 Hera 任务的首席科学家、 国际天文联盟近地天体工作组主席 Michel 等人 [12][13][14][15] 将 SPH 模型与 N-body 模型结合，对撞击后碎片的演 化进行了一系列仿真， 这些仿真建立了毁灭性撞击事 件的动力学模型， 并模拟了碎片在长期引力作用下再 聚集的过程。结果显示，双小行星系统的形成是小行 星被撞击破坏后演化的一个自然结果。 美国天文学会 行星科学部成员 Durda 等人 [16,17] 也对碰撞过程进行 了仿真模拟， 其能够产生出与主带中观测到的在质量 上类似的双小行星系统。另外，所有基于碰撞过程理 解双小行星形成机制的仿真工作都发现了三星或多 星系统。Durda 等人 [16] 发现了临时存在的多星系统， Leinhard 和 Richardson [18] 发现在仿真过程中，10%的 三星系统和 3%的多星系统持续存在了数天时间。 自从 1993 年 Galileo 号探测器第一次发现双小行 星 Ida-Dactyl [19] 以来，航天强国已经对双小行星系统 的探测进行了尝试 [20][21][22][23][24][25][26][27][28][29] 。 美国宇航局 NASA 的 DART (DoubleAsteroid Redirection Test)任务 [20] ，已经于 2021 年 11 月 24 日发射，于 2022 年 9 月 26 日使用 535 kg 的动能撞击器以 6.6 km/s 的速度撞击双小行星 系统 Didymos 的从星 Dimorphos。此次撞击产生了大 量的溅射碎片， 同时改变了双小行星系统的自旋轨道 状态 [20,[23][24][25][26][27][28][29] 。在 DART 任务撞击 Dimorphos 的 4 年 后， 欧空局的 Hera 任务探测器将会进入环绕 Didymos 的轨道， 来抵近观察双小行星的自转周期以及详细的 表面地形、特征、尺寸等数据，同时测量撞击后双小 行星系统的动力学环境变化等 [20] 。 目前对双小行星系统形成机制的普遍理解是由 于撞击或者 YORP 效应导致小行星旋转破裂形成的 碎片的再聚集而成， 因此研究小天体附近的碎片对理 解双小行星的形成具有重要意义。另外，目前观测到 部分双小行星系统，如 Moshup-Squannit 和 Didymos 等，具有处于快速的自旋状态的主星，其部分表面的 物质在临界转速下可能被"甩出" [1] 。2019 年 1 月 6 日，美国宇航局的小行星探测器 OSIRIS-REx 抵达目 标小行星(101955)Bennu 附近一周之后，导航相机 拍摄的长曝光照片显示出 Bennu 附近出现了若干碎 片 [26] 。事实上，太阳系内活跃的小天体并不罕见，所 有处于活跃期的彗星表面，都在喷发着气流和尘埃， 如小行星(6478) Gault [31] 、 Bennu [30] 、 ( 136108) Haumea [32] 、 (7968)Elst-Pizarro [ [40,41] 。 因此， 21 世纪初，学者们开展了对溅射碎片的研究 [8,42] 。在 建立碎片的动力学模型的过程中， 主要涉及的难点包 括小行星引力场的近似方法的选取、 太阳系多种作用 力的计算以及小行星表面的撞击模型的建立等。 Dobrovolskis 和 Burns [43] 研究了火卫一表面陨石坑溅 射碎片的运动仿真。Chauvineau 和 Mignard [44] 研究了 太阳引力对小天体附近碎片的运动影响。Hamilton 和 Burns [45,46] 研究了溅射碎片在小行星附近的轨道运 动。 Richter 和 Keller [47] 研究了碎片在小天体附近的运 动稳定性。 Chauvineau 等人 [48] 使用均质椭球模型建立 了小天体引力场， 研究了碎片的轨道运动。 Richardson 和 Melosh [49] [50] 研究了 Moshup-Squannit 被撞击后碎片的运 动仿真。Yu 等人 [51] [52] 提出的形状模型来描述 双小行星系统的主星，使用 Micheal 等人 [24] 提出的形 状模型来描述双小行星系统的从星， 双小行星系统的 部分物理参数请参考表 1，假设撞击方向与从星的轨 道速度方向相反，将动量传递系数设置为 1(动量传 递系数的具体计算方法请参考 [53] ) 。对于双小行星引 力场的描述， 由于需要考虑小行星内部结构对碎片的 影响，本章采用本人前期工作 [54] ...
