胡壽村

(中國科學院紫金山天文臺 南京 210033)

接觸雙小行星是一類明顯由兩部分結構相接而構成的單小行星.地面雷達觀測結果表明直徑大于200 m的近地小行星中大約14%為接觸雙小行星,而且目前3個小天體探測任務(隼鳥號、嫦娥二號和羅塞塔號)的探測目標也都具有接觸雙星結構.接觸雙小行星是一類重要的小行星類型,對其形成機制開展研究能夠為深入理解小行星的形成演化提供重要線索.

(4179) Toutatis是一顆受關注較多的S型近地小行星,自從1989年發(fā)現(xiàn)以來地面雷達和光學望遠鏡就對該小行星進行了大量觀測,發(fā)現(xiàn)其具有緩慢的非主軸自轉特性,并且從反演的雷達形狀模型判斷其是一顆接觸雙小行星.嫦娥二號于2012年12月13日從距離其表面770 m處飛越了該小行星,獲得了大量高精度光學圖像數(shù)據(jù),結果證實Toutatis確實是一顆明顯由兩部分結構相接組成的接觸雙小行星,并且在接觸位置有一個邊緣清晰的直角結構,其體積較大的部分(主瓣)有明顯的延長型形狀,且兩部分的連接點位于主瓣的長軸上.從動力學角度來看Toutatis的形狀結構處于一個較不穩(wěn)定的狀態(tài).多數(shù)學者猜測Toutatis的形狀是由其兩個組成部分在低速碰撞下形成,但具體的形成過程,包括如何產生這種不穩(wěn)定的結構仍不清楚.利用Toutatis的雷達形狀模型以及嫦娥二號獲得的光學探測數(shù)據(jù),本文主要開展了以下3個部分的研究工作.

首先,利用嫦娥二號探測數(shù)據(jù)并結合已有的雷達形狀模型,通過輪廓匹配方法獲得了Toutatis新的3維形狀模型.在此基礎上,基于Toutatis的形狀參數(shù),假設其母體是一顆主星和衛(wèi)星均為球體的雙軌旋同步雙小行星,我們通過采用散體動力學數(shù)值模擬方法研究了在變化的參數(shù)空間下該雙小行星“母體”近距離飛越地球的動力學過程.結果表明地球引力攝動可能導致衛(wèi)星與主星發(fā)生m/s量級的低速相撞,但撞擊本身不會對主星的形狀產生顯著影響; 而在選定合適的飛越距離后(約1.4–1.5倍地球半徑),地球潮汐效應在主星和衛(wèi)星相撞之前會明顯改變衛(wèi)星和主星的形狀與自轉,并且衛(wèi)星和主星相撞并合后可以形成類似Toutatis形狀的延長型接觸雙小行星,因此該機制為延長型接觸雙小行星的形成提供了一種合理的解釋.

其次,從嫦娥二號獲得的Toutatis光學圖像上可以發(fā)現(xiàn)其表面分布有222顆直徑在10 m到61 m之間的碎石以及70多個撞擊坑,特別是在主瓣端部有一個直徑約800 m的撞擊坑.在強度域假設下,基于描述高速撞擊濺射物參數(shù)分布的標度律方法,我們獲得了從800 m撞擊坑內拋射出來的濺射物粒子的大小、拋射位置和拋射速度分布,并通過數(shù)值模擬研究了這些拋射出來的粒子回落到Toutatis小行星上的比例和位置,結果表明回落粒子的總數(shù)目和總體積均明顯低于嫦娥二號給出的觀測值,這說明Toutatis表面分布的碎石大部分都不來自于撞擊,而有可能來源于其形成時候的“母體”.

最后,小行星附近的引力場環(huán)境可能對小行星的形成演化機制提供重要約束.為了研究從800 m撞擊坑內拋射出的濺射物粒子回落到Toutatis表面的位置分布情況,需要對濺射物粒子在小行星引力場影響下的軌道進行外推計算,此時若采用多面體法計算引力場會顯著增加計算成本.為了克服這一問題,我們提出應用3維空間中的Chebyshev多項式擬合方法來計算不規(guī)則形狀小行星附近的引力場.該工作比較了4種引力加速度擬合方式,在充分運用小行星附近引力場變化規(guī)律的基礎上,提出了一種先沿著地平坐標系方向分解再擬合的處理方式,并且提出采用自適應八叉樹算法來減小小行星表面附近的引力場擬合誤差.以Toutatis為例的數(shù)值算例表明該方法能顯著提高引力場計算效率,在精度要求不是特別高的情況下可用該方法做軌道積分.

Contact binary asteroids are a kind of single asteroids with bifurcated (or bi-lobed)configurations.Ground-based radar observations have shown that about 14% of near-Earth asteroids larger than 200 meters in diameter may be contact binaries.Specially,the targets of the three minor planet missions,Hayabusa,Chang’e-2,and Rosetta,have contact binary configurations.Contact binaries are an important type of asteroids for completely understanding the formation and evolution of asteroids in the solar system.

(4179) Toutatis is a prominent S-type near-Earth asteroid,and has been observed by many ground-based radar and optical campaigns since it was discovered in 1989.These observations reveal that the asteroid is rotating very slowly around a non-principal axis,and its 3D shape model constructed by radar data indicates that it is a contact binary.Chang’e-2 spacecraft flew by Toutatis on 13 December 2012,with a nearest distance of approximately 770 meters away from its surface.A series of high-resolution optical images taken during the flyby confirm that Toutatis is a distinct contact binary composed of two components.A sharply perpendicular silhouette is observed near the connection area,the big lobe has an obviously elongated shape,and the connection locates at the long axis of the big lobe.From a dynamical point of view,the configuration of Toutatis is in an unstable state.Many researchers suggest that the Toutatis’ configuration may come from a lowspeed impact between two components,but the detailed formation process that how such an unstable state become realistic is still not well understood.By employing the radarderived shape model and the optical images obtained by Chang’e-2,the research presented in this dissertation mainly includes the following three parts.

First,a new 3D shape model of Toutatis is derived by matching the silhouette between the Chang’e-2’s optical images and the existing radar model.With that,we assume the precursor of Toutatis is a doubly synchronous binary asteroid composed of two spherical bodies.The dynamical scenario that the binary precursor closely encounters the Earth is investigated by applying the granular dynamical simulations in a wide parameter space.The results show that the gravitational perturbation of Earth may lead to a m/s-level low-speed impact between the primary and secondary,while the impact has a negligible influence on the shape of the primary.But if we choose an appropriate flyby distance (about 1.4–1.5 Earth radii),the Earth’s tide may significantly alter the shape and spin of the components prior to their mutual impact,and a Toutatis-like contact binary asteroid may be reconstructed after the impact coalescence.This mechanism gives a new reasonable interpretation for the formation of Toutatis-like elongated contact binary asteroids.

Second,the optical images obtained by Chang’e-2 show that 222 boulders from 10 m to 61 m across,and as well as over 70 craters,are identified from the optical images obtained by Chang’e-2,especially a depression with a diameter of 800 meters locates in the endpoint of the big lobe.We use a scaling-law method to obtain the size,position,and velocity distribution of ejecta particles from the depression under strength regime.Numerical simulations of the particles’ orbits are conducted,and the re-impact portions and their position distributions are obtained.The results show that the total number and the volume of reimpact ejecta particles are obviously lower than the results identified by the observations of Chang’e-2,which means that most of the boulders on the surface of Toutatis did not come from the crater,but may originate during formation process of the parent body.

Finally,we discuss the constraint of the gravitational field nearby an asteroid on its formation and evolution.In order to study the distribution of re-impact ejecta coming from the depression on Toutatis,we need to compute the orbits of these ejecta under the gravitational acceleration of Toutatis.However,the computation cost will be high if we use the polyhedral method to calculate the gravity.To eliminate this problem,we present a new method to calculate the gravity near an irregularly-shaped asteroid by adopting the 3D Chebyshev polynomial interpolation.We have compared four different gravity interpolation methods,and the best one is recommended for the efficiency,in which the gravitational acceleration will be decomposed along the local horizontal coordinate system,and then interpolated separately.An error-adaptive octree division scheme is also introduced to reduce the interpolation error near the surface of asteroid.We take Toutatis as an example to show that the new method may greatly improve the computation efficiency of near-surface gravitational acceleration,and it may be well used to perform the orbit propagation in case that the precision is not rigorous.