logo

SCIENTIA SINICA Physica, Mechanica & Astronomica, Volume 48 , Issue 12 : 129501(2018) https://doi.org/10.1360/SSPMA2018-00084

Determination of mass and bulk density of asteroid (21) Lutetia using Rosetta radio tracking data

More info
  • ReceivedMar 27, 2018
  • AcceptedJun 19, 2018
  • PublishedOct 8, 2018
PACS numbers

Abstract


Funding

国家自然科学基金(41374024,41604004)

湖北省自然基金创新群体(2015CFA011)

贵州省射电天文数据处理重点实验室开放基金(KF201813)


Acknowledgment

感谢欧洲太空局在PDS网站上公布Rosetta飞掠Lutetia期间的数据, 感谢德国慕尼黑联邦国防军大学空间技术与空间应用研究所Thomas Paul Andert博士对数据处理给予的指导.


References

[1] Godard B, Budnik F, Muñoz P, et al. Orbit determination of Rosetta around Comet 67P/Churyumov-Gerasimenko. In: Proceedings of 25th International Symposium on Space Flight Dynamics. Munich, 2015. Google Scholar

[2] Accomazzo A, Ferri P, Hubault A, et al. Rosetta visits asteroid (21) Lutetia. Acta Astronaut, 2012, 72178-184 CrossRef ADS Google Scholar

[3] Pätzold M, Neubauer F M, Wennmacher A, et al. Rosetta radio science investigations. In: Dynamics and Astrometry of Natural and Artificial Celestial Bodies. Berlin: Springer, 1997. 141–148. Google Scholar

[4] Sierks H, Lamy P, Barbieri C, et al. Images of asteroid 21 Lutetia: A remnant planetesimal from the early solar system. Science, 2011, 334487-490 CrossRef PubMed ADS Google Scholar

[5] Fienga A, Manche H, Laskar J, et al. INPOP06: A new numerical planetary ephemeris. Astron Astrophys, 2008, 477315-327 CrossRef ADS Google Scholar

[6] Baer J, Chesley S, Britt D. Asteroid masses V1.0 EAR-A-COMPIL-5-ASTMASS-V1.0, NASA Planetary Data System, 2009. Google Scholar

[7] Pätzold M, Andert T P, Asmar S W, et al. Asteroid 21 Lutetia: Low mass, high density. Science, 2011, 334491-492 CrossRef PubMed ADS Google Scholar

[8] Morley T, Budnik F, Croon M, et al. Rosetta navigation for the fly-by of asteroid 21 Lutetia. In: Proceedings of 23rd International Symposium on Space Flight Dynamics. Pasadena, 2012. Google Scholar

[9] Ye M, Li F, Yan J G, et al. Wuhan university deep-space orbit determination and gravity recovery system WUDOGS and its application analysis (in Chinese). Acta Geod Cartogr Sin, 2017, 46: 288–296 [叶茂, 李斐, 鄢建国, 等. 深空探测器精密定轨与重力场解算软件系统WUDOGS及其应用分析. 测绘学报, 2017, 46: 288–296]. Google Scholar

[10] Yan J, Yang X, Ye M, et al. Independent Mars spacecraft precise orbit determination software development and its applications. Astrophys Space Sci, 2017, 362123 CrossRef ADS Google Scholar

[11] Andert T P. Masses of Small Bodies: Mass Estimation of Small Solar System Bodies Using Radio Science Data from Close Flybys. Dissertation for Doctoral Degree. Germany: University of Cologne, 2010. Google Scholar

[12] Pätzold M, Andert T P, Häusler B, et al. Pre-flyby estimates of the precision of the mass determination of asteroid (21) Lutetia from Rosetta radio tracking. Astron Astrophys, 2010, 518L156 CrossRef ADS Google Scholar

[13] Yeomans D K, Barriot J P, Dunham D W, et al. Estimating the mass of asteroid 253 mathilde from tracking data during the NEAR flyby. Science, 1997, 2782106-2109 CrossRef ADS Google Scholar

[14] Moyer T D. Formulation for observed and Computed Values of Deep Space Network Data Types for Navigation. New York: John Wiley & Sons, 2005. Google Scholar

[15] Pätzold M, Wennmacher A, Häusler B, et al. Mass and density determinations of 140 Siwa and 4979 Otawara as expected from the Rosetta flybys. Astron Astrophys, 2001, 3701122-1127 CrossRef ADS Google Scholar

[16] Liu Q H, Chang S Q, Huang Y, et al. Mars spacecraft tracking and analysis of VLBI orbit determination (in Chinese). Sci Sin-Phys Mech Astro, 2017, 47099504 CrossRef ADS Google Scholar

[17] Anderson J D. Feasibility of determining the mass of an asteroid from a spacecraft flyby. In: Proceedings of Physical Studies of Minor Planets. Tucson: NASA Special Publication, 1971. Google Scholar

[18] Pätzold M. Radio Science Predicted and Reconstructed Orbit Data: Specifications. RORSI-IGM-MA-3121, Issue 2, Revision 3, 2005. Google Scholar

[19] Richner M, G Gebauer, Leissle T. Coordinate Systems for Rosetta. RO-DSS-TN-1081, Issue 6, 2003. Google Scholar

[20] Acton C H Jr. Ancillary data services of NASA’s navigation and ancillary information facility. Planet Space Sci, 1996, 4465-70 CrossRef ADS Google Scholar

[21] Pätzold M, IFMS Doppler Processing Software: Level 1a to Level 2. RO-RSI-IGM-MA-3118, Issue 5, Revision 0, 2005. Google Scholar

[22] Folkner W M, Williams J G, Boggs D H. The planetary and lunar ephemeris DE 421. IPN Progress Report, Jet Propulsion Laboratory, California Institute of Technology, 2008, 42: 178. Google Scholar

[23] Milani A, Nobili A, Farinella P. Non-gravitational Perturbations and Satellite Geodesy. Bristol: IOP Publishing Ltd, 1987. Google Scholar

[24] Saastamoinen J. Atmospheric correction for the troposphere and stratosphere in radio ranging satellites. In: The Use of Artificial Satellites for Geodesy. Washington DC: American Geophysical Union, 1972. 247–251. Google Scholar

[25] Ifadis I. The Atmospheric Delay of Radio Waves: Modelling the Elevation Dependence on a Global Scale. Technical Report, Chalmers University of Technology. 1986. Google Scholar

[26] Boehm J, Niell A, Tregoning P, et al. Global mapping function (GMF): A new empirical mapping function based on numerical weather model data. Geophys Res Lett, 2006, 33L07304 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) Rosetta flyby geometry in the fly-by plane at asteroid (21) Lutetia. The time of the closest approach is t0. The fly-by plane at t0 is formed by the position vectors from spacecraft to asteroid r0 and the relative velocity vector v0. Line-of-sight direction at any time t is one from spacecraft to the ground antenna.

  • Figure 2

    (Color online) Solar phase angle, Lutetia-sun-earth angle and relative distance during Rosetta flyby at asteroid (21) Lutetia. SPA changes rapidly from (t0–2) to (t0+6) min due to high relative flyby velocity. SPA is larger than 157° from (t0+16) min; LSEA is about 98.9° during the flyby.

  • Figure 3

    (Color online) Frequency changes due to asteroid mass during Rosetta flyby from analytical method.

  • Figure 4

    (Color online) Frequency changes at X-band due to asteroid mass during Rosetta flyby by neglecting HGA motion.

  • Figure 5

    (Color online) Coordinate system for Rosetta (Central body frame ROS_SPACECRAFT, HGA elevation frame ROS_HGA_EL, HGA azimuth frame ROS_HGA_AZ and HGA frame ROS_HGA).

  • Figure 6

    (Color online) Frequency changes at X-band due to asteroid mass during Rosetta flyby accounting for HGA motion.

  • Figure 7

    (Color online) Post-fit residuals after subtracting the least-squares fit from observation for scenario 1.

  • Figure 8

    Post-fit residuals after subtracting the least-squares fit from the observation for scenario 2.

  • Figure 9

    (Color online) Correlation matrix of solve-for parameters with scenario 1.

  • Figure 10

    (Color online) Correlation matrix of solve-for parameters with scenario 2.

  • Figure 11

    (Color online) Geometry angles for correlation analysis. Vx-LOS Angle denotes angle between vs0(x) and LOS, which is approach to 180° during flyby. Vx-HGA Angle denotes angle between HGA motion and vs0(x), which is not constant due to HGA rotation. Vx-Gm Angle denotes angle between vs0(x) and acceleration due to asteroid mass, which is approach to 0° before t0, with rapid change at t0 and is approach to 180° after (t0+40) min. SRP-GM Angle denotes angle of acceleration between solar radiation pressure and asteroid mass, which has the same trend as the former.

  • Figure 12

    (Color online) Results and formal error bars of solving for 50 random GM values case with scenario 1 setup.

  • Figure 13

    (Color online) Results and formal error bars of solving for 50 random GM values case with scenario 2 setup.

  • Figure 14

    Comparison of results and error bars between this paper and other references.

  • Table 1   Observation window and number of two-way coherent Doppler tracking data at X-band during Rosetta flyby at asteroid (21) Lutetia

    波段

    观测数据时段(2010-07-10T, UTC)

    观测数据个数

    X波段

    12:13:21.500–16:05:59.500

    13959

    16:47:40.500–19:22:49.500

    9310

    19:48:46.500–21:57:42.500

    7737

    S波段

    12:14:09.500–16:06:21.500

    13933

    18:27:13.500–19:27:33.499

    3621

    19:48:42.500–21:57:36.500

    7735

  • Table 2   Flyby parameters of the asteroid (21) Lutetia

    飞掠参数

    参数数值

    d

    (3168±7.5) km

    v0

    14.99 km/s

    α

    171.2°

    αp

    172.18°

    β

    探测器日心距离

    2.71AU

    探测器地心距离

    3.03AU

    SPA最小值

    0.15°

    SPA最小值时刻

    t0–18 min

    LSEA

    98.9°

  • Table 3   Fixed vectors of coordinate systems for Rosetta

    几何参数

    参数取值 (m)

    rc

    (–0.0170, 0.0011, 1.2508)2)

    rb

    (2.1515, 0.0000, 0.0800)[19]

    rg

    (1.3045, 0.0000, 0.1500)[20]

    rp

    (0.0000, 0.0000, 0.0000)1)

  • Table 4   Configuration of determining mass of asteroid (21) Lutetia with Rosetta flyby data

    €€€€€€€€€解算配置

    €€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€配置说明

    €€€€€€€€€力模型

    中心引力(以太阳为中心天体[11]); 三体摄动(DE421历表[22], (21) Lutetia历表[20,21]); 广义相对论摄动(太阳、木星点质量引力场[14]); 太阳光压摄动(Box-Wing模型[23], 探测器质量2851 kg, Rosetta单侧太阳能帆板以及主箱体表面积, 吸收, 镜面反射以及漫反射光学参数[11])

    €€€€€€€€€观测模型

    双程多普勒Sky-Frequency模型[11,21]

    €€€€€€€€€对流层改正

    测站气压、温度以及相对湿度来自Level 2数据集中的气象文件; 干分量天顶延迟: Saastamoinen模型[24]; 湿分量天顶延迟: Ifadis模型[25]; 映射函数GMF (Global Mapping Function)[26]

    €€€€€€€€€待估参数及初值

    探测器初始轨道根数rs0, vs0, 初值从Rosetta探测器对应的SPICE Kernel文件中读取[20]; 小行星(21) Lutetia的GM, 初值为0.1087 km3/s2[8]; 探测器质心至HGA相位中心向量rch的比例因子(Scale Factor) kch, 初值为1.0; 太阳光压摄动力比例因子kso(可选参数), 初值为1.0

    €€€€€€€€€观测值权重

    与实测数据噪声水平相同: 5.7 mHz[7]

  • Table 5   Results and formal error bars of solve-for parameters for scenario 1 and 2

    待估参数

    策略一解算结果

    策略二解算结果

    rs0(x)

    (–400904659.571898±0.000004) km

    (–400904659.571891±0.000004) km

    rs0(y)

    (-–67933330.567693±0.000005) km

    (–67933330.567688±0.000005) km

    rs0(z)

    (–6951958.400240±0.000005) km

    (–6951958.400265±0.000004) km

    vs0(x)

    (–10.384308±1×10–9) km/s

    (–10.384308±1×10–9) km/s

    vs0(y)

    (–14.521395±4×10–9) km/s

    (–14.521395±4×10–9) km/s

    vs0(z)

    (–6.460574±4×10–9) km/s

    (–6.460574±4×10–9) km/s

    kch

    0.970±0.002

    0.969±0.002

    GM

    (0.1132±0.00016) km3/s2

    (0.1137±0.0002) km3/s2

    kso

    1.019±0.003

  • Table 6   Effects of GM solution due to errors of asteroid Lutetia ephemeris

    星历偏差 (km)

    变化百分数

    GM解算值 (km3/s2)

    GM解算值相对变化 (%)

    飞掠最近点相对误差 (%)

    0

    0.11316

    0

    0

    4.24

    0.11331

    0.132

    0.134

    8.48

    0.11290

    0.265

    0.268

    12.73

    0.11359

    0.380

    0.402

qqqq

Contact and support