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基于最小轨道交叉距离的小行星顺访探测目标预筛选方法

张佳文 郑建华 李明涛

张佳文, 郑建华, 李明涛. 基于最小轨道交叉距离的小行星顺访探测目标预筛选方法[J]. 空间科学学报, 2022, 42(5): 973-983. doi: 10.11728/cjss2022.05.210906097
引用本文: 张佳文, 郑建华, 李明涛. 基于最小轨道交叉距离的小行星顺访探测目标预筛选方法[J]. 空间科学学报, 2022, 42(5): 973-983. doi: 10.11728/cjss2022.05.210906097
ZHANG Jiawen, ZHENG Jianhua, LI Mingtao. Target Pre-screening Method for Asteroid Exploration Based on Minimum Orbital Intersection Distance (in Chinese). Chinese Journal of Space Science, 2022, 42(5): 973-983 doi: 10.11728/cjss2022.05.210906097
Citation: ZHANG Jiawen, ZHENG Jianhua, LI Mingtao. Target Pre-screening Method for Asteroid Exploration Based on Minimum Orbital Intersection Distance (in Chinese). Chinese Journal of Space Science, 2022, 42(5): 973-983 doi: 10.11728/cjss2022.05.210906097

基于最小轨道交叉距离的小行星顺访探测目标预筛选方法

doi: 10.11728/cjss2022.05.210906097
详细信息
    作者简介:

    张佳文:E-mail:zhangjiawen0109@163.com

  • 中图分类号: V41

Target Pre-screening Method for Asteroid Exploration Based on Minimum Orbital Intersection Distance

  • 摘要: 小行星探测有助于研究太阳系演化等重要科学问题,在深空探测任务转移途中实施小行星顺访探测可增加科学研究回报。直接通过轨道递推筛选小行星探测目标计算量大、效率低,针对该问题提出了基于最小轨道交叉距离的目标预筛选方法。在推导出适用于计算双曲线轨道的最小轨道交叉距离公式后,将此理论应用到小行星顺访探测目标筛选中。首先基于探测器与小行星轨道的形状、空间位置计算二者轨道在空间中的几何最近距离,预筛选出可能满足接近距离标准的小行星目标;然后基于轨道递推模型,筛选出真实最近距离小于可接近标准的目标小行星。仿真结果显示,基于最小轨道交叉距离的预筛选方法可有效减少计算量,降低计算时间,提高小行星顺访目标筛选的效率。

     

  • 图  1  基准椭圆近焦点坐标系与中心坐标系的空间位置关系

    Figure  1.  Position relationship between perifocal reference and central frame of primary ellipse

    图  2  平面内一点与椭圆之间距离

    Figure  2.  In-plane distances between an ellipse and a coplanar point

    图  3  探测器相对于中心天体(焦点F)的双曲线轨道

    Figure  3.  Hyperbolic orbit of the spacecraft relative to the central body ( focus F )

    图  4  基于MOID计算的小行星顺访探测目标筛选流程

    Figure  4.  Screening process of asteroid follow-up exploration targets based on MOID calculation

    图  5  探测器飞越小行星搜索状态

    Figure  5.  Search results of TNOs flyby

    表  1  平面内一点与椭圆之间最近距离的封闭解情况

    Table  1.   Cases of minimum distance between an ellipse and a coplanar point with closed-form solution

    $e = 0$$0 < e < 1$
    $\alpha = 0,\;\;\beta = 0$$\alpha = 0,\;\;\beta > 0$$\alpha > 0,\;\;\beta = 0$
    $\alpha > {e^2}a$$\alpha \leqslant {e^2}a$
    ${u^{E'}}$${{\rm{arctan}} }\dfrac{\beta }{\alpha }$$ \pm \dfrac{\pi }{2}$$\dfrac{\pi }{2}$0${ {\rm{arctan} } }\left(\dfrac{ {a{y^{E'} } } }{ {b{x^{E'} } } }\right)$
    ${x^{E'}}$$\dfrac{{a\alpha }}{{\sqrt {{\alpha ^2} + {\beta ^2}} }}$00$a$$\dfrac{\alpha }{{{e^2}}}$
    ${y^{E'}}$$\dfrac{{a\beta }}{{\sqrt {{\alpha ^2} + {\beta ^2}} }}$$ \pm b$$b$0$ \pm a\sqrt {\left( {1 - {e^2}} \right)\left( {1 - \dfrac{{{\alpha ^2}}}{{{e^4}{a^2}}}} \right)} $
    ${d^{E'}}$$\left| {\sqrt {{\alpha ^2} + {\beta ^2}} - a} \right|$$b$$\left| {b - \beta } \right|$$\left| {\alpha - a} \right|$$\sqrt {\left( {1 - {e^2}} \right)\left( {{a^2} - \dfrac{{{\alpha ^2}}}{{{e^2}}}} \right)} $
    下载: 导出CSV

    表  2  平面内一点与双曲线(左支)之间最近距离的封闭解情况

    Table  2.   Cases of minimum distance between a hyperbola (left branch) and a coplanar point with closed-form solution

    $\alpha = 0,\;\;\beta \ne 0$$\beta = 0$
    $\alpha = 0$$\alpha > 0$$\alpha < 0$
    $\dfrac{\alpha }{{{e^2}}} > - a$$\dfrac{\alpha }{{{e^2}}} \leqslant - a$
    ${u^{H'}}$${{\rm{arsinh}}} \dfrac{ { {y^{H'} } } }{b}$000${ {\rm{arsinh} } } \left(\dfrac{ { {y^{H'} } } }{b} \right)$
    ${x^{H'}}$$ - \sqrt {{a^2} + {\beta ^2}\dfrac{{{e^2} - 1}}{{{e^4}}}} $$ - a$$ - a$$ - a$$\dfrac{\alpha }{{{e^2}}}$
    ${y^{H'}}$$\beta \dfrac{{{e^2} - 1}}{{{e^2}}}$000$ \pm \sqrt {\dfrac{{{e^2} - 1}}{{{e^4}}}{\alpha ^2} - {a^2}\left( {{e^2} - 1} \right)} $
    ${d^{H'}}$$\sqrt {{a^2} + \dfrac{{{\beta ^2}}}{{{e^4}}}} $$a$$\alpha + a$$\left| {\alpha + a} \right|$$\sqrt {\left( {{e^2} - 1} \right)\left( {\dfrac{{{\alpha ^2}}}{{{e^2}}} - {a^2}} \right)} $
    下载: 导出CSV

    表  3  椭圆轨道间MOID计算结果

    Table  3.   Calculation results of MOID between ellipses

    试验组第1组第2组第3组第4组
    椭圆1[1.3, 0.8, 20, 40, 30][1.3, 0, 5, 25, 70][0.8, 0.6, 50, 90, 15][5, 0, 1, 23, 160, 38]
    椭圆2[1.6, 0.2, 10, 10, 40][2, 0.2, 25, 60, 10][2, 0, 5, 5, 45][40, 0.5, 10, 5, 12]
    MOID参考值/km13607164.668744898348.7506109321147.53692202694177.5332
    MOID /km1.36071661×1074.48983535×1071.09321159×1082.20269441×109
    误差/km1.433934124.7314271511.52041380232.122031
    误差率/(%)1.05380816×10–51.05380872×10–51.05381384×10–51.05380962×10–5
    下载: 导出CSV

    表  4  椭圆轨道与双曲线轨道间MOID计算结果

    Table  4.   Calculation results of MOID between ellipse and hyperbola

    轨道试验组第1组第2组
    椭圆[5, 0.1, 123, 160, 38][3, 0.6, 18, 110, 60]
    双曲线[2, 1.1, 10, 10, 50][8, 1.9, 40, 25, 30]
    双曲线为次要轨道MOID/km3.963177176748018×1086.298038462422734×108
    双曲线为基准轨道MOID/km3.963177176747759×1086.298038462422662×108
    误差/km2.59280205×10–57.27176666×10–6
    下载: 导出CSV

    表  5  仿真算例轨道详细参数

    Table  5.   Detailed parameters of simulation example

    事件数值
    地球出发时间(UTC)13 Oct. 2026
    地球出发C3/(km2·s–2)16.4445
    VGA时间(UTC)25 Mar. 2027
    VGA相对速度/(km·s–1)8.5820
    1st EGA时间(UTC)9 Feb. 2028
    1st EGA相对速度/(km·s–1)11.2555
    2nd EGA时间(UTC)4 Feb. 2031
    2nd EGA相对速度/(km·s–1)12.0082
    JGA时间(UTC)7 Jun. 2032
    JGA相对速度/(km·s–1)14.1421
    NGA时间(UTC)10 Jul. 2037
    NGA相对速度/(km·s–1)26.9402
    1 Oct. 2049日心距离/AU101.0975
    1 Oct. 2049方向
    黄经,黄纬/(°)
    51.4184,
    –1.8973
    下载: 导出CSV

    表  6  小行星顺访探测目标筛选计算时间

    Table  6.   Calculation time of asteroid follow-up exploration targets screening

    可接近标准/km基于MOID计算的目标筛选方法传统筛选方法
    预筛选耗时/s预筛选出目标个数总耗时/s总耗时/s
    108263.6291734822443.9787711328.379607
    1.5×108286.5525696843623.88103711345.618512
    2×108269.3190308614028.85912712544.087489
    2.5×108308.69746710055181.53538212985.271235
    3×108316.48333211366319.31741812993.934105
    下载: 导出CSV

    表  7  接近距离小于2×108 km的小行星

    Table  7.   Approaching asteroids less than 2×108 km away

    小行星名称MOID/km接近时间(UTC)最近距离/km半长轴/AU偏心率轨道倾角/(o)
    2015 RT27775019596.20199424 Mar. 204082959415.77960939.5790.1785.5
    2015 RC27854281258.74510315 Sept. 203994084697.70855243.6650.0814.6
    2013 WG114107052981.8872298 Nov. 2039121224575.68090044.3060.0681.5
    2013 UR2250935517.0614769 Nov. 2040196735855.18788543.9580.0851.4
    2006 QB18197924800.04877417 May 2030186030288.03778043.6870.042.2
    2003 QV9065773073.62096112 Nov. 2039130834664.64132643.8140.0522.4
    2001 QQ297132369997.4978042 Jun. 2040170037438.43219944.3430.0854.4
    2001 QO29777750095.88543622 Oct. 2039122746214.30173843.0520.0341.1
    下载: 导出CSV
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  • 收稿日期:  2021-09-06
  • 录用日期:  2022-03-31
  • 修回日期:  2022-04-25
  • 网络出版日期:  2022-09-29

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