﻿ 地基激光清除空间碎片的策略
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Strategy of removing space debris using ground-based lasers
WANG Chenglin, ZHANG Yan, WANG Kunpeng
Beijing Institute of Tracking and Telecommunications Technology, Beijing 100094, China
Abstract: The removal strategy of space debris is one of the most key technologies to achieve the goal of clearing space debris in a wide range of sizes from 1 to 10 cm actively using ground-based lasers. In order to develop an effective strategy for removing space debris, we firstly studied on the influences, which the changes of different velocity components had on the altitude of new orbit's perigee, finding that the same velocity increment along different velocity components has different effects on lowering the altitude of perigee. And then combined with the geometrical and physical of ground-based lasers, the constraint conditions that determine the area of orbit transfer were deduced. Finally, a general strategy, removing space debris in the way of continuous impulse orbit transfer using ground-based lasers, was proposed based on those mentioned above. Moreover, space debris removal using ground-based lasers is realized and the effectiveness of the clearing strategy is also verified through simulation experiments.
Key words: ground-based lasers     space debris     removal strategy     orbital variation     simulation

1 改变不同速度分量的降轨效果

1.1 空间碎片轨道速度分解

 A-远地点;P-近地点;r-失径 图 1 轨道速度分解示意图 Fig. 1 Orbital velocity decomposition diagram

1.2 脉冲变轨

 图 2 脉冲变轨示意图 Fig. 2 Impulse orbit transfer diagram

1.3 不同速度分量的影响结果分析

 图 3 改变不同速度分量的降轨效果图 Fig. 3 Diagram of effect that changing different velocity components has on orbit transfer

1) 改变切向速度.

2) 改变法向速度.

3) 改变侧向速度.

 图 4 3个速度分量变化的影响程度对比 Fig. 4 Comparison of influence degree of changing three different velocity components

2 变轨区域和速度增量的确定 2.1 确定变轨区域

 图 5 确定变轨区域示意图 Fig. 5 Diagram of determining orbit transfer area

1) 水平视场范围[f1,f2].

L作垂直rL的直线交椭圆轨道与1、2两点,交点对应的真近点角分别为f1f2,则[f1,f2]称为激光站的水平视场范围.在数学上,可用rL·rLS≥0表示该物理含义.

2) 激光束有效作用距离hef.

L为圆心,hef为半径作圆,交椭圆轨道于3、4两点,则3、4之间的轨道部分处于激光束的有效作用距离以内.在数学上为:rLShef.

3) 激光束与速度v夹角.

4) 激光束与轨道平面夹角.

2.2 确定速度增量

3 仿真实验及结果分析

3.1 仿真实验方案

1) 考虑地球自转和非球形(J2摄动)的影响,不考虑其他摄动力,此时碎片的运动满足摄动方程式(12).

2) 地基激光站固定在地球表面,并且给定经纬度.

3) 激光器可以自主变焦寻得,即只要满足变轨条件,激光器总能准确聚焦在碎片上.

4) 激光辐照在碎片表面产生的速度增量沿着激光束的方向.

5) 碎片面质比保持不变.

 图 6 连续脉冲变轨仿真计算流程图 Fig. 6 Simulating calculation flow diagram of orbit transfer by continuous impluse

1) 根据给定空间碎片的初始轨道参数和地基激光站的经纬度,将其转换成地球赤道惯性坐标系下的空间碎片位置rS(t)、速度vS(t)以及激光站的位置rL(t).

2) 根据空间碎片位置rS(t)和速度vS(t),计算此时轨道的hP.若hP比预定值小,空间碎片在大气阻力的作用下会很快烧毁,结束计算;否则,进入下一步骤.

3) 根据空间碎片位置rS(t)和速度vS(t)以及激光站的位置rL(t),判断此时是否满足变轨条件.若满足变轨条件,保持rS(t)和rL(t)不变,令vS(t)变成vS(t)+Δv；否则,rS(t)、rL(t)和vS(t)都保持不变.

4) 利用摄动方程进行数值积分,求解一个积分步长Ts后空间碎片位置rS(t+Ts)和速度vS(t+Ts);并根据地球自转,计算Ts时间后激光站的位置rL(t+Ts).(注:如果满足变轨条件,积分步长Ts应该不大于激光器的脉冲周期TL;否则,积分步长Ts可以适当取较大的值,本文取为脉冲周期TL的整数倍.)

5) 把更新后的空间碎片位置rS(t+Ts)、速度vS(t+Ts)以及激光站的位置rL(t+Ts)返回步骤2),继续计算,直至循环结束.

3.2 仿真结果分析

 类别 参数名称 数值 初始轨道 近地点高度hP/km 800 远地点高度hA/km 1 200 轨道倾角i/(°) 30 升交点赤经Ω/(°) 80 近地点辐角ω/(°) 0 过近地点时间τ/s 0 轨道周期Tg/s 6 306.9 地基激光站 激光站经纬度/(°) E120°,N30° 激光器频率fL/Hz 10 有效作用距离hef/km 1 500 hef处激光单脉冲速度 增量大小Δv0/(km·s-1) 1.078×10-5 地球 地心引力常数μ/(km3·s-2) 3.986 004 36×105 地球平均半径Re/km 6 378.14 自转周期Te/s 86 164 仿真程序 近地点高度预定值h0/km 150 仿真步长Ts/s 0.1

 图 7 轨道近地点高度随时间变化曲线 Fig. 7 Orbital perigee height curves over time

 工况 脉冲总数/个 速度增量总和/(km·s-1) 激光有效作用时长/s hP减少量/km φ无限制 24 238 0.468 6 2 423.8 650.0 φ<5° 8 051 0.168 8 805.1 255.4

4 结 论

1) 不同速度分量的变化对新轨道近地点高度的影响是不同的.其中,切向速度分量变化的影响最为显著,法向速度分量次之,侧向速度分量影响最小.

2) 对于不同位置、不同视角的空间碎片,需要根据地基激光站的特性来确定实施变轨的有效区域.

3) 仿真结果表明连续脉冲变轨降低轨道近地点高度的策略方案更加有效,可行性更高.

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#### 文章信息

WANG Chenglin, ZHANG Yan, WANG Kunpeng

Strategy of removing space debris using ground-based lasers

Journal of Beijing University of Aeronautics and Astronsutics, 2015, 41(11): 2137-2143.
http://dx.doi.org/10.13700/j.bh.1001-5965.2014.0696