CAJ | 학술논문

最大碰撞概率的计算在空间目标碰撞风险评估中具有重要意义.基于碰撞概率的显式表达式,利用一元函数和二元函数求极值的方法分别讨论了目标误差椭球形状固定和不定两种情况下最大碰撞概率的计算方法,得到了两种情况下最大碰撞概率的表达式.对于误差椭球形状固定的情况得到了碰撞概率最大时两目标位置协方差的取值,对于误差椭球不定情况得到了碰撞概率最大时径向联合方差的取值和水平面内联合方差所满足的关系.分析了最大碰撞概率的影响因素,讨论了水平面内误差方差的耦合特性.对今年二月发生的美俄卫星碰撞事件进行了分析,得到误差椭球任意形状时最大碰撞概率为1.864E-3.
최대팽당개솔적계산재공간목표팽당풍험평고중구유중요의의.기우팽당개솔적현식표체식,이용일원함수화이원함수구겁치적방법분별토론료목표오차타구형상고정화불정량충정황하최대팽당개솔적계산방법,득도료량충정황하최대팽당개솔적표체식.대우오차타구형상고정적정황득도료팽당개솔최대시량목표위치협방차적취치,대우오차타구불정정황득도료팽당개솔최대시경향연합방차적취치화수평면내연합방차소만족적관계.분석료최대팽당개솔적영향인소,토론료수평면내오차방차적우합특성.대금년이월발생적미아위성팽당사건진행료분석,득도오차타구임의형상시최대팽당개솔위1.864E-3.
The calculation of maximum collision probability is significant in the risk assessment of collision between space objects. Based on explicit expression of collision probability, by maximizing the one-variable function and multivariable function, the maximum collision probability calculational problem is analyzed both in certain error ellipsoid shape case and in arbitrary error ellipsoid shape case, respectively. Analytical expressions of maximum probability of collision in two cases are obtained. In case of certain error ellipsoid shape, the covariance that conduce maximum probability is presented. In case of arbitrary shape, on the other hand, the relation of joint variance conducing maximum probability is obtained. The influencing factors of maximum probability of collision are discussed; the coupling property of variance in horizontal plane is also analyzed. As an example, the U.S. and Russian satellite collision event is analyzed, indicating that the maximum probability is as high as 1.864E-3 in arbitrary error ellipsoid shape.