在目前和将来的LAGOS Lense-Thirring试验中，地球位的第一偶纬向谐波的抵消有多精确？
How accurate is the cancelation of the first even zonal harmonic of the geopotential in the present and future LAGEOS-based Lense-Thirring tests?
摘要：
用LAGEOS型激光测距卫星在地球引力场中进行或提出的广义相对论Lense-Thirring效应的实验，迄今所遵循的策略是消除由第一偶纬向谐波系数J_（？）2的多极展开的牛顿部分的地球引力位的适当设计的线性组合的手段，多个航天器的节点Ω。实际上，这种去除确实取决于所采用的组合的系数可以实际已知的精度。在LAGEOS和LAGEOS II的半长轴a上取2厘米量级的不确定度，在倾角I上取0.5毫角秒量级的不确定度，将其代入到目前为止所使用的节点组合的系数c_1的表达式中，得到的不确定度δc_1 = 1.30 10^-8。它给出了一个不完全抵消的J_2信号，其值为10.8毫角秒/年，相当于Lense-Thirring特征的23%。在倾角为10-30微弧秒量级时，δc_1=7.9 × 10^-9，这相当于每年6.5毫弧秒的未被抵消的J_2信号，也就是兰斯-蒂林信号的14%。对于未来的LAGEOS-LAGEOSII-LARES组合，如果系数为k_1和k_2，则α的不确定度和I的不确定度与以前一样，不确定度δk_1=1.1 × 10^-8，δk_2=2 × 10^-9;这意味着J_2的剩余组合岁差为每年14.7毫角秒，相当于兰斯-瑟林趋势的29%。在约10微弧秒的水平上，倾角的不抵消给出δk_1=5 × 10^-9，δk_2 = 2 × 10^-9;未抵消的J_2效应为7.9毫弧秒/年，即相对论效应的16%。
英文摘要：
The strategy followed so far in the performed or proposed tests of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with laser-ranged satellites of LAGEOS type relies upon the cancelation of the disturbing huge precessions induced by the first even zonal harmonic coefficient J_2 of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential by means of suitably designed linear combinations of the nodes Ωof more than one spacecraft. Actually, such a removal does depend on the accuracy with which the coefficients of the combinations adopted can be realistically known. Uncertainties of the order of 2 cm in the semimajor axes a and 0.5 milliarcseconds in the inclinations I of LAGEOS and LAGEOS II, entering the expression of the coefficient c_1 of the combination of their nodes used so far, yield an uncertainty δc_1 = 1.30 10^-8. It gives an imperfectly canceled J_2 signal of 10.8 milliarcseconds per year corresponding to 23% of the Lense-Thirring signature. Uncertainties of the order of 10-30 microarcseconds in the inclinations yield δc_1=7.9 10^-9 which corresponds to an uncanceled J_2 signature of 6.5 milliarcseconds per year, i.e. 14% of the Lense-Thirring signal. Concerning a future LAGEOS-LAGEOS II-LARES combination with coefficients k_1 and k_2, the same uncertainties in a and the less accurate uncertainties in I as before yield δk_1=1.1 10^-8, δk_2=2 10^-9; they imply a residual J_2 combined precession of 14.7 milliarcseconds per year corresponding to 29% of the Lense-Thirring trend. Uncertainties in the inclinations at about 10 microarcseconds level give δk_1=5 10^-9, δk_2 = 2 10^-9; the uncanceled J_2 effect is 7.9 milliarcseconds per year, i.e. 16% of the relativistic effect.
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