论文标题
相对论重力贡献的太阳四极力矩估计的前景
An outlook on the estimate of the solar quadrupole moment from relativistic gravitation contributions
论文作者
论文摘要
在所有太阳能基本参数（质量，直径，表面的重力，...）中，过去经常被忽略，这主要是由于很难获得可靠的估计值。即使现在已知$ 10^{ - 7} $的太阳能四极矩$ J_2 $的数量级，仍在讨论其准确值。实际上，旋转体的重力潜力的多物中的膨胀$ j _ {（l，〜l = 2，...）} $在相对论水平上影响行星的轨道运动。我们将在这里回想起最近通过第一个太阳四极力时刻的贡献来测试一般相对论的最新进展。使用Eddington-Robertson参数，我们回想起理论和实验观点的约束。加上$γ$，它编码每单位休息质量的时空曲率量，newtonian参数$β$有助于行星的相对论进攻。后一个参数编码重力叠加定律中的非线性量。即使从原则上讲，也可以从行星胚层中提取$ j_2 $，但我们观察到它与其他溶液参数显着相关（行星的半高轴，小行星质量...）。关注$ j_2 $相关性，我们表明，当释放〜$β$和〜$γ$时，相关性〜[$β，j_2 $]和〜[$γ，j_2 $]分别为$ 45 \％\％\％和$ \ $ \ $ 55 \％。此外，所有基于行星动力学的值都会偏向裂缝效应，直到到目前为止，它从未对其进行建模和求解，但可以估计$ \ $ \ $ 7 \％。因此，可以对太阳四极力矩进行良好的估计：$ 1.66 \ times10^{ - 7} $$ \ leq $$ j_2 $$ j_2 $$ \ leq $$ 2.32 \ times10^{ - 7} $。
Of all the solar fundamental parameters (mass, diameter, gravity at the surface,...), the gravitational moments have been quite often ignored in the past, mainly due to the great difficulty to get a reliable estimate. Even though the order of magnitude of the solar quadrupole moment $J_2$ is now known to be $10^{-7}$, its accurate value is still discussed. Indeed, the expansion in multipoles $J_{(l,~ l = 2, ...)}$ of the gravitational potential of a rotating body affects the orbital motion of planets at a relativistic level. We will recall here the recent progresses made in testing General Relativity through the contribution of the first solar quadrupole moment. Using the Eddington-Robertson parameters, we recall the constraints both on a theoretical and experimental point of view. Together with $γ$, which encodes the amount of curvature of space-time per unit rest-mass, the Post--Newtonian Parameter $β$ contributes to the relativistic precession of planets. The latter parameter encodes the amount of non-linearity in the superposition law of gravitation. Even though in principle, it would be possible to extract $J_2$ from planetary ephemerides, we observe that it is significantly correlated with other solution parameters (semi-major axis of planets, mass of asteroids...). Focusing on the $J_2$ correlations, we show that in general, when ~$β$ and ~$γ$ are freed, the correlations ~[$β, J_2$] and ~[$γ, J_2$] are $\approx$ 45\% and $\approx$ 55\% respectively. Moreover, all the planetary dynamics-based values are biased by the Lense--Thiring effect, which has never been modeled and solved for so far, but can be estimated to $\approx$ 7\%. It is thus possible to get a good estimate of the solar quadrupole moment:$1.66\times10^{-7}$$\leq$$J_2$$\leq$$2.32\times10^{-7}$.
