The nutations of Mars are about to be estimated to a few milliarcseconds accuracy with the radioscience experiments onboard InSight and ExoMars 2022. The contribution to the nutations due to the liquid core and tidal deformations will be detected, allowing to constrain the interior of Mars. To avoid introducing systematic errors in the determination of the core properties, an accurate precession and nutation model for a rigidly behaving Mars is needed. Here, we develop such a model with adequate accuracy based on the Torque approach and compare it to previous models. We include in the model the forcings by the Sun, Phobos, Deimos, and the other planets of the solar system. We also include the geodetic precession and nutations. We use semi-analytical developments for the solar and planetary torques, and analytical solutions for the effect of Phobos and Deimos and for the geodetic precession and nutations. With a truncation criterion of 0.025 milliarcseconds in prograde and/or retrograde amplitude, we identify 43 nutation terms. The uncertainty on our solution mainly derives from the observational uncertainty on the current determination of the precession rate of Mars. Uncertainties related to our modeling choices are negligible in comparison. Given the current determination of the precession rate ( $$7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02.052 ), our model predicts a dynamical flattening $$H_{{D}}=0.00538017\pm 0.00000148$$ and a normalized polar moment of inertia $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$ for Mars.

中文翻译：

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刚性火星的岁差和章动

通过 InSight 和 ExoMars 2022 上的无线电科学实验，火星的章动将被估计到几毫秒的精度。将检测到由于液体核心和潮汐变形对章动的贡献，从而限制了火星的内部。为避免在确定核心属性时引入系统误差，需要为行为僵硬的火星建立准确的进动和章动模型。在这里，我们基于 Torque 方法开发了一个具有足够精度的模型，并将其与以前的模型进行比较。我们在模型中包括了太阳、火卫一、火卫二和太阳系其他行星的强迫。我们还包括大地进动和章动。我们对太阳和行星扭矩使用半解析发展，Phobos 和 Deimos 的影响以及大地进动和章动的解析解。使用 0.025 毫弧秒的顺行和/或逆行振幅截断标准，我们确定了 43 个章动项。我们解决方案的不确定性主要来自目前确定的火星进动率的观测不确定性。相比之下，与我们的建模选择相关的不确定性可以忽略不计。鉴于目前确定的进动率 ($7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02. 052 )，我们的模型预测动态平坦 $$H_{{D}}=0.00538017\pm 0.00000148$$ 和归一化的极惯性矩 $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$火星。使用 0.025 毫弧秒的顺行和/或逆行振幅截断标准，我们确定了 43 个章动项。我们解决方案的不确定性主要来自目前确定火星进动速率的观测不确定性。相比之下，与我们的建模选择相关的不确定性可以忽略不计。鉴于目前确定的进动率 ($7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02. 052 )，我们的模型预测动态平坦 $$H_{{D}}=0.00538017\pm 0.00000148$$ 和归一化极惯性矩 $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$火星。使用 0.025 毫弧秒的顺行和/或逆行振幅截断标准，我们确定了 43 个章动项。我们解决方案的不确定性主要来自目前确定火星进动速率的观测不确定性。相比之下，与我们的建模选择相关的不确定性可以忽略不计。鉴于目前确定的进动率 ($7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02. 052 )，我们的模型预测动态平坦 $$H_{{D}}=0.00538017\pm 0.00000148$$ 和归一化的极惯性矩 $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$火星。我们解决方案的不确定性主要来自目前确定火星进动速率的观测不确定性。相比之下，与我们的建模选择相关的不确定性可以忽略不计。鉴于目前确定的进动率 ($7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02. 052 )，我们的模型预测动态平坦 $$H_{{D}}=0.00538017\pm 0.00000148$$ 和归一化的极惯性矩 $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$火星。我们解决方案的不确定性主要来自目前确定火星进动速率的观测不确定性。相比之下，与我们的建模选择相关的不确定性可以忽略不计。鉴于目前确定的进动率 ($7608.3\pm 2.1$$ mas/yr, Konopliv et al. in Icarus 274:253–260, 2016. https://doi.org/10.1016/j.icarus.2016.02. 052 )，我们的模型预测动态平坦 $$H_{{D}}=0.00538017\pm 0.00000148$$ 和归一化的极惯性矩 $$C/\mathrm{MR}^2=0.36367\pm 0.00010$$火星。