Abstract—

The article considers the attitude stability of synchronous rotation and the most significant relativistic effects in the rotational dynamics of the inner satellites of Jupiter: Metis (J16), Adrastea (J15), Amalthea (J5), and Thebe (J14). It is established that the plane synchronous rotation of all inner satellites of Jupiter for the most probable values of the parameters of their shapes is stable with respect to tilting the axis of rotation. For the first time, the most significant secular, periodic, and mixed terms of the geodetic rotation of the inner satellites of Jupiter in the Euler angles relative to their own coordinate systems and in the angles of their rotation with respect to the fixed equator of the Earth and the vernal equinox (for the J2000.0 epoch) are determined. It is shown that there are objects in the Solar System with significant geodetic rotation caused primarily by their proximity to the perturbing central body rather than its mass. In particular, the value of the geodetic precession of the inner satellites of Jupiter (for which Jupiter is a less massive perturbing central body than the Sun) is 10⁵ times greater than that of Jupiter rotating around its more massive central body (the Sun) and comparable with their precession in Newton approximation.

中文翻译：

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木星内部卫星的旋转动力学

摘要-

本文考虑了同步旋转的姿态稳定性以及木星内部卫星旋转动力学中最显着的相对论效应：梅蒂斯（Metis）（J16），阿德拉斯特亚（J15），阿玛尔蒂亚（J5）和塞贝（J14）。已经确定，对于木星的所有内部卫星，其形状参数的最可能值的平面同步旋转相对于旋转轴的倾斜是稳定的。木星内部卫星的大地旋转的最重要的世俗，周期和混合项首次以相对于其自身坐标系的欧拉角以及相对于其固定赤道的旋转角而言。确定地球和春分点（对于J2000.0时期）。结果表明，太阳系中的某些物体发生大地旋转，这主要是由于它们靠近扰动的中心体而不是其质量。特别是，木星内部卫星的大地测量值（木星对太阳的扰动小于太阳的质量）为10比木星绕其更大的中心天体（太阳）旋转大⁵倍，与它们在牛顿近似中的岁差相当。