When a test particle moves about an oblate spheroid, it is acted upon, among other things, by two standard perturbing accelerations. One, of Newtonian origin, is due to the quadrupole mass moment \(J_2\) of the orbited body. The other one, of order \({\mathcal {O}}\left( 1/c^2\right) \), is caused by the static, post-Newtonian field arising solely from the mass of the central object. Both of them concur to induce indirect, mixed orbital effects of order \({\mathcal {O}}\left( J_2/c^2\right) \). They are of the same order of magnitude of the direct ones induced by the post-Newtonian acceleration arising in presence of an oblate source, not treated here. We calculate these less known features of motion in their full generality in terms of the osculating Keplerian orbital elements. Subtleties pertaining the correct calculation of their mixed net precessions per orbit to the full order of \({\mathcal {O}}\left( J_2/c^2\right) \) are elucidated. The obtained results hold for arbitrary orbital geometries and for any orientation of the body’s spin axis \(\hat{\mathbf {{k}}}\) in space. The method presented is completely general, and can be extended to any pair of post-Keplerian accelerations entering the equations of motion of the satellite, irrespectively of their physical nature.

当测试粒子围绕扁球体运动时，除其他外，它会受到两个标准扰动加速度的作用。其一源于牛顿，是由于轨道物体的四极质量矩\(J_2\)造成的。另一种是\({\mathcal {O}}\left( 1/c^2\right) \)阶，是由仅由中心物体的质量产生的静态后牛顿场引起的。它们都共同引起了阶数为\({\mathcal {O}}\left( J_2/c^2\right) \) 的间接混合轨道效应。它们与扁圆源存在时产生的后牛顿加速度引起的直接加速度具有相同的数量级，此处不予处理。我们根据密切开普勒轨道元素来计算这些鲜为人知的运动特征的全部一般性。阐明了正确计算每个轨道的混合净进动到\({\mathcal {O}}\left( J_2/c^2\right) \)完整阶数的微妙之处。所获得的结果适用于任意轨道几何形状以及空间中物体旋转轴\(\hat{\mathbf {{k}}}\)的任何方向。所提出的方法是完全通用的，并且可以扩展到进入卫星运动方程的任何一对后开普勒加速度，而不管它们的物理性质如何。