Abstract In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration.

中文翻译：

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月球摄动对日-地-月系统能量曲线和平衡点的影响

摘要 在本文中，我们认为月球绕地球运动是日地系统中极小体运动摄动的一个来源。扰动效应是通过使用日-地-月双圆模型（BCM）来分析的。我们已经确定了这种扰动对拉格朗日点和零速度曲线的影响。我们已经得到了无穷小体在三角形平衡点的等效平衡点附近的运动。此外，为了了解轨迹的性质，我们估计了从所提出的系统中三角形平衡点附近发出的轨迹的一阶李雅普诺夫特征指数。注意到由于月球运动产生的扰动，结果受到显着影响，当月球绕地球运动时，雅可比常数会周期性波动。最后，我们强调该模型适用于发送卫星或望远镜进行深空探测。