Earlier in the 18th century, when scientists were trying to relate Newton’s theory of gravitation to the observations of the motion of planets and satellites, Perturbation methods for differential equations became important. Initially in the stating it became clear that a dynamical theory of the solar system based on a superposition of only two-body motions, produces a reasonable but not very accurate fit to the observations. With the consideration of effects as the influence of satellites such as the Moon in the case of the Earth, the resistance of the ether and other effects, the above deviations can be explained. These considerations led to the formulation of perturbed two-body motion and the development of perturbation theory as exact solutions were clearly not available. In the first half of the 18th century, first attempts took place which involved a numerical calculation of the increments of position and velocity variables from the differentials during successive small intervals of time. Various ingenious expansions of the perturbation terms to make the process tractable in practice were involved in the actual calculations involve. Very soon it became clear that this process leads to the construction of astronomical tables but not necessarily to general insight into the dynamics of the problem. Wilson  presented an extensive study of early perturbation theory and the construction of astronomical tables.
在第十八个世纪前，当科学家们试图与牛顿的引力理论的行星和卫星的运动微分方程的摄动方法观察，成为重要的。最初在说明它变得清晰，只是基于二体运动的叠加的太阳能系统动力学理论，产生一个合理的但不太精确的适合观测。随着影响考虑，如在地球的月球卫星的影响，的醚和其他影响电阻，上述偏差可以解释的。这些考虑导致制定的摄动二体运动和摄动理论的精确解，显然是不可用的发展。在第十八个世纪的前半，第一次发生涉及数值计算的位置和速度变量的增量的差异在连续的小间隔时间。的扰动项进行的实践中的各种巧妙的扩展参与实际的计算涉及。很快，很明显，这个过程导致的天文表建设而不是一般的洞察问题的动力学。威尔逊[ 289 ]提出了一个广泛的研究，早期的摄动理论和天文表的结构。