A pure two-body problem has seven integrals including the Kepler energy, the Laplace vector, and the angular momentum vector. However, only five of them are independent. When the five independent integrals are preserved, the two other dependent integrals are naturally preserved from a theoretical viewpoint; but they may not be either from a numerical computational viewpoint. Because of this, we use seven scale factors to adjust the integrated positions and velocities so that the adjusted solutions strictly satisfy the seven constraints. Noticing the existence of the two dependent integrals, we adopt the Newton iterative method combined with the singular value decomposition to calculate these factors. This correction scheme can be applied to perturbed two-body and N-body problems in the solar system. In this case, the seven quantities of each planet slowly vary with time. More accurate values can be given to the seven slowly-varying quantities by integrating the integral invariant relations of these quantities and the equations of motion. They should be satisfied with the adjusted solutions. Numerical tests show that the new method can significantly reduce the rapid growth of numerical errors of all orbital elements.

中文翻译：

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一种新的准开普勒轨道修正方法

纯二体问题有七个积分，包括开普勒能量、拉普拉斯矢量和角动量矢量。然而，其中只有五个是独立的。当保留五个独立积分时，另外两个从属积分从理论角度自然也保留了；但它们可能不是从数值计算的角度来看的。因此，我们使用七个比例因子来调整综合位置和速度，以便调整后的解决方案严格满足七个约束条件。注意到两个依赖积分的存在，我们采用牛顿迭代法结合奇异值分解来计算这些因子。这种校正方案可以应用于太阳系中的扰动二体和 N 体问题。在这种情况下，每个行星的七个量随时间缓慢变化。通过对这些量的积分不变关系和运动方程进行积分，可以为这七个缓慢变化的量提供更准确的值。他们应该对调整后的解决方案感到满意。数值试验表明，新方法可以显着降低所有轨道元素数值误差的快速增长。