Verifying this relationship throughout the orbital cycle, however, required very extensive calculation; to simplify this task, by late 1602 Kepler reformulated the proportion in terms of geometry: planets sweep out equal areas in equal times—Kepler's second law of planetary motion.
然而，想要在整个轨道周期证实这种关系，需要进行非常广的计算；为简化计算任务，1602年底，开普勒运用几何学重新阐述了这个比例：行星在同样的时间内扫过同样的面积——开普勒关于行星运动的第二定律。