摘要: 基于地球现今年龄、历时年龄与地球自转速度三者之间的关系提出地球自转速度表达式为：ω_x=Aω_q/(A-T_x) 。该式显示地球自转速度(ω_x)与地球历时年龄(A−T_x)呈反比例变化，即：随年龄增长地球自转速度减慢，相应地，地球的日长增加。该式所对应的图像为反比例函数在第一象限的单支双曲线，它可划分为三大区段(其第II区段可分为两个亚区段)，分别对应了地球自转速度衰减的三个阶段，并可进一步区分出12个可能的地球自转速度半衰期。在距今4282Ma时，赤道自转速度已经衰减到第一宇宙速度之下，此为水成变质岩的年龄值上限。元古代半衰期和显生代半衰期的计算结果可得到化石生长线证据的验证，其余结果有待发现古老日长的可靠数据来校验。地球的历时年龄与该年龄时的自转速度之积为常数，称地球自转行程常数。本文还计算了未来两个时间点的日长，预测209.6 Ma后地球日长可达25小时。

Abstract: Based on the relationships among the Earth’s present age, the lasted ages and the rotation speeds, a calculating formula for the Earth’s rotation speeds, ω_x = Aω_q/(A − T_x), is put forward in this paper. The expression comprehends that an inverse proportion existing between the Earth’s rotation speeds (ω_x) and the Earth's lasted ages (A − T_x), namely, with accretion of the Earth’s age, the rotation speed decreases gradually, and correspondingly, the Earth’s day-long becomes longer. The relevant graph of the expression is a branch of hyperbola in the first quadrant with an inverse proportion function. The branch of hyperbola which describes the attenuation of the earth's rotation speeds can be divided into three major sections, and the second section divided further into two sub-sections. They should be homological with the three main stages of the attenuation of the Earth’s rotation speeds respectively, and 12 possible half-lives of attenuation can be distinguished. By 4282 Ma, the rotation linear speed of the Earth’s equator might attenuate to less than the first universal velocity, and the last window for air and water vapor escaping from the Earth might be closed, so that the hydro-metamorphic rocks with an age more than 4300 Ma, might not be found. The calculated results for the half-lifes of the Proterozoic Era and the Phanerozoic Era can be verified by the fossil’s growth lines preserved in the strata, and the rest part of the branch curve needs to be verified by finding more reliable data on older day-longs. The products of the Earth’s lasted ages and the rotation speeds at that time point should be a constant, which is named the throw constant of the Earth’s rotation. Also, the paper calculates two examples for the day-longs in the future, and forecasts that after 209.6 Ma, the Earth will have 25 hours per day.