Kepler's Equal-Area Planet Motion

Kepler's second law explains how a planet moves faster and slower in its orbit around the Sun. Johannes Kepler, a German astronomer and mathematician in the early 17th century, developed three laws for planetary motion. His first law says that planets travel in elliptical orbits, with the Sun at one focus of the ellipse. Bec...

考虑一颗行星沿椭圆轨道绕太阳运动，从 A 点移动到 A₁ 点，在时间 dt 内产生角位移 dθ。那么，在时间 dt 内扫过的扇形面积 dA 等于行星径向距离与弧长 rdθ 乘积的一半。扇形速度 dA/dt 则等于 r²dθ/dt 的一半。

这里，dθ/dt 是行星的角速度。因此，将该方程乘以行星的质量，即可得到用行星角速度表示的面积速度。

然而，mr...