接着开普勒证明了这个椭圆轨道也能很有效解释其他行星的运行轨迹。然后他提出了行星运动定律，牛顿定律就是以此为理论基础的。
Kepler went on to show that an elliptical orbit is sufficient to explain the movement of the other planets and to devise the laws of planetary motion that Newton built on.
这项分析暗示，或许有比从前预想的更多的潜在“地球”在进行着轨道运动，这一原则将会拓展到还没被开普勒轨道天文台扫描到的地区。
Traub's analysis hints that there may be even more potential 'Earths' orbiting them than previously thought - and that this' principle 'would extend to stars not yet scanned by Kepler.
接着开普勒提出了他的定律，他说行星基本上是绕太阳作椭圆运动，它们在椭圆上有特殊的运动规律。
And then Kepler came with these laws that said basically that planets move in an ellipse around the sun, and that they move in a very specific way along that ellipse.
开普勒第二定律说到，首先每个行星的运动都保持在同一平面内。
So, what Kepler's second law says is that the motion of planets is, first of all, they move in a plane.
事实上，如果你观察带电粒子，在点电荷引起的电场中的运动，它也满足开普勒第二定律。
So, actually, if you look at motion of charged particles in an electric field caused by a point charged particle, it also satisfies Kepler's law, satisfies the same law.
在那时候，开普勒尝试观察天上行星的移动，并尝试提出它运动的理论。
So, what happened back then was Kepler was trying to observe the motion of planets in the sky, and trying to come up with general explanations of how they move.
牛顿和开普勒关于行星运动的数学解释是科学史上极其重要的两大成就。
The mathematical explanations about planets′ motion given by Newton and Kepler are two of the most important achievements in science history.
其物理意义，开普勒方程是关于行星运动微分方程组的一个积分，由于引入了辅助量E，使数学表达式大为简化。
It also has its physical significance. Kepler equation is an integral of differential equation set. The introduction of assistant quantity E leads to the simplification of mathematic expression.
这项分析暗示，或许有比从前预想的更多的潜在q“地球”在进行着轨道运动，这一原则将会拓展到还没被开普勒轨道天文台扫描到的地区。
Traub's analysis hints that there may be even more potential 'Earths' orbiting them than previously thought - and that this' principle 'would extend to stars not yet scanned by Kepler.
这项分析暗示，或许有比从前预想的更多的潜在q“地球”在进行着轨道运动，这一原则将会拓展到还没被开普勒轨道天文台扫描到的地区。
Traub's analysis hints that there may be even more potential 'Earths' orbiting them than previously thought - and that this' principle 'would extend to stars not yet scanned by Kepler.
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