温伯格《TO EXPLAIN THE WORLD》中这段话是不是有误


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送交者: gulfmoon 于 2017-03-07, 04:35:28:

在“科学革命”一章的注释中有这样一段:
The main effect of the ellipticity of planetary orbits is not so much the ellipticity itself as the fact that the Sun is at a focus rather than the
center of the ellipse. To be precise, the distance between either focus and the center of an ellipse is proportional to the eccentricity, while
the variation in the distance of points on the ellipse from either focus is proportional to the square of the eccentricity, which for a small
eccentricity makes it much smaller. For instance, for an eccentricity of 0.1 (similar to that of the orbit of Mars) the smallest distance of the
planet from the Sun is only ½ percent smaller than the largest distance. On the other hand, the distance of the Sun from the center of this
orbit is 10 percent of the average radius of the orbit.
他说偏心率为0.1(火星的偏心率为0.093)的椭圆到一个焦点(太阳)的最短距离只比最大距离小0.5%。这不对吧。椭圆上的一点到焦点的最小距离与最大距离的比值不是应该等于(1-e)/(1+e)吗。(e为偏心率),最短距离比最大距离差18.2%。偏心率为0.1的椭圆短轴比长轴只差0.5%,他是不是说差了。



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