全部

1·I multiply both sides with R squared.

两边都乘以R的平方。

2·But now notice, I can substitute now for this v squared, I can substitute the square of this that is the orbital speed and then I get M G over R.

现在注意我能,代替这个v平方，我能代入这个平方,那是轨道速度,然后得到MG在R上。

3·So instead of being equal to negative z squared, now we're equal to negative z effective squared times r h all over n squared.

这里不再等于-z的平方，现在我们等于-有效的z的平方,乘以RH除以n的平方。

4·a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.

在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。

5·We came exactly to that conclusion-- that the gravitational acceleration falls off as one over r squared.

我们得到结论-,重力加速度,随r的平方而减少。

6·So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.

如果我们要讨论它的体积，我们要用的是表面面积，也就是4πr的平方，乘以厚度dr

7·the force, gravitational force, falls off as one over r squared.

,力，重力，随着r的平方而减少。

8·Therefore, you cannot escape the conclusion that the centripetal acceleration which is the result of gravity, falls off as one over R squared.

因此得出无懈可击的结论,这向心加速度,是由引力引起，并呈1/r2递减。

9·So, the number of nuclei, 119 if we were to sit and count these as well, is 119. So, we'll multiply that by just pi, r squared, to get that cross-section, and divide all of that by 1 .

如果你们数的话，原子核的数是，我们用它乘以πr的平方，得到横截面积，除以1。