均匀球体对球体外物体的万有引力等效于位于球心处的质点
\begin{aligned}
\cos\alpha &= \frac{D-z}{\sqrt{x^2+y^2+(D-z)^2}} \\
&= \frac{D-r\cos\phi}{\sqrt{r^2\sin^2\phi\cos^2\theta
+r^2\sin^2\phi\sin^2\theta+D^2-2rD\cos\phi+r^2\cos^2\phi}} \\
&= \frac{D-r\cos\phi}{\sqrt{r^2+D^2-2rD\cos\phi}}
\end{aligned}
\begin{aligned}
F &= \iiint\frac{Gm\rho\text{d}V}{x^2+y^2+(D-z)^2}\cos\alpha \\
&= Gm\rho\iiint\frac{r^2\sin\phi(D-r\cos\phi)}
{(r^2+D^2-2rD\cos\phi)^{\frac{3}{2}}}\text{d}V
\end{aligned}令
\begin{aligned}
A(\phi) &= r^2\sin ...
