- #1

coki2000

- 91

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I wonder that the gauss' theorem for gravitational force area.

[tex]\int\int_S \vec{g}\hat{n}dS=-4\pi GM=\int\int\int_V \vec{\nabla}\stackrel{\rightarrow}{g}dV[/tex]

[tex]\vec{g}=-G\frac{M}{r^2}\hat{r}\Rightarrow\hat{r}=\frac{\vec{r}}{r}\Rightarrow\vec{g}=-G\frac{M}{r^3}\vec{r}[/tex]

for [tex]\vec{r}=x\hat{x}+y\hat{y}+z\hat{z}[/tex] and [tex]r=\sqrt{x^2+y^2+z^2}[/tex]

[tex]\vec{\nabla}\vec{g}=-\frac{\partial}{\partial x}G\frac{M}{r^3}x-\frac{\partial }{\partial y}G\frac{M}{r^3}y-\frac{\partial }{\partial z}G\frac{M}{r^3}z=0[/tex]

The divergence of g has 0 so [tex]\int\int_S\vec{g}\hat{n}dS=0[/tex]

Where do I wrong please help me.Thanks.