Can someone please explain why the graph is linear from the start to the surface?
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What is that graph for? Can you provide higher resolutions of it? – AHB Jan 08 '17 at 06:54
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Magnitude of gravitational field to distance from centre of sphere. – Anonymous Jan 08 '17 at 07:05
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Use Gauss's law. The enclosed mass grows with $r^3$, but the area of the Gaussian surface increases with $r^2$ so there remains $r$. Got it? – AHB Jan 08 '17 at 07:21
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what does the graph mean? – Darth Ewok Jan 08 '17 at 09:21
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From Gauss's law for gravity we have:
$$\frac{1}{4\pi}\int\mathbf{g}\cdot d\mathbf{a}=-G M_{enc}$$
$$\frac1{4\pi}g(r)\cdot4\pi r^2=-G\rho\cdot\frac 43\pi r^3$$
$$\mathbf{g}(r)=-\frac43\pi\rho G r \mathbf{\hat r}$$
AHB
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