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A uniform thin straight rod of length $2a$ and mass per unit lenth $p$ lies along the $z$-axis for $-a\le z\le a$. Find the gravitational potential of the rod, letting $r^2=x^2+y^2$.

Also check that the gravitational potential is $GM/r$ plus higher order terms as $r$ tends to infinity.

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1 Answer

At distance $R=x^2+y^2$, one will see a potential proportional to:

$$\int_{-a}^a\frac{G\rho}{\sqrt{(t-x)^2+y^2}}dt$$

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