Question 4

Consider a circular ring of radius $a$ and mass $M$. Show that the gravitational potential in the plane of the ring at a distance $x$ much larger than $a$ is approximately

$$\Phi \approx -{GM\over x} - {GM a^2\over 4x^3} .$$

[In calculating the potential due to a small segment of the ring, you should make a Taylor expansion of the result in powers of $x/a$. You will need to keep terms up to second order in this expansion.]

[Hints can be found here, but do not follow this link until you have attempted the question on your own.]