TITLE: Catenary curve under non-uniform gravitational field
QUESTION [15 upvotes]: The catenary curve is the shape of a chain hanging between two equal-height poles under the influence of gravity.  But the derivation of the (hyperbolic cosine) curve equation from the physics traditionally assumes a uniform gravitational field.  Suppose instead one uses the non-uniform gravitational field that
diminishes with distance from the center of the Earth.  (Perhaps this would be relevant for
a very long chain that sags significantly.)  Does this lead to an interesting curve, known in some
closed form?  Or just to a differential equation that can only be solved numerically?
I ask this primarily out of curiosity, so please interpret in that spirit!

REPLY [3 votes]: Have a look at 

J.Denzler, A.M.Hinz, Catenaria Vera---the True Catenary, Exposition. Math.
17 (1999), 117--142. (MR 2000e:49006, ZB 943.49001).

—A.M.Hinz (Maribor, Slovenia)

(Image from the cited paper added by J.O'Rourke:)