Curve for chain in NON-homogeneous gravitational field?

[Gene Partlow]

What would be the equation and curve for a perfect chain suspended in an
non-homogeneous gravitational field, analogous to the catenary or
hyperbolic
cosine, which would be the locus taken in a homogeneous field?

Eg: As an example, consider the curve taken by such a chain suspended
from the tops of a pair of ~five-thousand-mile-high towers, which have
bases
separated by, say, a few thousand miles distance, on a static Earth.

Thanks,
Gene