formula for astronomical midnight at Greenwich, in UT?

Hi, I mentioned this in another thread but thought I'd give it a
thread of its own.

Can someone help with a formula for astronomical midnight at
Greenwich, in UT, given the Julian Day Number? I.e. the UT of the
first astronomical midnight (lower culmination of the apparent Sun)
following JDN = x.

Ideally I need an accuracy of a few seconds.

Many thanks in advance.

Michael