The equations for relative orbital motion are commonly known as "Hill's equations" (also Clohessy-Wiltshire equations), and the citation given to G. W. Hill's 1878 "Researches in Lunar Theory" in the American Journal of Mathematics (usually citing only the first segment of pages and overlooking the fact that it is continued into two more segments). I've looked through the whole paper (on JSTOR Segment 1, Segment 2, Segment 3) and not found anything that resembles the equations as we know them today. Does anyone know if they are hidden in a notation that is unfamiliar to the modern eye, or did they appear in another of his papers? One thing I noticed is that the end of the third segment on page 260, it says "to be continued" as it does at the end of the first two segments, but JSTOR doesn't list any more segments that I can find. Is there more to this paper?