Is there such a thing as an ephemerides equation?
An ephemeris is more complex than an equation.
Ephemerides is the plural of ephemeris. An ephemeris gives the positions of astronomical bodies. Traditionally these were tables from which positions could be looked up.
Modern ephemerides are complex computer models of positions. The data consists of coefficients of polynomial equations which give the coordinates of a body at a given time. The time origin is an epoch which is often J2000 - 2000-01-01 12:00:00. The coordinates are calculated by evaluating the polynomials for the time the position is required. Time is measured in Julian centuries from the epoch.
So an ephemeris is not an equation as such. It is three or more complex time polynomials for each body.