Comment by TeMPOraL

If all you care about is measurements/predictions relative to Earth, then it makes no sense to transform everything into Sol-centric frame, do the math there, and then untransform results back to Earth-centric frame.

Put another way, there's a reason we use latitude/longitude for terrestrial positioning, instead of Cartesian coordinates with Sol being at (0, 0, 0). For one, it keeps the math time-invariant.