Compare like with like before judging a simulation

A model and an observation can use different coordinate origins, axes, units or time scales. Their numbers are not directly comparable until these definitions match. JPL’s Horizons documentation distinguishes output types and reference choices because an ephemeris is meaningful only with its surrounding conventions.

A geometric state vector describes a position and velocity under specified definitions. An apparent observed direction can include light-time and other observational effects. Treating these as identical quantities can create a discrepancy that is due to the comparison rather than a missing physical force.

For a fictional one-dimensional comparison, a model predicts 3.2 kilometers from a shared origin at a stated time, while the observation is 3,250 meters. Convert the prediction to 3,200 meters. Observed minus predicted is then +50 meters, before considering uncertainty.

Subtracting 3.2 directly from 3,250 would mix units and produce a meaningless value. Matching units is necessary but not sufficient: the origin, direction, timestamp and quantity must also agree. A precise numerical subtraction cannot rescue incompatible definitions.

Match units before taking a difference

A mismatch can reflect measurement uncertainty, an initial-state error, omitted physics or a numerical problem. Compare residuals over time and examine whether changing the step size changes the result. Use an independent reference where appropriate and record which data were used to tune the model.

Suppose a fictional discrepancy remains almost unchanged when the step is halved twice. That suggests the particular step-size error may not dominate, but it does not identify the true cause. Check other assumptions and measurement definitions. A model should be accepted for a stated purpose and tolerance — open definition, with its remaining limits visible.