One of the main assumptions used in Chapter 1 is that the dynamical model is deterministic. This assumption can be too optimistic for celestial bodies small enough to be significantly affected by complex non-gravitational interactions. Both drag and radiation pressure can be so poorly known that the errors in the dynamical model can affect the predictions by amounts exceeding, by orders of magnitude, the measurement accuracy.

When this is the case, there are three possible ways out, including the multi-arc strategy presented in this chapter. The others are the use of on-board accelerometers, see Chapters 16, 17, and the empirical parameterization of the unknown effects, see Section 14.5.

The multi-arc approach gives up the attempt to model the orbit of the spacecraft, over the entire time span of the observations, in a deterministic way with a single set of initial conditions. The time span of the observations is decomposed into shorter intervals and the set of observations belonging to each interval is called an observed arc, or just an arc. Each arc has its own set of initial conditions, as if there were a new spacecraft for each one of them. This results in over-parameterization, with the additional initial conditions absorbing the dynamical model uncertainties. Other parameters, e.g., in the dynamic model, can also be local to a single arc.