Orbit determination methods for interplanetary missions: development and use of the Orbit14 software

Reconstructing the cruise-phase trajectory of deep-space probes in a general relativistic framework: An application to the Cassini gravitational wave experiment

“…1 in Ref. [1] for example. Typically, in orbit determination problems, the goal is to obtain Gaussian residuals with zero mean.…”

“…Precise radiometric tracking data obtained during planetary flybys and dedicated body-centric missions have provided ample opportunity for scientific exploration of the mass, gravitational field, atmosphere, and orbits of celestial bodies; see Ref. [1] and references therein for an overview of notable space missions dedicated to planetary sciences.…”

Nested modalities in astrophysical modeling

“…In other words, the usual procedure consists in building a suitable theoretical model, running a computer simulation on its basis and then comparing the output of the simulation with the available data sets. At this point, simulated and "observed" observables can be directly compared by different sort of fitting algorithms, in order to check the validity of the theoretical model (e.g., Lari et al, 2021).…”

“…26 The first step consists in setting the values of the PN parameters to those predicted by GR (we will call them PN\ set\ 0). Then, given the GR PN model with PN\ set\ 0, it is possible to run the orbit determination code, ORBIT14 (see Lari et al, 2021): the resulting simulation represents the initial "nominal" solution of the problem. The output of this solution consists in a set of simulated radio observations.…”

“…A well-known example is the case of Lunar Laser Ranging.25 Moreover, the model accounts also for perturbative effects due to the other planets and the main bodies of the solar system (asteroids, etc. ).26 The details of the dynamical model adopted can be found inMilani et al (2002Milani et al ( , 2010.27 The difference is defined in terms of the residuals between simulated, i.e., computed, and observed observations (see, e.g.,Lari et al, 2021, for details).28 In some detail, the whole iterative procedure can be described as follows (for a deeper description, see, e.g.,Schettino & Tommei, 2016;Lari et al, 2021):•Iteration 1: the nominal simulated observations (obtained by setting the values of the PN parameters to the nominal ones, PN set 0) are compared with the data set and the fit provides an updated set of values for the PN parameters, PN set 1; • Iteration 2: we run again the orbit determination code, updating the dynamical model with the new values for the PN parameters, given by PN set 1; the output is an updated set of simulated observations, which are again compared with the data set; the new fit provides a new set of values of PN parameters, PN set 2: such new set represents an improved fit of the values of the PN parameters and the residuals between simulated and observed observations should be smaller than at the previous iteration; • Iteration 3: then PN set 2 is used as the updated input parameters for the dynamical model to run an updated simulation; the updated simulated observations are again fitted with the data set and an updated fit of the values PN parameters, PN set 3, is determined; • Iteration n: the process continues by iterating the previous steps until the residuals between iteration (n−1) and iteration n are small enough that the differential correction process has arrived at convergence, that is, the best fit of the values of the PN parameters has been obtained (where by "best fit", we mean the set of values which minimizes the residuals, i.e., the difference, between simulated and observed observations).…”