Abstract
Context. The apparent close encounters of two satellites in the plane of the sky, called mutual approximations, have been suggested as a different type of astrometric observation to refine the moons' ephemerides. The main observables are then the central instants of the close encounters, which have the advantage of being free of any scaling and orientation errors. However, no analytical formulation is available yet for the observation partials of these central instants, leaving numerical approaches or alternative observables (i.e. derivatives of the apparent distance instead of central instants) as options. Aims. Filling that gap, this paper develops an analytical method to include central instants as direct observables in the ephemerides estimation and assesses the quality of the resulting solution. Methods. To this end, the apparent relative position between the two satellites is approximated by a secondorder polynomial near the close encounter. This eventually leads to an expression for mutual approximations' central instants as a function of the apparent relative position, velocity, and acceleration between the two satellites. Results. The resulting analytical expressions for the central instant partials were validated numerically. In addition, we ran a covariance analysis to compare the estimated solutions obtained with the two types of observables (central instants versus alternative observables), using the Galilean moons of Jupiter as a test case. Our analysis shows that alternative observables are almost equivalent to central instants in most cases. Accurate individual weighting of each alternative observable, accounting for the mutual approximation's characteristics (which are automatically included in the central instants' definition), is however crucial to obtain consistent solutions between the two observable types. Using central instants still yields a small improvement of 1020% of the formal errors in the radial and normal directions (RSW frame), compared to the alternative observables' solution. This improvement increases when mutual approximations with low impact parameters and large impact velocities are included in the estimation. Conclusions. Choosing between the two observables thus requires careful assessment, taking into account the characteristics of the available observations. Using central instants over alternative observables ensures that the state estimation fully benefits from the information encoded in mutual approximations, which might be necessary depending on the application of the ephemeris solution.
Original language  English 

Article number  A93 
Number of pages  23 
Journal  Astronomy and Astrophysics 
Volume  652 
DOIs  
Publication status  Published  2021 
Keywords
 Astrometry
 Ephemerides
 Methods: analytical
 Planets and satellites: individual: Galilean moons
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Data underlying the publication: Analytical framework for mutual approximations  Derivation and application to Jovian satellites
Dirkx, D. (Creator), Visser, P. N. A. M. (Creator), FayolleChambe, M. S. (Creator) & Lainey, V. (Creator), TU Delft  4TU.ResearchData, 25 Jul 2024
DOI: 10.4121/11271E6CAA4A45B6807F6A0EC5B7FE65
Dataset/Software: Dataset