Measuring Titan’s rapid orbital expansion combining Cassini radio science normal points and astrometry

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Table C.2

Comparison of Titan’s estimated gravity-field parameters with respect previous analyses.

Parameter (×10⁻⁶)	This Work	Durante et al. (2019)	Petricca et al. (2025)	Goossens et al. (2024)
J₂	33.973 ± 0.710	33.089 ± 0.609	33.511 ± 0.471	36.256 ± 3.108
C₂₁	0.183 ± 0.255	0.513 ± 0.215	0.483 ± 0.116	−0.738 ± 0.261
C₂₂	10.306 ± 0.101	10.385 ± 0.084	10.107 ± 0.062	11.263 ± 1.285
S₂₁	−0.083 ± 0.478	0.612 ± 0.359	0.695 ± 0.263	−1.082 ± 0.625
S₂₂	0.014 ± 0.081	−0.064 ± 0.066	0.053 ± 0.052	0.515 ± 0.143
J₃	0.026 ± 1.000	−0.179 ± 0.720	0.992 ± 0.612	0.628 ± 1.199
C₃₁	1.275 ± 0.317	1.481 ± 0.254	1.909 ± 0.175	1.045 ± 0.346
C₃₂	0.264 ± 0.233	0.183 ± 0.153	−0.260 ± 0.129	0.720 ± 0.322
C₃₃	−0.220 ± 0.029	−0.222 ± 0.017	−0.233 ± 0.018	−0.113 ± 0.031
S₃₁	−0.488 ± 0.551	0.811 ± 0.402	1.318 ± 0.323	−3.363 ± 0.705
S₃₂	0.083 ± 0.142	−0.027 ± 0.099	0.391 ± 0.060	−0.337 ± 0.216
S₃₃	−0.222 ± 0.026	−0.226 ± 0.019	−0.231 ± 0.019	−0.099 ± 0.030
J₄	0.982 ± 1.945	−1.077 ± 1.844	2.056 ± 1.425	−3.074 ± 2.640
C₄₁	−0.367 ± 0.318	−0.842 ± 0.299	−0.473 ± 0.149	−0.285 ± 0.492
C₄₂	0.242 ± 0.133	0.183 ± 0.107	−0.007 ± 0.077	1.132 ± 0.202
C₄₃	−0.048 ± 0.050	−0.012 ± 0.039	−0.131 ± 0.025	0.031 ± 0.059
C₄₄	−0.009 ± 0.004	0.014 ± 0.003	−0.011 ± 0.003	−0.003 ± 0.005
S₄₁	−1.275 ± 0.850	0.191 ± 0.717	−0.527 ± 0.546	−3.868 ± 1.053
S₄₂	0.205 ± 0.134	0.198 ± 0.106	0.513 ± 0.067	−0.206 ± 0.157
S₄₃	−0.014 ± 0.037	−0.062 ± 0.033	−0.086 ± 0.030	−0.046 ± 0.051
S₄₄	−0.009 ± 0.004	−0.012 ± 0.004	−0.004 ± 0.003	0.002 ± 0.005
J₅	1.019 ± 2.198	1.118 ± 2.022	3.008 ± 1.467	−4.762 ± 3.270
C₅₁	0.144 ± 0.405	0.361 ± 0.406	0.240 ± 0.268	0.340 ± 0.535
C₅₂	0.031 ± 0.134	−0.097 ± 0.118	−0.056 ± 0.064	0.347 ± 0.184
C₅₃	−0.012 ± 0.023	−0.016 ± 0.019	−0.057 ± 0.012	0.061 ± 0.030
C₅₄	−0.003 ± 0.005	0.007 ± 0.004	0.004 ± 0.003	0.003 ± 0.006
C₅₅	0.001 ± 0.000	0.000 ± 0.001	0.000 ± 0.001	−0.001 ± 0.001
S₅₁	−0.667 ± 0.722	0.267 ± 0.604	−0.028 ± 0.481	−1.587 ± 0.830
S₅₂	0.156 ± 0.115	0.044 ± 0.094	0.173 ± 0.069	−0.159 ± 0.156
S₅₃	−0.007 ± 0.016	−0.004 ± 0.012	0.003 ± 0.011	0.067 ± 0.019
S₅₄	−0.003 ± 0.005	−0.002 ± 0.004	−0.005 ± 0.004	−0.019 ± 0.007
S₅₅	0.001 ± 0.001	0.000 ± 0.001	0.001 ± 0.001	0.000 ± 0.001

Parameter (unscaled)

k₂	0.596 ± 0.094	0.616 ± 0.067	0.608 ± 0.048	0.375 ± 0.060

Notes. Parameters are unnormalized, with a reference radius of 2575 km, derived from the radio science local analysis used to generate the normal points. All reported uncertainties are 1σ.

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