Table 1
Initial conditions and other parameters of Neptune and integrated satellites used in the dynamical modeling and relevant analysis.
| Parameter | Nominal value | Uncertainty |
|---|---|---|
| x1,2(t0) (a) | Values from NEP081 ephemerides (Jacobson 2009) | |
| μs [km3 s−2] | 6836527.100580397 (Jacobson 2009; Brozović et al. 2020), which is also adopted by DE440 (Park et al. 2021) | 10.0 (Jacobson 2009) |
| μ1 [km3 s−2] | 1427.598140725034 (Jacobson 2009; Brozović et al. 2020) | 1.9 (Jacobson 2009) |
| μ2 [km3 s−2] | 0 (Jacobson 2009) | 2.4, 100% of the gravitational parameter value based on a default density of 1.5 g cm3 and the size adopted from Kiss et al. (2016) |
| J2 (×10−6) | 3409.138069414930 (Brozović et al. 2020) | 2.9 (Brozović et al. 2020) |
| J4 (×10−6) | − 33.39891759006578 (Jacobson 2009; Brozović et al. 2020) | 2.9 (Jacobson 2009) |
| αp(t0) (a) [°] | 299.3751265701683 (Jacobson 2009; Brozović et al. 2020) | 0.14 (Jacobson 2009) |
| δp(t0) (a) [°] | 42.94918452997446 (Jacobson 2009; Brozović et al. 2020) | 0.03 (Jacobson 2009) |
 |
15903.13513325206, based on the rotational period, 17.4581 hr, and the inertia factor, 0.25 (Helled et al. 2010; Podolak & Helled 2012) | 637, based on the uncertainty of the rotational period, 0.0007 h, and that of the inertia factor, 0.01 (Helled et al. 2010; Podolak & Helled 2012) |
Notes. The epoch t0 is 1989 September 1 TDB (Barycentric Dynamical Time). The value x denotes the state referred to the ICRS centered at Neptunian system barycenter and μ the gravitational parameter (GM), with subscripts i denoting Neptune and its integrated satellites. Here, i = 0 are Neptune, i = 1, 2 are Triton and Nereid, respectively. Besides, μs is GM of Neptunian system. The reference radius for Neptune is 25225 km. The values J2 and J4 are the second and fourth zonal harmonics of the gravitational potential of Neptune, respectively, αp and δp the ascension and declination of Neptune’s pole referred to the ICRS, respectively, and
the ratio of the magnitude of Neptune’s rotational angular momentum (L) to the mass of Neptune (m).
(a) To-be-determined parameters. They are adjusted in our orbit fitting process, with the results provided in Table 4.
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