3 Calculation of the state vector for Nereid

The difference between the state vectors computed in JRT, is presented in Table 5. Its is given at Julian ephemeris date 2447680.5 and referred to the barycenter of the Neptunian system and to the equator and equinox J2000.0. Observe that the difference is about 0.1% of the state vector. This corroborate the good quality of the JRT state vector which fits well ours observations made up to nine years after its computation.

We can see in Fig. 3, that the set of observations are well distributed on the orbit and there are many positions near the periapsis. The observed minus calculated residuals for fitted observations as function of time are presented in Fig. 4. The residuals have a significant reduction for the observations made later than 1975. The same result is presented in Fig. 5, in this case referred to the true anomaly. As seen, the periapsis positions have small residuals.

  

Figure 6: The means and their errors for the fitted observations grouped by observer and opposition. The cases corresponding to one or two observations are represented by triangles. For many points the bars corresponding to the RMS are so small that they can not be seeing

In Fig. 6 are presented the means and the errors for the fitted observations which were grouped by observer and opposition. The cases corresponding to only one or two observations are marked by triangles. The quality of the observations after 1980 is evident. The RMS for the observed minus calculated fitted observations and the means and the standard deviations for the fitted 284 positions and for our 229 observations are given in Table 6.

In order to compare the orbits defined in this paper and in JRT, we list in Table 7 the elliptical osculating elements computed with our state vector and their differences from the Jacobson's osculating elements. As expected (see Table 5), the orbits are very similar.