Resonant Trans-Neptunian Object - Classification Methods

Classification Methods

As the orbital elements are known with a limited precision, the uncertainties may lead to false positives (i.e. classification as resonant of an orbit which is not).

A recent approach considers not only the current best-fit orbit but also two additional orbits corresponding to the uncertainties of the observational data. In simple terms, the algorithm determines whether the object would be still classified as resonant if its actual orbit differed from the best fit orbit, as the result of the errors in the observations.

The three orbits are numerically integrated over a period of 10 million years. If all three orbits remain resonant (i.e. the argument of the resonance is librating, see formal definion), the classification as a resonant object is considered secure.

If only two out of the three orbits are librating the object is classified as probably in resonance. Finally, if only one orbit passes the test, the vicinity of the resonance is noted to encourage further observations to improve the data.

The two extreme values of the semi-major axis used in the algorithm are determined to correspond to uncertainties of the data of at most 3 standard deviations. Such range of semi-axis values should, with a number of assumptions, reduce the probability that the actual orbit is beyond this range to less than 0.3%.

The method is applicable to objects with observations spanning at least 3 oppositions.