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We examine intermediate perturbed orbits proposed by the first author previously, defined from the two position vectors and three angular coordinates of a small celestial body. It is shown theoretically, that at a small reference time interval covering the measurements the approximation accuracy of real movements by these orbits corresponds approximately to the third order of osculation. The smaller reference interval of time, the better this correspondence. Laws of variation of the methodical errors in constructing intermediate orbits subject to the length of reference time interval are deduced. According to these laws, the convergence rate of the methods to the exact solution (upon reducing the reference interval of time) is higher by two orders of magnitude than in the case of conventional methods using the Keplerian unperturbed orbit. The considered orbits are among the most accurate in set of orbits of their class determined by the order of osculation. The theoretical results are validated by numerical examples.