Long-term numerical theories of comet motion

We propose a method of constructing numerical theories of comet motion that cover long time intervals. The method involves the determination of individual values of the constants A ₁, A ₂, and A ₃ (radial, transversal, and normal components of nongravitational acceleration) and photocenter shifts for each appearance with the presence of a sufficient quantity of observations. Moreover, in the case of close planetary approaches, bursts of brightness, or heavy shifts in the cometary gas production maxima against the perihelion when standard models of nongravitational acceleration cannot provide an accurate presentation of the observations, we propose the use of instant velocity measurements. This method was used to construct a unified numerical theory of motion of the Kopff comet in the interval of 1906–2002. The theory encompassed 16 appearances of the comet with the mean error of unit weight σ = 1.40.