Statistics of orbital inclinations of “new” comets and capture hypothesis

Abstract

The capture hypothesis postulated by Hasegawa [ Publ. astr. Soc. Japan 28, 259 (1976)] has been reformulated here in such a way that it also takes into consideration explicitly the effect of external force fields on the capture of comets by the Sun. It is found that, on the basis of the present formulation of the capture hypothesis, the observed number of direct and retrograde orbits and their ratio for “new” comets observed in the last 180 years is very well explained by taking n ( number density of comets per pc 3) = 1.5 × 10 14, σ ( α = 1.77 × 10 14 km s −1 is the most probable speed of comets) = 1.25 km s −1, V 0 (magnitude of Sun's relative velocity w.r.t. the cometary medium) = 1.00 km s −1, U′ (magnitude of perturbative part of cometary velocity due to external force fields) = 0.20 km s −1 and Ω (the statistically averaged position of the ascending node for the ensemble of comets) ≈90° and 250°. Furthermore, in this paper the observed distribution of longitudes and latitudes (in the solar-motion coordinate system) of aphelia of long-period comets is well explained on the basis of the capture hypothesis. It may be added here that the theoretically predicted forms of these distributions are in good consonance with those obtained by Hasegawa (1976). It is worth noting that, with the help of the above-mentioned magnitudes of the parameters n, σ, V 0 and U′ capture rate, anisotropy and distribution of orbital elements e, 1/ a and periods have also been reproduced well on the basis of the present formulation [Khanna, Ph.D. thesis, Punjabi University, Patiala, India (1986)]. Moreover, these magnitudes are in good agreement with those obtained by other researchers such as Hasegawa (1976), Valtonen and Innanen [ Astrophys. J. 255, 307 (1982)], Tomanov and Radzievskii [ Solar System Res. 9, 28 (1975)] and Ketakara [MSS 2964, Pune Jayakar Granth Mala, Pune University, Pune, India (1911)] etc. on the basis of their different approaches to the problem of the statistics of comets.