All Tables

Table 3: Values of exponents m,n,k, the scale distance $r_{\rm {0}}$ , and coefficient $\alpha$ (g(r)-like function, Eq. (2a)) estimated from observed water sublimation rates for C/1995 O1 Hale-Bopp and C/1996 B2 Hyakutake (Szutowicz et al. 2002a,b).
Table 5: Comparison between mean values of the NG parameters derived from models with constant $A_{\rm {1}}, A_{\rm {2}}$ , $A_{\rm {3}}$ and from models with a rotating spherical nucleus for the investigated sample of long-period (LP) comets and 20 short-period comets. Comets C/1991 T2 and C/1995 Y1 were excluded from the basic statistical analysis (17 LP comets) because another relations of h(r) (g^*(r) with k=0 i.e. the power law or g(r)-like function with $r_{\rm {0}}\neq 2.808$ AU) probably are more adequate for them (see Table 2). Two next two comets (C/1998 P1 and C/1993 A1) with the greatest NG parameters and $(1/a)_{\bf {ori}} < 10^{-4}$ are excluded from the sample of 15 LP comets. LP models of a rotating spherical nucleus are taken from Table 4.
Table 1: General characteristics of the observational material. The succesive columns signify: comet designation and name (Col. 1) perihelion time, T, and perihelion distance, q(2), observational arc and number of all observations (3), rms for the pure gravitational orbital fitting to pre-periherlion (4), post-perihelion (5) and all (6) observations, rms for the NG orbital fitting to all observations (7), original (8) and future (9) reciprocals of semimajor axes in units of 10^-6 AU^-1.
Table 2: NG parameters derived from positional observations for assumed function h(r) (Eq. (5)) represented by: standard function g(r), g^*(r) - modified function g(r), $g_{\rm {S}}$ (r) - Sekanina's function, f(r) - Yabushita's function describing CO sublimation, respectively. NG parameters $A^*_{\rm {1}}, A^*_{\rm {2}}, A^*_{\rm {3}}$ are given in units of 10^-8 AU day^-2; these parameters are the standard $A_{\rm {1}}, A_{\rm {2}}$ and $A_{\rm {3}}$ for the NG models including the standard g(r); $\tau$ is given in days. First line for each individual comet shows the NG parameters $A_{\rm {1}}$ and $A_{\rm {2}}$ taken from MW Catalogue or Minor Planet Circulars (if there are). The g^*(r) functions for C/1995 O1 Hale-Bopp ( $g^*_{\rm {HB}}$ (r)) and C/1996 B2 Hyakutake ( $g^*_{\rm {Hya}}$ (r)) are described in Table 3. For comet C/1959 Y1 Burnham the models with displacement, D, of photometric centre from the gravitational one are also presented; the values of this displacement (in paranthesis) are given in units of 10^-5 AU. Models with subscript ^R indicate solutions based on 37 observations of Comet Burnham made by Roemer et al. (1966).
Table 4: Forced precession model for assumed function h(r) represented by: standard function g(r), f(r), g^*(r) - modified function g(r), respectively. NG parameters $A_{\rm {1}}, A_{\rm {2}}, A_{\rm {3}}$ are given in units of 10^-8 AU day^-2, and precession factor $f_{\rm p}$ - in units of 10⁶ day AU^-1. Subscript "0'' in $I_{\rm {0}}$ and $\phi _{\rm {0}}$ denotes the values on the starting epoch of integration given in the Col. 1. The g^*(r) functions for C/1995 O1 Hale-Bopp ( $g^*_{\rm {HB}}$ (r)) and C/1996 B2 Hyakutake ( $g^*_{\rm {Hya}}$ (r)) are described in Table 3; subscripts ^(a) and ^(b) denote solutions taken from Szutowicz et al. (2002a,b). In the case of comet Hyakutake models with subscript ^(a)additionally include the observed comet fragmentation on 1996 March 21.
Table 6: Comparison between two kinds of NG models for four short-period comets. NG parameters were derived from 8 of 12 detected apparitions for Comet 31P/Schwassmann-Wachmann 2, 8 of 9 detected apparitions for Comet 46P/Wirtanen (the last one were excluded), 15 of 19 apparitions for Comet 26P/Grigg-Skjellerup and all available observations (5 apparitions span over 9 perihelion passages) in the case of Comet 88P/Howell. Standard NG parameters $A_{\rm {1}}, A_{\rm {2}}, A_{\rm {3}}$ and parameter A (forced precession model) are given in units of 10^-8 AU day^-2. The precession factor $f_{\rm p}$ is in units of 10⁷ day/AU, Subscript "0'' in $I_{\rm {0}}$ and $\phi _{\rm {0}}$ denotes the values for the starting epoch of integration (Epoch: 2003 12 27). For two comets (31P and 46P) the assumption about the asymmetry of function g(r) was necessary, and the time shifts $\tau$ (in days) were derived. The forced precession model of 26P was taken from Sitarski (2003).