3c3
< % Miroslav Broz (miroslav.broz@email.cz), Nov 1st 2004
---
> % Miroslav Broz (miroslav.broz@email.cz), Sep 14th 2004
13d12
< % There is an error in iauc.cls file, which causes ambigous footnote labeling!
71,72c70,71
<  $6$~asteroids located inside the high-eccentricity quasi-regular
<  stable island, which previously seemed empty.
---
>  $5$~asteroids located inside the higher-eccentricity quasi-regular
>  stable island A, which previously seemed empty.
83,114c82,97
< The structure of the Jovian mean motion resonances (MMRs)
< has been thoroughly studied for a long time. In 1980's, there
< seemed to be a gap, almost void of any asteroids, in the 2/1 MMR,
< and that was in contrast with the 3/2 MMR, where numerous
< asteroids (so called Hildas) were observed.
< %
< The first 3-body models of motion in the 2/1 MMR
< (Murray 1986; Henrard \& Lema\^{\i}tre 1987; Lema\^{\i}tre \& Henrard 1990)
< failed to find any large chaotic regions inside, which could increase
< the eccentricity of the resonant objects and drive them to planet-crossing orbits,
< which was a preferred theory for the depletion of resonances since
< the work of Wisdom (1982).
< %
< However, the early N-body numerical simulations
< (Wisdom 1987) showed the mechanism should work.
< %
< Improved 3-body models (Morbidelli \& Moons 1993),
< with main secular perturbations of Jupiter's orbit,
< allowed to calculate borders of secular resonances embedded
< in the 2/1 MMRs.
< %
< The key point was to use at least a 4-body model (Ferraz-Mello 1994,
< Henrard \etal\ 1995), because only then low- and high-eccentrcity
< chaotic regions, caused by overlapping secondary or secular resonances,
< are interconnected and allow large scale diffusion.
< %
< The extensive \hbox{N-body} simulations (Nesvorn\'y \& Ferraz-Mello 1997)
< and semi-analytical analysis (Moons \etal\ 1998) allowed to map
< the structure of the 2/1 MMR in detail.
< The two macroscopic islands of stability, separated by $\nu_{16}$
< secular resonance, were denoted A and B (see also Fig.~\ref{fig:arerir}).
< In 1990's, there were already 10 resonant asteroids discovered.
---
> Unlike higher-order mean motion resonances (MMRs), for which
> the embedded secular resonances and multiplets given by various 
> combinations of secular angles often overlap causing overall 
> instability, the first-order MMRs with Jupiter contain, apart from 
> large dynamically unstable regions, also stable ones
> (e.g. Nesvorn\'y \& Ferraz-Mello 1997). The structure of the 2/1 
> Jovian MMR has been thoroughly studied by means of semi-analytic methods
> (e.g.~Henrard \& Lema\^{\i}tre 1987; Lema\^{\i}tre \& Henrard 1990;
> Morbidelli \& Moons 1993; Moons \etal\ 1998) and using numerical
> integrations (e.g.~Murray 1986; Henrard \etal\ 1995; Nesvorn\'y \&
> Ferraz-Mello 1997). Two macroscopic islands of stability,
> previously called A and B, were found inside this resonance,
> confined by large chaotic regions due to numerous secondary and 
> secular resonances. The stable islands A and B are separated by 
> $\nu_{16}$ secular resonance, making orbits in the island B have smaller
> mean values of eccentricity and inclination.
116,117c99,100
< In general, observations support the latest theoretical results,
< confirming that the 2/1 Jovian MMR harbors a small population of asteroids.
---
> In general, observations support these theoretical results, confirming
> that the 2/1 Jovian MMR harbors a small population of asteroids.
123c106
<  (ii)~{\em Griquas\/} residing on orbits, whose dynamical
---
>  (ii)~{\em Griquas\/} residing on semi-stable orbits, whose dynamical
166c149
< $e$ satisfy $e > {0.45\over 0.14} (3.24 - [a]_{\rm AU}) \mbox{ and }
---
> $e$ satisfy $e > {0.45\over 0.14} (3.24 - [a]_{\rm AU}) \land
310c293
<  indicating some clones may be long-lived, while others are short-lived.
---
>  indicating some clones may be long-lived, while others short-lived.
344c327
< (ii)~asteroids with larger values of $t_{\rm J2/1}$ reside on marginally stable
---
> (ii)~asteroids with larger values of $t_{\rm J2/1}$ reside on semi-stable
358c341
< marginally stable Griquas or stable Zhongguos.%
---
> semi-stable Griquas or stable Zhongguos.%
411,412c394,395
< 0^\circ \mbox{ and } \dot\sigma_{\rm J2/1} < 0 \mbox{ and } \varpi-\varpi_{\rm J}=0^\circ 
< \mbox{ and } \Omega-\Omega_{\rm J}= 0^\circ$, where $(\Omega, \varpi;
---
> 0^\circ \land \dot\sigma_{\rm J2/1} < 0 \land \varpi-\varpi_{\rm J}=0^\circ 
> \land \Omega-\Omega_{\rm J}= 0^\circ$, where $(\Omega, \varpi;
416,417c399,400
< used a weakened condition $\sigma_{\rm J2/1}\le 5^\circ\,\mbox{ and }\,\Delta
< \sigma < 0\,\mbox{ and }\, |\varpi-\varpi_{\rm J}|\le 5^\circ$ (where $\Delta
---
> used a weakened condition $\sigma_{\rm J2/1}\le 5^\circ\,\land\,\Delta
> \sigma < 0\,\land\, |\varpi-\varpi_{\rm J}|\le 5^\circ$ (where $\Delta
436c419
< (iii)~the marginally stable (Griqua-like) are right at the outskirts
---
> (iii)~the semi-stable (Griqua-like) are right at the outskirts
451,454c434,437
<  three sub-populations. We assumed the albedo of all asteroids to be 0.05.
<  Arrows in the left-most plot indicate a horizontal displacement
<  of the distributions, if we assume different values of the albedo
<  --- 0.1 and 0.02.}
---
>  three sub-populations. Arrows in the left-most plot indicate a
>  horizontal displacement of the distribution for two values
>  of the albedo -- 0.1 and 0.02 -- different from the nominally used
>  value 0.05.}
480,484c463,466
< Zhongguos and Griquas -- are partly ambiguous, because these populations
< are not well separated. The current division at $t_{\rm J2/1} = 1\,{\rm Gy}$
< was chosen a little arbitrarily.
< If the whole long-lived population (i.e. with $t_{\rm J2/1}\ge 70$~My)
< is considered together its SFD has an exponent $-3.5\pm 0.2$.}
---
> Zhongguos and Griquas -- are partly ambiguous because they depend
> on the arbitrary division at $1$~Gy. If the whole long-lived
> ($t_{\rm J2/1}\ge 70$~My) population is considered together its
> SFD has an exponent $-3.5\pm 0.2$.}
499c481
< of the main belt population is well approximated by a power-law
---
> of the main belt population is well approximated with a power-law
504c486
< \footnote[1]{In fact, when we discard the extremely unstable asteroids
---
> \footnote{In fact, when we discard the extremely unstable asteroids
515,517d496
< %
< These models, however, cannot be extended to Zhongguos,
< because of their anomalously steep SFD.
527,529c506,507
<  calculated from $H$ using the value of albedo 0.05.
<  The last column is the classification: G -- Griquas, Z -- Zhongguos.
<  Asteroid (4177) Kohman is a border-line case (see the text for discussion).}
---
>  calculated from $H$ using the value of albedo 0.05. Asteroid (4177)
>  Kohman is a border-line case (see the text for discussion).}
532c510
< \begin{tabular}{rlrrrrrrrrrc}
---
> \begin{tabular}{rlrrrrrrrrr}
544,545c522
< \multicolumn{1}{c}{$D$} &
< \multicolumn{1}{c}{Class.} \\
---
> \multicolumn{1}{c}{$D$} \\
557,558c534
< \multicolumn{1}{c}{[km]} &
< \\
---
> \multicolumn{1}{c}{[km]} \\
571c547
< we found $6$~cases that lie above the separatrix of the $\nu_{16}$ 
---
> we found $5$~cases that lie above the separatrix of the $\nu_{16}$ 
578c554,555
< with an approximate amplitude of $20^\circ$ and period $\simeq\!9\,{\rm ky}$.
---
> with an approximate amplitude of $20^\circ$ and period $\simeq\!9\,
> {\rm ky}$.
585,587d561
< However, this ratio has only a low statistical significance,
< because the number of A-Zhongguos, discovered upto now, is too small
< and new discoveries will change the ratio a~lot.
590,592c564,565
< of the stable population in the 2/1 MMR should consider the differences
< between island~A and island~B population as important constraints.
< For instance, \cite{ferrazmello_etal1998}
---
> of the stable population in the 2/1 MMR should consider this
> ratio as an important constraint. For instance, \cite{ferrazmello_etal1998}
626c599
< 153~resonant asteroids, and among them six new located
---
> 153~resonant asteroids, and among them five new located
646c619
< \footnote[2]{Note the Yarkovsky-driven origin of the unstable population would,
---
> \footnote{Note the Yarkovsky-driven origin of the unstable population would,
665,668d637
< \bibitem[Ferraz-Mello (1994)]{ferrazmello_1994}
< {Ferraz-Mello, S.} 1994,
< in \textit{Asteroids, Comets, Meteors 1993}, eds. A.~Milani \etal, Kluwer Academic Publishers, Dordrecht, 1994, p.~175
< 
720,724d688
< 
< \bibitem[Wisdom \etal\ (1982)]{wisdom1982}
< {Wisdom, J.} 1982,
< \textit{Astron. J.} 87, 577
< 
