All Figures

$\begin{figure} \par\includegraphics[width=5.8cm,clip]{1683f1.eps} \end{figure}$ Figure 1: Critical Jacobi constant curve in the planetocentric $a \times e$ space in opposition at pericenter for a prograde orbit. The curve to the right corresponds to the case of Jupiter with its present mass (320 $M_\oplus$ ), and the left curve corresponds to the case of Jupiter with $10\%$ of its present mass (32 $M_\oplus$ ).
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In the text

$\begin{figure} \par\includegraphics[width=5.6cm,clip]{1683f2a.eps}\hspace*{2mm} ... ....eps}\hspace*{2mm} \includegraphics[width=5.6cm,clip]{1683f2h.eps} \end{figure}$ Figure 2: Mass of Jupiter at the moment of escape for satellites with initial conditions in the planetocentric $a \times e$ space. Initially Jupiter has its present mass (320 $M_\oplus$ ), and the orbits were integrated backward in time with a decreasing mass for Jupiter. In the four figures in the left column, the orbital inclination considered was zero degrees. The time scale for the mass to decrease from its present mass to 10% of its mass was: a) 10² yr, c) 10³ yr, e) 10⁴ yr, and g) 10⁵ yr. There are also three figures where we adopted the time scale 10⁵ yr, but with orbital inclinations b) $20\hbox {$^\circ $ }$ , d) $40\hbox {$^\circ $ }$ , and f) $60\hbox {$^\circ $ }$ . The only figure that is not the result of direct numerical integration is h). It presents contour plots given by Eq. (3).
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In the text

$\begin{figure} \par\includegraphics[width=5cm,clip]{1683f3a.eps}\par\vspace*{3mm... ...s}\par\vspace*{3mm} \includegraphics[width=5cm,clip]{1683f3c.eps} \end{figure}$ Figure 3: Evolution of the semi-major axis of a sample of satellites as a function of Jupiter's mass. This is a representative sample from the simulations with mass variation time scale equal to 10⁵ years. The initial conditions are: (i) $a=100 {R}_{\jupiter}$ and e=0.0 ( left); (ii) $a=200 {R}_{\jupiter}$ and e=0.2 ( middle); (iii) $a=300 {R}_{\jupiter}$ and e=0.4 ( right). The dashed lines indicate the corresponding values given by Jeans' relation, Eq. (2).
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In the text

$\begin{figure} \par\includegraphics[width=4.4cm,clip]{1683f4a.eps}\includegraphi... ...m,clip]{1683f4h.eps}\includegraphics[width=4.4cm,clip]{1683f4i.eps} \end{figure}$ Figure 4: Evolution of the eccentricity of a sample of satellites as a function of Jupiter's mass. This is a representative sample from the simulations with mass variation time scale equal to 10⁵ years. The initial conditions are $a=100 {R}_{\jupiter}$ ( first row), $a=200 {R}_{\jupiter}$ ( second row) and $a=300 {R}_{\jupiter}$ ( third row) with e=0.0 ( first column), e=0.2 ( second column) and e=0.4 ( third column).
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{1683f5a.eps}\par\vspace*{3mm... ...}\par\vspace*{3mm} \includegraphics[width=7cm,clip]{1683f5c.eps} \end{figure}$ Figure 5: Evolution of the orbital radius of a sample of satellites as a function of Jupiter's mass. This is a representative sample from the simulations with mass variation time scale equal to 10⁵ years. The initial conditions are $a=100 {R}_{\jupiter}$ (dark gray), $a=200 {R}_{\jupiter}$ (light gray), and $a=300 {R}_{\jupiter}$ (black) with e=0.0 ( top), e=0.2 ( middle), and e=0.4 ( bottom). The dotted lines correspond to 85% ${R}_{{\rm Hill}}~$ and 45% ${R}_{{\rm Hill}}~$ for the given mass.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1683f6.eps} \end{figure}$ Figure 6: Evolution of the resonant argument $\varpi - \lambda _\odot$ as a function of the planet's mass for the satellite with initial conditions $a=100 {R}_{\jupiter}$ and e=0.
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In the text

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1683f7.eps} \end{figure}$ Figure 7: Diagram of the orbital radius versus Jupiter's mass. The grey area corresponds to the condition where the object would be orbiting the planet as a satellite. The line labeled Jean's Relation gives the evolution of the orbital radius as a function of the mass of Jupiter for an object that would be orbiting as a satellite of Jupiter at the present moment in a circular orbit with $a=100 {R}_{\jupiter}$ . The particle's orbital radius increases while the gravitational capture radius of the planet decreases. The distance at which these two radii coincides is the escape radius.
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{1683f8a.eps} \includegraphics[width=7.8cm,clip]{1683f8b.eps} \end{figure}$ Figure 8: Schematic diagrams indicating the relative velocities for prograde ( top) and retrograde ( bottom) trajectories.
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In the text

$\begin{figure} \par\includegraphics[width=5.8cm,clip]{1683f1.eps} \end{figure}$	Figure 1: Critical Jacobi constant curve in the planetocentric $a \times e$ space in opposition at pericenter for a prograde orbit. The curve to the right corresponds to the case of Jupiter with its present mass (320 $M_\oplus$ ), and the left curve corresponds to the case of Jupiter with $10\%$ of its present mass (32 $M_\oplus$ ).
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$\begin{figure} \par\includegraphics[width=8.8cm,clip]{1683f6.eps} \end{figure}$	Figure 6: Evolution of the resonant argument $\varpi - \lambda _\odot$ as a function of the planet's mass for the satellite with initial conditions $a=100 {R}_{\jupiter}$ and e=0.
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{1683f8a.eps} \includegraphics[width=7.8cm,clip]{1683f8b.eps} \end{figure}$	Figure 8: Schematic diagrams indicating the relative velocities for prograde ( top) and retrograde ( bottom) trajectories.
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