Figure 1: Critical Jacobi constant curve in the planetocentric 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 ), and the left curve corresponds to the case of Jupiter with of its present mass (32 ). | |
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Figure 2: Mass of Jupiter at the moment of escape for satellites with initial conditions in the planetocentric space. Initially Jupiter has its present mass (320 ), 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) 10^{2} yr, c) 10^{3} yr, e) 10^{4} yr, and g) 10^{5} yr. There are also three figures where we adopted the time scale 10^{5} yr, but with orbital inclinations b) , d) , and f) . 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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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 10^{5} years. The initial conditions are: (i) and e=0.0 ( left); (ii) and e=0.2 ( middle); (iii) and e=0.4 ( right). The dashed lines indicate the corresponding values given by Jeans' relation, Eq. (2). | |
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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 10^{5} years. The initial conditions are ( first row), ( second row) and ( third row) with e=0.0 ( first column), e=0.2 ( second column) and e=0.4 ( third column). | |
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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 10^{5} years. The initial conditions are (dark gray), (light gray), and (black) with e=0.0 ( top), e=0.2 ( middle), and e=0.4 ( bottom). The dotted lines correspond to 85% and 45% for the given mass. | |
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Figure 6: Evolution of the resonant argument as a function of the planet's mass for the satellite with initial conditions and e=0. | |
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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 . 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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Figure 8: Schematic diagrams indicating the relative velocities for prograde ( top) and retrograde ( bottom) trajectories. | |
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