The effect of Jupiter’s Mass
Growth on Satellite’s Capture
Othon Cabo Winter
Ernesto Vieira Neto
Tadashi Yokoyama
Grupo de Dinâmica Orbital & Planetologia
UNESP - Guaratinguetá and Rio Claro
Acknowledgments: FAPESP, CNPq and CAPES
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.1/22
Satellites
REGULAR
Equatorial : i ≈ 0 (prograde)
Circular: e ≈ 0
close to the planet : a < 100Rplanet
IRREGULAR
Inclined : i >> 0 (many are retrograde)
Elliptic: e >> 0
far from the planet : a >> 100Rplanet
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.2/22
Satellites
REGULAR
Equatorial : i ≈ 0 (prograde)
Circular: e ≈ 0
close to the planet : a < 100Rplanet
==> Formed within a proto-planetary disc
IRREGULAR
Inclined : i >> 0 (many are retrograde)
Elliptic: e >> 0
far from the planet : a >> 100Rplanet
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.2/22
Satellites
REGULAR
Equatorial : i ≈ 0 (prograde)
Circular: e ≈ 0
close to the planet : a < 100Rplanet
==> Formed within a proto-planetary disc
IRREGULAR
Inclined : i >> 0 (many are retrograde)
Elliptic: e >> 0
far from the planet : a >> 100Rplanet
==> Planetesimal captured by the planet
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.2/22
Irregular Satellites
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.3/22
Numerology
Planet Regular Prograde Retrograde
Jupiter
8
7
50
Saturn
19
7
7
Uranus
18
1
8
Neptune
6
3
4
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.4/22
Capture Process
• First Stage:
Temporary Gravitacional Capture
• Second Stage:
Dissipative Effects: conversion of a temporary
capture into a permanent one:
- gaseous drag,
- planetary migration,
- mass variation,
- ...
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.5/22
0.05
0.05
●
L2
y
L1
o
0
0
−0.05
−0.05
−0.1
−0.1
0.8
0.85
0.9
0.95
1
x
1.05
1.1
1.15
1.2
Capture by L1
0.8
L1
0.85
L2
●
0.9
0.95
o
0.1
o
0.1
o
y
Temporary Capture
1
x
1.05
1.1
1.15
1.2
Capture by L2
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.6/22
Mass Variation Effect
Planet with
decreasing mass
Particle’s
Orbital
Radius
Escape
Radius
Gravitational
Capture
Radius
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.7/22
Escape/Capture Condition
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.8/22
Evolution of the semi-major axis
Jeans Relation
initial orbit: a = 100 JR e = 0.0
500
initial orbit: a = 100 Jupiter radius e = 0.1
600
semi-axes
Jeans fit
500
a (Jupiter radius)
400
a (JR)
300
200
100
0
-100
10
400
300
200
100
20
30
40
50
60
70
80
Jupiter mass (%)
Prograde
90
100
0
10
20
30
40
50
60
70
80
90
100
Jupiter mass (%)
Retrograde
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.9/22
Escape/Capture Time
103 years
-
Prograde
percent of Jupiter mass
0.5
100
90
0.4
eccentricity
80
0.3
70
60
0.2
50
0.1
40
0
30
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.10/22
Escape/Capture Time
104 years
-
Prograde
percent of Jupiter mass
0.5
100
90
0.4
eccentricity
80
0.3
70
60
0.2
50
0.1
40
0
30
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.11/22
Escape/Capture Time
105 years
-
Prograde
percent of Jupiter mass
0.5
100
90
0.4
eccentricity
80
0.3
70
60
0.2
50
0.1
40
0
30
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.12/22
Escape/Capture Time
–
M (a, e) = k0 + k1 a + k2 e + k3 a2
Prograde
percent of Jupiter mass
0.5
100
90
0.4
eccentricity
80
0.3
70
60
0.2
50
0.1
40
0
30
100
150
200
250
300
semi-major axes
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.13/22
Escape/Capture Condition - PROGRADE
initial eccentricity = 0.0
initial eccentricity = 0.2
1000
800
radial distance (Jupiter radius)
initial semi-major axes
100
200
300
80% RH
45% RH
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
initial semi-major axes
100
200
300
80% RH
45% RH
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
initial eccentricity = 0.4
1000
radial distance (Jupiter radius)
radial distance (Jupiter radius)
1000
initial semi-major axes
100
200
300
80% RH
45% RH
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.14/22
Escape/Capture Time
103 years
-
Retrograde
percent of Jupiter mass
0.5
100
90
eccentricity
0.4
80
70
0.3
60
50
0.2
40
30
0.1
20
0
10
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.15/22
Escape/Capture Time
104 years
-
Retrograde
percent of Jupiter mass
0.5
100
90
eccentricity
0.4
80
70
0.3
60
50
0.2
40
30
0.1
20
0
10
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.16/22
Escape/Capture Time
105 years
-
Retrograde
percent of Jupiter mass
0.5
100
90
eccentricity
0.4
80
70
0.3
60
50
0.2
40
30
0.1
20
0
10
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.17/22
Escape/Capture Time
M (a, e) = k0 + k1 a + k2 e + k3 a2 + k4 e2 Retrograde
percent of Jupiter mass
0.5
100
90
eccentricity
0.4
80
70
0.3
60
50
0.2
40
30
0.1
20
0
10
100
150
200
250
300
semi-major axis
350
400
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.18/22
Escape/Capture Condition -RETROGRADE
initial eccentricity = 0.1
initial eccentricity = 0.25
1000
radial distance (Jupiter radius)
initial semi-major axes
100
225
350
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
initial semi-major axes
100
225
350
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
initial eccentricity = 0.4
1000
radial distance (Jupiter radius)
radial distance (Jupiter radius)
1000
initial semi-major axes
100
225
350
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.19/22
Prograde versus Retrograde
percent of Jupiter mass
0.5
percent of Jupiter mass
100
0.5
100
90
90
0.4
0.4
80
0.3
eccentricity
eccentricity
80
70
60
0.2
70
0.3
60
50
0.2
40
50
0.1
30
0.1
40
0
20
0
30
100
150
200
250
300
semi-major axis
350
400
10
100
150
initial eccentricity = 0.0
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
350
400
initial eccentricity = 0.1
1000
initial semi-major axes
100
200
300
80% RH
45% RH
radial distance (Jupiter radius)
radial distance (Jupiter radius)
1000
200
250
300
semi-major axis
80
90
100
initial semi-major axes
100
225
350
800
600
400
200
0
10
20
30
40
50
60
70
Jupiter mass (%)
80
90
100
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.20/22
Prograde versus Retrograde
Prograde
Vplanet
Vsat
Vsat
Sun
e≠0
Jupiter
e=0
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.21/22
Prograde versus Retrograde
Retrograde
Vplanet
Vsat
Vsat
Jupiter
Sun
e≠0
e=0
The effect of Jupiter’s Mass Growth on Satellite’s Capture – p.22/22