Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Mathematica® Notebook Index

Chapter 1 : Structure of the Solar System

Section 1.3

Figure 1.2 (Kepler's laws)

Section 1.5

Section 1.5 (Orbital period fits for random sets of Uranian satellites)
Figure 1.3 (Orbital period fit for actual Uranian satellites)

Section 1.7

Figure 1.8 (Satellites close to exact commensurability)

Chapter 2 : The Two-Body Problem

Section 2.3

Figure 2.4 (Conic sections)

Section 2.5

Section 2.5 (Commonly used series expansions for elliptical motion)

Section 2.6

Section 2.6 (Guiding centre approximation)
Figure 2.10 (Guiding centre motion)

Section 2.8

Figure 2.14 (The orbit in three dimensions)
Figure 2.15 (Planetary orbits and positions)

Chapter 3 : The Restricted Three-Body Problem

Section 3.6

Section 3.6 (Derivation of series for location of collinear points)
Figure 3.7 (Equilibrium points and critical curves)
Figure 3.8 (Equilibrium points on Jacobi "surface")
Figure 3.10 (Radial distance to equilibrium points as function of mass)

Section 3.7

Section 3.7 (Stability calculation for L₁ and L₄ points)
Figure 3.11 (Initial velocity vectors on two zero velocity curves)
Figure 3.12 (Roots of characteristic equation for L₁ point)
Figure 3.13 (Roots of characteristic equation for L₄ and L₅ points)

Section 3.8

Section 3.8 (Analytical solution in the vicinity of L₄)

Section 3.9

Figure 3.16 (Numerical solution for two tadpole orbits)
Figure 3.17 (Numerical solution for two horseshoe orbits)

Section 3.10

Figure 3.22 (H(theta) plot for angular extent of tadpole orbit)

Section 3.12

Figure 3.27 (Minimum angular separation as function of total mass)

Section 3.13

Figure 3.28 (Zero velocity curves in Hill's problem)
Figure 3.30 (Particle trajectories in Hill's problem)

Section 3.14

Figure 3.32 (Four types of stability around L₄)

Chapter 4 : Tides, Rotation and Shape

Section 4.6

Section 4.6 (Darwin-Radau relation)

Section 4.7

Figure 4.10 (Rotational and tidal distortion)

Section 4.14

Figure 4.19 (Evolution of the Moon's orbit)

Chapter 5 : Spin-Orbit Coupling

Section 5.4

Figure 5.9 (Rotation of Mercury around its orbit)
Figure 5.10a (The p=3/2 spin-orbit resonance)
Figure 5.11 (The p=1/2 spin-orbit resonance)
Figure 5.12 (The p=4/3 spin-orbit resonance)
Figure 5.13 (The p=0 spin-orbit resonance)

Chapter 6 : The Disturbing Function

Section 6.5

Section 6.5 (Derivation of second-order expansion of the disturbing function)

Section 6.10

Section 6.10.1 (Coefficients for 3:1 Jovian resonance)
Section 6.10.2 (Coefficient for one term for 18:7 Jovian resonance)

Section 6.11

Section 6.11 (Rates of change of pericentre and node due to oblateness)

Chapter 7 : Secular Perturbations

Section 7.3

Section 7.3 (Secular perturbation theory for Jupiter and Saturn)

Section 7.5

Section 7.5 (Forced elements for objects perturbed by Jupiter and Saturn)

Section 7.8

Section 7.8 (Brouwer and van Woerkom's secular theory)

Section 7.10

Figure 7.12 (Free precession rates in the inner and outer solar system)
Figure 7.16 (Forced elements in the vicinity of the asteroid belt)

Chapter 8 : Resonant Perturbations

Section 8.2

Figures 8.1-3 (Orbital path in the rotating frame at the 2:1 resonance)
Figures 8.4ac (Orbital paths for first-order resonances)
Figures 8.4bd (Orbital paths for second-order resonances)

Section 8.5

Table 8.5 (Coefficients for first- and second-order resonances)

Section 8.7

Figure 8.7 (Widths of first- and second-order resonances)

Section 8.8

Figure 8.8 (Equilibrium point locations for resonances)

Section 8.8.1

Figures 8.9-11 (Resonance plots for first-order resonances)

Section 8.8.2

Figure 8.12 (Resonance plots for second-order resonances)

Section 8.8.3

Figure 8.13 (Resonance plots for third-order resonances)

Section 8.8.4

Figures 8.14a-c (Mixed resonance plots for c=1)
Figures 8.14d-f (Mixed resonance plots for c=10)
Figures 8.14g-i (Mixed resonance plots for c=20)
Figure 8.15 (Mixed resonance plots for c=-5)

Section 8.12

Figure 8.22 (Resonance encounter for increasing delta)
Figure 8.23 (Resonance encounter for increasing delta - capture/passage)
Figure 8.24 (Resonance encounter for decreasing delta)
Figures 8.25-28 (Capture probabilities for resonances)

Section 8.15

Figure 8.29a (Orbital evolution in the Saturnian system)
Figure 8.29b (Orbital evolution in the inner Uranian system)

Section 8.17

Figure 8.30 (Conjunctions between Io, Europe and Ganymede)

Chapter 9 : Chaos and Long-Term Evolution

Section 9.6

Figure 9.23 (Chaos and the encounter map)

Section 9.9

Figures 9.33-34 (The Neptune-Pluto system)
Figure 9.35 (The Neptune-Pluto 3:2 resonance)

Chapter 10 : Planetary Rings

Section 10.2

Figure 10.1 (Locations of planetary rings and satellites)

Section 10.3.1

Figure 10.7 (Libration at the 3:2 corotation resonance)

Section 10.3.2

Figure 10.8 (Streamline paths for m=0, 1, 2 and 7)
Figure 10.9 (Streamline paths at the 7:6 Lindblad resonance)
Figure 10.10 (Coefficients for Lindblad resonances)

Section 10.3.4

Table 10.1 (Locations of ring resonances with Mimas)

Section 10.4

Figure 10.11 (Density waves)
Figure 10.12 (Bending waves)

Section 10.5.2

Figure 10.15 (Ring wave intersections)

Section 10.5.4

Figure 10.19 (Precessional pinch)

Section 10.7

Figure 10.25 (Orbits in the F ring system)