List of Figures

• 1.1. A snapshot of the globular cluster M15
• 1.2. An image of the central region of our galaxy
• 1.3. The Orion Nebula
• 1.4. The open star cluster M67
• 3.1. Two-body orbit with a forward-Euler integrator, time step $dt = 0.01$
• 3.2. Two-body orbit with a forward-Euler integrator, time step $dt = 0.001$
• 3.3. Two-body orbit with a forward-Euler integrator, time step $dt = 0.0001$
• 3.4. Two-body orbit with a forward-Euler integrator, time step $dt = 0.00001$
• 3.5. Two-body orbit with a forward-Euler integrator, time step $dt = 0.000001$
• 4.1. Two-body orbit with a leapfrog integrator, time step $dt = 0.01$
• 4.2. Two-body orbit with a leapfrog integrator, time step $dt = 0.001$
• 5.1. Three stars on a circle, leapfrog, $dt = 0.01$, $t_{end} = 10$
• 5.2. Three stars on a circle, leapfrog, $dt = 0.01$, $t_{end} = 100$
• 5.3. Three stars on a circle, leapfrog, $dt = 0.001$, $t_{end} = 100$
• 5.4. Three stars on a circle, leapfrog, $dt = 0.0001$, $t_{end} = 100$
• 5.5. Three stars on a circle, leapfrog, $dt = 0.00001$, $t_{end} = 100$
• 5.6. Three stars on a circle, leapfrog, $dt = 0.000001$, $t_{end} = 100$
• 5.7. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.01$, $t_{end} = 10$
• 5.8. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.01$, $t_{end} = 100$
• 5.9. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.001$, $t_{end} = 100$
• 5.10. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.0001$, $t_{end} = 100$
• 5.11. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.00001$, $t_{end} = 100$
• 5.12. Three stars on a circle, leapfrog, $dv_{init}=0.0001$, $dt = 0.00001$, $t_{end} = 120$
• 5.13. Three stars on a figure-8 orbit, $dt = 0.01$, $t_{end} = 100$
• 5.14. Three stars on a figure-8 orbit, $dv_{init}=0.0001$, $dt = 0.001$, $t_{end} = 100$
• 6.1. Three stars on a circle, Hermite, $dv_{init}=0.0001$, $dt = 0.01$, $t_{end} = 100$
• 6.2. Three stars on a circle, Hermite, $dv_{init}=0.0001$, $dt = 0.001$, $t_{end} = 100$
• 6.3. Three stars on a circle, Hermite, $dv_{init}=0.0001$, $dt = 0.0001$, $t_{end} = 100$
• 6.4. Three stars on a figure-8 orbit, Hermite, $dv_{init}=0.0001$, $dt = 0.001$, $t_{end} = 100$
• . xy plot of sphere1a output
• . xz plot of sphere1a output
• . xy plot of sphere1a output
• . xz plot of sphere1a output
• . xy plot of sphere1 output
• . xz plot of sphere1 output
• 10.1. 1st frame of movie #1
• 10.2. 2nd frame of movie #1
• 10.3. 3rd frame of movie #1
• 10.4. 4th frame of movie #1
• 10.5. 5th frame of movie #1
• 10.6. 6th frame of movie #1
• 10.7. 7th frame of movie #1
• 10.8. 8th frame of movie #1
• 10.9. 9th frame of movie #1
• 10.10. 10th frame of movie #1
• 10.11. last frame of movie #2