More About Orbits

1. More About Orbits Orbits can be ellipses, parabolas or hyperbolas

2. All Orbit Shapes are Conic Sections

3. Why Do We Call it a “Focus?”

4. Escape Velocity • Every object has an escape velocity • Anything launched with less than escape velocity will fall back • Anything launched with greater than escape velocity will keep going and never return • Escape velocity from Earth’s surface is 11 km/sec or 25,000 miles per hour. • For anything in a circular orbit, escape velocity is 1.4 times its orbital velocity.

5. Orbits and Escape Velocity • Anything moving with less than escape velocity will travel in an elliptical orbit • Anything moving exactly with escape velocity will travel in a parabolic orbit (Think of it as an infinitely long ellipse) • Anything moving with more than escape velocity will travel in a hyperbolic orbit

6. Orbits and Escape Velocity

7. What About Three Objects? • Kepler and Newton solved the problem of one object orbiting about another • Are there formulas for three interacting bodies? • Bottom Line: No (After much effort) • Except for a few special cases...

8. The Lagrangian Points

9. Gravity Assist • Gravity assist happens naturally. It can capture comets into short-period orbits or expel them from the Solar System • We use gravity assist to speed up, slow down, or redirect spacecraft • The Cassini mission to Saturn was launched with only one-fifth the energy needed to reach Saturn

10. We’re Pretty Good At It

11. In Gravity Assist, a Massive Object Causes a less Massive One to Speed Up or Slow Down

12. Gravity Assist Can Speed Objects Up

19. Gravity Assist Can Slow Things Down