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More About Orbits
Orbits can be ellipses, parabolas or hyperbolas
All Orbit Shapes are Conic Sections
Why Do We Call it a “Focus?”
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.
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
Orbits and Escape Velocity
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...
The Lagrangian
Points
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
We’re Pretty Good At It
In Gravity Assist, a Massive Object Causes a less Massive One
to Speed Up or Slow Down
Gravity Assist Can Speed Objects Up
Gravity Assist Can Slow Things Down