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