1. Or Stop this Crazy Thing, I have to Go to the Bathroom
Satellite Motion
Or Stop this Crazy Thing, I have to Go to the Bathroom

2. Orbit Speeds and Types Newton’s Mountain argument
Speed in tangential or sideways direction
Smallest orbital speed allows satellite to fall same amount as Earth surface falls away from tangent line
Results in circular orbit
Question: What is the minimum speed needed for a object to orbit the Earth? In which direction is this speed directed? What type of orbit will result?

3. Check Question
How would the minimum orbital speed of a satellite launched from the surface of a planet 2 times the diameter of Earth but the same mass compare to the speed on Earth?
The planet’s minimum orbital speed should be larger than that of Earth
The planet’s minimum orbital speed should be smaller than that of Earth
The planet’s minimal orbital speed should equal that of Earth

4. Circular Orbit 8 km/s on surface neglecting A.R.
Force of Gravity and velocity of satellite are perpendicular implying no work done
Constant v, h, KE, PE, ME, and Force
one vtangent results in circular orbit at each altitude
Question: How do the force of gravity, KE, Peg, ME and velocity vary in a circular orbit? Given a specific altitude, how many speeds will result in a circular orbit?

5. Elliptical Orbit 8 km/s<v<11.2 km/s Force, v, KE max @ perigee
PEg, h apogee
ME constant
Speeds up as moves towards planet, slows as moves away
Gravity does positive work when satellite speeds up, negative when slows down.
Question: How do the force of gravity, KE, Peg, ME and velocity change in an elliptical orbit? What range of values will result in elliptical orbits near the surface of the Earth, neglecting air resistance?

6. Escape Velocity and Path
Vtan>11.2 km/s sideways
Fg not perpendicular to v so work done
Speed, KE and force decrease with distance,
h and PEg increase with distance
Can achieve escape speed with one push or constant force acting on object
Question: What is the escape speed of the Earth? What happens to the force of gravity, KE, PE and velocity as an object moves away from Earth? What is the maximum speed ameteorite, initially stationary will hit the Earth?

7. Check Questions
A rock starts out at rest relative to the Earth. What is the maximum speed it can hit the Earth?
How do asteroids hit the Earth with even a greater speed than above?

8. The Advantage of Altitude
At higher distances from the center of the earth, gravity becomes weaker and the circular, elliptical and escape speeds all become less.
Each altitude still only has one speed resulting in circular motion.
Geostationary orbits
Launching from orbit

9. Trajectory Table speeds will decrease as altitude increases
Question: Near the surface of the Earth what speeds correspond to the following trajectories: a) parabolic b) circular c) elliptical d) hyperbolic As you move away from the surface of the Earth what happens to these speeds?
speeds will decrease as altitude increases
periods will increase as altitude increases
speeds vary directly w/ planet mass and as the inverse square of the planet’s radius

10. Kepler’s Laws for Planets
All planets orbit in ellipses
Only one speed at each distance will result in circle so odds are against it
Planets cover equal areas in equal times
Planet moves faster when closer to sun
R3/T2 = constant for each planet
Planets closer to sun move faster than those further away
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