Transcript Satellite Motion Ch. 14

Satellite Motion
Curvature of Earth
8000 meters
5 meters
The Earth’s surface
drops 5 vertical
meters for every
8000 meters tangent
to its surface
How fast does an object need to go to
become an Earth satellite?
• How far does an object fall in 1 second?
– 5m
• How far along the horizon must you go for the
Earth to curve 5m down?
– 8000m
8km/s for orbital speed
close to Earth!
Circular Orbit
• Does the force of gravity affect the speed of a
bowling ball down an alley?
The period for a
satellite
in
low-Earth
Similarly, the force of gravity of the Earth does
orbit
90in circular
not affect the
speedisofabout
a satellite
orbit.
minutes.
– Why?
– Nope!
•
– 90 degrees between force and direction of
motion…No Work!
At which position does the satellite have its
greatest speed? Why?
C
Same speed
Everywhere
along path!
B
D
A
A close Earth
satellite has a
period of
about 90
minutes.
Kepler’s 1st Law of Planetary Motion
• What if an object above the
atmosphere has a horizontal
speed of more than 8km/s?
– Its path is that of an ellipse
instead a circle.
• Most satellites actually have
elliptical paths!
• Speed varies in elliptical orbit
Johannes Kepler
Ellipse
• Foci- Where the main body of an orbiting pair
lies
At which position does the satellite have its
greatest speed? Why?
Lowest Speed
C
D
B
Greatest Speed
A
Kepler’s 2nd Law of Planetary Motion
Apogee- when
satellite is at
farthest
position
Slower when
far away
Equal areas
swept out over
same amounts
of time time!
Perigee- when
object is at
closest position
Faster closer to
other source of
gravity
Energy Conservation and Satellite Motion
The sum of potential
and kinetic energies of
a satellite remains
constant
PE
KE+
KE+PE
KE+PE
KE+PE
KE+PE
KE+PE
KE+PE
KE+PE
“What goes up must come down”
or does it???
Escape Velocity
• The speed necessary to put a payload
infinitely far from Earth.
• 11.2 km/s horizontally or about 25,000 mph
2GM
vesc 
11.2km/s on Earth
r
Bonus
• List all the planets in our solar system from
lowest escape velocity to highest and explain
how you did it.