Transcript CH10 – Projectile and Satellite Motion

CH10 – Projectile
and Satellite Motion
Satellite Motion
Circular and Elliptical Orbits
Kepler’s Laws
Satellites
Satellites are fast moving projectiles at
great distances (for earth above
atmosphere, not above gravity).
 Satellites fall around other objects—moon
around earth, space station around earth,
earth around sun, etc.
 The speed must be enough to keep the
projectile from falling into the earth, sun,
planet, etc.

Satellites
The earth’s curvature requires a projectile
to be moving about 8,000 m/s.
 This speed would cause most objects to
burn up in earth’s atmosphere, thus
satellites typically orbit above the
atmosphere 150,000 m.
 There still is gravity above the
atmosphere!

Satellites
Objects in space must have the correct
speed, or they get pulled into the sun
(largest gravity)
 This happened a long time ago for most
objects.

Satellite Example
Is the following explanation valid?
Satellites remain in orbit instead of
falling to the Earth because they are
beyond the main pull of Earth’s gravity.
NO!
Satellites remain in orbit because they are
being pulled by gravity!
Circular Orbit


Objects with a circular orbit have a constant
speed which is high enough to fall around the
earth. Mostly only man-made satellites have
very circular orbit.
Geosynchronous satellites
 Communication
satellites are geosynchronous
 Located at about 5.5 x radii above the surface of
earth
 At this location, satellites take 24 hours to complete
their orbit
 They stay above the same point on the earth.
Circular Orbit



“Period” is the time it takes to complete one
orbit.
The higher the orbit  less speed needed 
longer path  therefore, longer period.
Rocket launches—
mostly vertical, then
tipped horizontal and
given “push” for
speed to fall around
the earth.
Elliptical Orbit
When projectiles have velocity > 8,000
m/s, but not fast enough to “get away”,
they will orbit in an oval shape called an
ellipse.
 Parabolic paths are a portion of an ellipse.

Elliptical Orbit

Ellipse is a curve that results when the
sum of the distances from 2 fixed points is
always the same (constant). The 2 points
are each called a focus (foci).
Foci
Elliptical Orbit

Satellites with elliptical orbits will change their
speed (unlike circular). As they approach,
gravity pulls them and speed increases. As they
whip by and pass, gravity will pull back to slow
them down. Closer to planet means faster and
farther away means slower.
Kepler’s Laws
Johannes Kepler
(1571-1630) was a
German astronomer.
 He spent many years
studying our solar
system
 Explain planetary
motion with 3 laws
(but did not
understand gravity)

Kepler’s Laws
First Law:
 Planets
move in elliptical orbits around sun, and sun
is at 1 focus
Second Law:
 [Planets
speed up and slow down during orbit (like
throw up & down)] Using imaginary spokes from the
sun to any planet, the planet will sweep out the same
area in its orbit during a specific amount of time.
Third Law:
 A planet’s
time for 1 revolution (period) is proportional
to the distance away from the sun, specifically, T2 ~ d3
Orbital Review
1.
Why does the force of gravity change the speed of a
satellite in an elliptical orbit?
2.
What is so special about communication satellites?
3.
The period of a satellite (the time it takes for a
complete revolution), depends on what?