Integrated Science
Projectile and Satelitte Motion
Projectile Motion
• Any object projected by any means that
continues in motion is called a projectile.
• A free falling object gains 10 m/s during each
second it falls.
• This acceleration is due to gravity 10 m/s2
• If an object falls from rest it’s speed at the
end of 1 second is 10 m/s.
• At the end of 2 seconds the speed is 20 m/s
Projectile Motion
• The falling stone gains a
speed of 10 m/s each
second. Fill in the
speedometer readings
for the times 3 & 4
seconds.
• There is an error for the
2 second reading.
Projectile Motion
• Although the change in speed is the same
each second. The distance of fall keeps
increasing for the object.
• If there was no gravity and you threw a
stone horizontally after each second the
stone would be the same distance apart.
• The reason because there is no force
acting on the stone.
• There
is no difference
in the spacing of a
object thrown
horizontally (if there
was no gravity).
•The initial force of
throwing the ball is the
only force acting on
the ball.
Projectile Motion
• With gravity a stone falls following a
curved path.
• This curve is because of two kinds of
motion occurring at the same time.
• There is vertical motion and horizontal
motion.
• The curve is called a parabola.
• The vertical path
(dashed line) is for a
stone dropped from at
rest. The horizontal
path (dashed line)
would occur with no
gravity. The solid line
shows the path that
results from both the
vertical and horizontal
motions.
Projectile Motion
A.
B.
Their masses are different, but the blue and green balls
fall at the same rate.
The yellow ball is a projectile, following a curved path.
A.
Their masses are different, but the blue and green balls fall at the
same rate.
Why do they fall act the same rate, even though the blue
and green balls have different masses?
• A stone thrown at an
upward angle would
follow the dashed line
in the absence of
gravity. Because of
gravity, it falls beneath
this line and describes
the parabola shown by
the solid curve.
• Stone thrown at a
downward angle
follows a somewhat
different parabola.
• The velocity of the ball
(light blue vector) has
vertical and horizontal
components. The
vertical component
relates to how high
the ball will go. The
horizontal component
relates to the
horizontal range of the
ball.
• The horizontal and
vertical components
are completely
independent of each
other. They act as if
the other didn’t exist.
• The combined
effects produce the
curved path of
projectiles.
• The velocity of a projectile at various points. Note
that the vertical component changes while the
horizontal component is the same everywhere.
• No horizontal force exists to change the horizontal
component. (assuming negligible air drag).
Concept Check
1.
2.
At what part of its trajectory does a projectile have minimum speed?
A tossed ball changes speed along its parabolic path. When the sun is
directly overhead, does the shadow of the ball across the field also
change speed? Answers on Click!
1. The minimum speed is reached at the top of its trajectory.
2. No, the shadow moves at a constant velocity due to the horizontal
component of the ball velocity.
Projectile Altitude and Range
We see the paths of several projectiles
in the absence of air drag. All have the
same initial speed, but different launch
angles. Notice they reach different
altitudes and some have different ranges
(distance traveled horizontally)
Projectile Altitude and Range
We see that the same range is obtained
from angles that add to 90o. The amount
of time in the air is the only difference.
Projectile Altitude and Range
• Without air drag speed lost
while going up equals speed
gained while coming down; time
going up equals time coming
down. (It takes 4 seconds to go
up and 4 seconds to come
down)
The effect of air drag
on Projectiles
• Air drag is a
major factor
for high
speed
projectiles.
• The result is
both range
and altitude
are less.
The effect of air drag
on Projectiles
• A baseball
could be hit
about 6 times
the ideal range
on the moon
because of no
air drag and
gravity is 1/6
that of earth.
Satellites
• If a cannon fires a cannonball so fast that
its curved path matches the curvature of
the earth, (without air drag) it would
become a satellite.
• Any satellite is simply an object that is
moving fast enough to continually fall
around the earth
• Throw a stone any speed and 1 second later
it falls 5 meters below where it would have
been if there was no gravity.
• To be a satellite the objects horizontal
velocity must be great enough for its falling
distance to match the curvature of the earth.
• The earth’s curvature drops a vertical distance of 5
meters for each 8000 meters tangent. (not to
scale)
• If you were floating in a calm ocean only be able to
see a 5 m mast on ship that was 8000 meters
(8km) away. We live on a round earth.
Earth Satellites
• A satellite is a projectile that is traveling
fast enough that covers a horizontal
distance of 8km during 1 second.
• This speed would allow it to follow the
curvature of the earth.
• The speed is 29,000 km/h or 18,000 mi/h
Earth Satellites
• At these high speeds atmospheric friction
would incinerate a projectile. This is what
occurs with meteorites the size of sand
particles, (falling stars).
• This is the reason satellites like the space
shuttle are launched to altitudes of 150 km
to get above the atmosphere.
Earth Satellites
• A common misconception is that satellites in
orbit are free from gravity. The truth is
that the force of gravity is nearly as great on
the surface of the earth as it is 150 km
above the surface. (Inverse Square Law)
• If there was no gravity, motion would be a
straight line, instead of curving around the
earth.
Earth Satellites
• High altitude puts satellites above the
atmosphere but not above the pull of gravity.
• The reason things appear to be “weightless”
is because the shuttle and everything in it
are falling at the same rate, so there is no
support force.
Earth Satellites
Newton thought if a cannon was
fired fast enough a cannonball
would circle the earth and go
into orbit.
Earth Satellites
• Why don’t planets crash into the sun?
• What would happen to planets if their
tangential velocity were zero?
• For a satellite close to the earth the time it
takes to complete an orbit is about 90
minutes.
Earth Satellites
• Communication satellites have altitude of 5.5
Earth radii and have a period of 24 hours.
• This means they stay above the same point
on the earth. Geosynchronous orbit.
• The moon is farther out its orbit period is 27.3
days. The higher the altitude the less its
speed and the longer its period.
Elliptical Orbits
• If a payload above the drag of the
atmosphere is given a horizontal speed
somewhat greater than 8 km/s, it will
overshoot a circular path and trace an
elliptical orbit.
• An ellipse is a specific curve. It is oval
shaped which any point has the sum of
distances between any two points (foci).
Elliptical Orbits
• If the foci are close together the ellipse
resembles more like circle.
• Unlike the constant speed of a satellite in a
circular orbit, speed varies in a elliptical orbit.
Elliptical Orbits
• For a satellite in elliptical orbit, half the time it
moves away from the earth and half the time
it moves towards the earth.
• When it moves away (against gravity) it
slows down, when it moves towards earth
(with gravity) it gains speed.
• The same amount of speed lost is regained,
like a stone thrown upwards.
Elliptical Orbits
Elliptical Orbits
• The orbital speed of a
planet varies so that a
line joining the Sun and
the planet will sweep over
equal areas in equal time
intervals.
• This means that a planet
moves faster closer to the
Sun and slower farther
away.
Escape Speed
• “What goes up must come down” isn’t always
true.
• “What goes up may come down” is more
accurate because there is a critical speed at
which a projectile can outrun gravity and
escape the Earth.
• This speed is called escape velocity.
Escape Speed
• From the surface of the earth escape velocity
is 11.2 km/s (Roughly 25,000 mph)
• Escape speed from the sun is 620 km/s
(Roughly 385.25 miles per second)
• At earth’s distance from the sun to escape
the sun that drops to 42.5 km/s
Escape Speed
• If a satellite is moving greater than 11.2
km/s but slower than 42.5 km/s it will
escape Earth but not the sun and thus will
take up an orbit (fall around) the sun.
Several positions of a satellite in an elliptical orbit are shown. At which position does
the satellite have the greatest ______? Some have Multiple Answers!!!
1.
2.
3.
4.
Speed?
Velocity?
Mass?
Gravitational attraction to the Earth?
5.
6.
7.
8.
Kinetic Energy?
Potential Energy?
Total Energy?
Acceleration (a=Force/mass)
Answers!!
1. Speed? A
2. Velocity? A
3. Mass? A,B,C,D
4. Gravitational attraction to the Earth? A
5. Kinetic Energy? A
6. Potential Energy? C
7. Total Energy? A,B,C,D
8. Acceleration (a=Force/mass) A
Several positions of a satellite in an elliptical orbit are shown. At which position does
the satellite have the greatest ______? Some have Multiple Answers!!!
1.
2.
3.
4.
Speed?
Velocity?
Mass?
Gravitational attraction to the Earth?
5.
6.
7.
8.
Kinetic Energy?
Potential Energy?
Total Energy?
Acceleration (a=Force/mass)