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.

A. Their masses are different, but the blue and green balls fall at the same rate.

B. The yellow ball is a projectile, following a curved path.

Projectile Motion

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 Check1. At what part of its trajectory does a projectile have minimum speed?2. 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 RangeWe 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 RangeWe 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.

1. Speed?2. Velocity?3. Mass?4. Gravitational attraction to the Earth?5. Kinetic Energy?

6. Potential Energy?7. Total Energy?8. Acceleration (a=Force/mass)

Several positions of a satellite in an elliptical orbit are shown. At which position does the satellite have the greatest ______? Some have Multiple Answers!!!

Answers on Click!

1. Speed?2. Velocity?3. Mass?4. Gravitational attraction to the Earth?5. Kinetic Energy?

6. Potential Energy?7. Total Energy?8. Acceleration (a=Force/mass)

Several positions of a satellite in an elliptical orbit are shown. At which position does the satellite have the greatest ______? Some have Multiple Answers!!!

Answers!!1. Speed? A2. Velocity? A3. Mass? A,B,C,D4. Gravitational attraction to the Earth? A5. Kinetic Energy? A6. Potential Energy? C7. Total Energy? A,B,C,D8. Acceleration (a=Force/mass) A

Answers on Click!