Satellite Motion
Chapter 4
Joseph F. Alward, PhD
Department of Physics
University of the Pacific
| Gravity and Satellite Motion Chapter 4 Joseph F. Alward, PhD Department of Physics University of the Pacific |
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Orbital Motion and Gravitation
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The moon's forward velocity v allows it to maintain the same distance, even though it's constantly being pulled toward the earth. |
Law of Universal Gravitation
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Isaac Newton: F = G m1m2 / d2 G = 6.67 x 10-11 N-m2/kg2 |
Calculating the Mass
of the Earth
| Radius of Earth = 6.4 x 106 m
Weight of one kilogram = 9.8 N |
Inverse Square Law
 Gravitational force falls off according to the square of the distance. |
Weight versus Distance from Earth's Center
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Weight on the Top of Mountains
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Objects weigh less on top of mountains for two reasons.
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Apparent Weight in an Elevator
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The weight of an object is the force of the earth's (or other large object's) pull. Whether falling or stationary, one's weight is the same.
Apparent weight is the
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Real and Apparent Weight
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Both of these persons' apparent weight is zero.
Which one has actual |
Space Station
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Space station and its occupants are both falling toward the earth as they move around it. Do the occupants feel as though they have weight? Do they have weight? How could gravity be simulated? |
Projectile Motion
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Horizontal and Vertical Motion of a Projectile
 Distance fallen below broken line is the same distance the object would have fallen if it had been fired horizontally. |
d = 1/2 g t2 g = 10 m/s2 (approximately) d = 5 t2 (approximately)
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Vertical and Horizontal Velocities
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Does the vertical velocity change? If so, why, and by how much? ---------------------------------------- Does the horizontal velocity change? If so, why, and by how much? |
Vertical and Horizontal Velocities
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Range versus Firing Angle
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Two angles whose sum is 90 degrees each give the same range.
At what angle is |
Projectile
Motion Applet
| Projectile Motion |
Maximum Range
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Maximum range is achieved if the projectile is fired at an angle of 45 degrees with respect to the horizontal. |
Effect of Air Resistance on Projectile Motion
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Projectile doesn't travel as high or as far horizontally as it would have if there were no air resistance |
Travel Time
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Ignoring air resistance, the cannon ball loses 10 m/s of upward speed each second. On its way down, the ball picks up 10 m/s of downward speed with each passing second. ------------------------------------- Time up = Time down |
Projectile Motion Problems
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Throwing a Rock Around the World
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The earth curves down 5 meters every 8000 meters (5 miles) traveled along its surface. With what horizontal speed must the ball be thrown in order to orbit the earth? ----------------------- Would the speed have to be greater, or less, at higher altitudes? |
18,000 Miles per Hour
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One meter = 3.28 ft One mile = 5280 ft One hour = 3600 s -------------------------------------------------------------------
If the rock is thrown with a speed of 8000 m/s
5 miles/s = 18,000 miles/hr |
| Projectile
Motion. Horizontal/Vertical Motion demonstrated simultaneously; dozen projectiles fired at same time |
Earth Orbits the Sun
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What would happen to the Earth if its tangential velocity were reduced to zero? |
Elliptical Orbits
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The two tacks represent the two different foci of the ellipse.
Where would the two |
Elliptical Orbits
 The sun is one of the foci of the ellliptical orbits of the planets. |
Elliptical Orbits
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Launching a Satellite
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For a near-Earth orbiting satellite, rocket reaches desired altitude, and turns right, reaching orbital speed. |
Energy Conservation in Satellite Motion
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When the satellite is closest to the Earth, its speed is greatest. |
Escape Speed: Pioneer 10
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Escape speed from the Earth is about 22,000 miles/hour, or 11.2 km/s.
Escaping the Sun requires |
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