Conceptual Physical Science 6 th Edition

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2 Conceptual Physical Science 6 th Edition Chapter 4: GRAVITY, PROJECTILES, AND SATELLITES Sections 4.1, only Pearson Education, Inc. This lecture will help you understand: The Universal Law of Gravity The Inverse-Square Law: Gravity and Distance Weight and Weightlessness Universal Gravitation Projectile Motion Fast-Moving Projectiles Satellites Circular Satellite Orbits Elliptical Orbits Escape Speed 4 2

The Legend of the Falling Apple Newton was not the first to discover gravity.

Legend Newton, sitting under an apple tree, realized that the force between Earth and the apple is the same

6 The Universal Law of Gravity Newton s Law of Universal Gravitation Every body in the universe attracts

3 The Legend of the Falling Apple Newton was not the first to discover gravity. Newton discovered that gravity is universal. Legend Newton, sitting under an apple tree, realized that the force between Earth and the apple is the same as that between moons and planets and everything else. 6 The Universal Law of Gravity Newton s Law of Universal Gravitation Every body in the universe attracts every other body with a mutually attracting force. For two bodies, this force is directly proportional to the product of their masses and inversely proportional to the square of the distance separating them, F = G m 1 m 2 d 2 7 G = N m 2 /kg 2 3

4 Newton s Law of Universal Gravity F = G m 1 m 2 d 2 The greater m 1 and m 2 the greater the force of attraction between them. The greater the distance of separation d, the weaker is the force of attraction weaker as the inverse square of the distance between their centers. 8 The Universal Law of Gravity Newton discovered that gravity is universal. Every mass pulls on every other mass. 9 4

5 Example If the mass of Earth somehow increased with no change in radius, your weight would A) increase also. B) decrease. C) remain the same. F = G m 1 m 2 d 2 10 Example An object is placed exactly halfway between the Earth and the Moon. The object will fall toward the A) Earth. B) Moon. C) neither F = G m 1 m 2 d

6 F = G m 1 m 2 d 2 Example When the distance between two stars decreases by half, the force between them A) decreases by one-quarter. B) decreases by one-half. C) increases to twice as much. D) increases to four times as much. E) stays the same. d d Projectile Motion Projectile is any object that moves through the air or through space under the influence of gravity. Curved path of projectile (parabola) Example: A stone thrown horizontally curves downward due to gravity. 13 6

7 Parabola Projectile Motion Note that only the vertical velocity component changes with time. The horizontal component remains constant. 14 Fired Horizontally vs. Dropped Vertical motions occur in parallel Arrow has an additional horizontal motion component They strike the ground at the same time! 15 7

Projectile Motion A rock is thrown upward at 50 with respect to the horizontal. As it rises, its horizontal component of velocity A) increases. B) remains unchanged. C) decreases.

8 Projectile Motion A rock is thrown upward at 50 with respect to the horizontal. As it rises, its horizontal component of velocity A) increases. B) remains unchanged. C) decreases. 16 Fast-Moving Projectiles Satellites The Earth s curvature drops a vertical distance of 5 meters for each 8000 m tangent to the surface. So to orbit Earth, a projectile must travel 8000 m in the time it takes to fall 5 m. 17 8

Fast-Moving Projectiles Satellites Satellite is any projectile moving fast enough to fall

To become an Earth satellite, the projectile's horizontal velocity must be great enough for its

18 Circular Satellite Orbits A payload into orbit requires control over direction of rocket

9 Fast-Moving Projectiles Satellites Satellite is any projectile moving fast enough to fall continually around the Earth. To become an Earth satellite, the projectile's horizontal velocity must be great enough for its trajectory to match Earth's curvature. 18 Circular Satellite Orbits A payload into orbit requires control over direction of rocket initially, rocket is fired vertically, then tipped once above the atmosphere, the rocket is aimed horizontally speed of rocket payload is given a final thrust to orbital speed of 8 km/s to fall around Earth and become an Earth satellite Orbit: 8-11Km/sec 22 9

to be above air drag. (Are they above Earth s field? NO!

10 Circular Satellite Orbits Positioning beyond Earth s atmosphere, where air resistance is almost totally absent gravitational Example: Space shuttles are launched to altitudes of 150 km or more, to be above air drag. (Are they above Earth s field? NO!) 23 Earth Satellites Artificial satellites must travel more than 320 km above Earth Must travel at least 8 km/s to maintain orbit Example - GPS 24 10

Elliptical Orbits Elliptical orbit speed of satellite varies initially, if speed is greater than needed for circular orbit, satellite overshoots a circular path and moves away from Earth satellite

11 Elliptical Orbits Elliptical orbit speed of satellite varies initially, if speed is greater than needed for circular orbit, satellite overshoots a circular path and moves away from Earth satellite loses speed and then regains it as it falls back toward Earth it rejoins its original path with the same speed it had initially procedure is repeated 25 Escape Speed Escape speed the initial speed that an object must reach to escape gravitational influence of Earth 11.2 kilometers per second from Earth s surface Escape velocity is escape speed when direction is involved 26 11

Escape Speed First probe to escape the solar system is Pioneer 10, launched from Earth in 1972.

12 Escape Speed First probe to escape the solar system is Pioneer 10, launched from Earth in accomplished by directing the probe into the path of oncoming Jupiter 27 Scientific Method Measurements Aristotle/Galileo Mass/Inertia Speed, velocity and acc. Newton s Laws Exam 1 Review Newton s First Law of Motion and Equilibrium Newton s Second Law of Motion Newton s Third Law of Motion Momentum/Impulse Work/Energy Newton s Law of Universal Gravity, Projectiles and Satellites 28 12

Conceptual Physics Fundamentals

Conceptual Physics Fundamentals Chapter 6: GRAVITY, PROJECTILES, AND SATELLITES This lecture will help you understand: The Universal Law of Gravity The Universal Gravitational Constant, G Gravity and Distance: