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Transcript
Universal Gravitation Universal Gravitation • Gravity… • Makes things such as leaves and rain fall • It made the Earth round • Builds up the pressures that kindle every star to shine • But… What is Gravity? Universal Gravitation • GRAVITY • Albert Einstein • Discovered that gravity arises from the “warping” of space and time • The way in which masses communicate with each other • Every mass in the universe reaches out to attract every other one, and every mass feels an attraction from every other one Universal Gravitation • The Falling Apple • Issac Newton • Credited for the idea that gravity extends throughout the universe • According to the popular legend • Idea of gravity occurred to Newton while he was sitting underneath an apple tree on his mother’s farm The Falling Apple • Newton • Understood the concept of inertia developed earlier by Galileo • Without an outside force, moving objects continue to move at constant speed in a straight line • Force is necessary for an object to undergo a change in speed or direction The Falling Apple • The Falling Apple, Newton observed, triggered what was to become one of the most far-reaching generalizations of the human mind • Newton saw the apple fall or perhaps felt it hit his head (Story unclear) • Perhaps he looked up through the apple tree branches and noticed the moon • Newton was probably puzzled by the fact that the moon does not follow a straight-line path, but instead circles the Earth • He knew circular motion is accelerated motion, which requires a force • But what was this force? The Falling Apple • Newton had the insight to see that the moon is falling toward the earth, just as the apple is • He reasoned that the moon is falling for the same reason the apple is • ** They are both pulled by Earth’s GRAVITY The Falling Moon • Newton compared the falling apple with the falling moon • He realized if the moon did not fall, it would move off in a straight line and leave its orbit • The moon must be falling around the earth • He hypothesized that the moon was simply a projectile circling the earth under the attraction of gravity falling toward the earth but with a great enough tangential velocity to avoid hitting the earth Gravitational Force • Earth and many of the other planets in our solar system travel in nearly circular paths around the sun • A centripetal force is keeping them in orbit • This centripetal force that holds the planets in orbit is the same force that pulls an apple towards the ground GRAVITATIONAL FORCE • One of Newton’s greatest discoveries Orbiting Objects are in Free Fall • Newton developed a Thought Experiment • Consider a cannon sitting on a high mountaintop • The path of each cannonball is a parabola • The horizontal distance that each cannonball covers increases as the cannonball’s initial speed increases • Newton realized if the initial speed of the cannonball was great enough, the curvature of Earth will cause the cannonball to continue falling without ever landing ** In other words, it would orbit Earth Orbiting Objects are in Free Fall • The gravitational force between the cannonball and Earth = Centripetal force that keeps the cannonball in orbit • Satellites stay in orbit for the same reason • Similarly, a gravitational attraction between Earth and our sun keeps Earth in its orbit around the sun Newton’s Law of Gravitation • The attractive force of gravity between 2 particles is proportional to the product of their masses and inversely proportional to the square of the distance between them • Gravitational Force Fg = G (m1m2 / r2) Fg = Gravitational Force (Newtons) G = Constant of universal gravitation (G = 6.67 x 10-11 N x m2/ kg2) m1 = Mass of object 1 (kg) m2 = mass of object 2 (kg) r2 = (Distance between the centers of the spherical masses (m)2 Gravitational Force • Gravitational Force • Exists between any two masses, regardless of size • Always attracts objects to one another • The force that the moon exerts on Earth is equal and opposite to the force that Earth exerts on the moon Newton’s Third Law of Motion Gravitational Force • If gravitational force acts between all masses, why doesn’t Earth accelerate up toward a falling apple? • In fact, it does! • But, Earth’s acceleration is so tiny you cannot detect it • Because Earth’s mass is so large and acceleration is inversely proportional to mass, the Earth’s acceleration is negligible • The apple has a much smaller mass and thus a much greater acceleration