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Universal Gravitation Sir Isaac Newton: The Universal Law of Gravitation

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The Falling Apple l Newton reasoned the moon is falling for the same reason the apple falls – they are both pulled by the Earth’s gravity.

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Newton’s Excellent Idea l Now came Newton's truly brilliant insight: if the force of gravity reaches to the top of the highest tree, might it not reach even further; in particular, might it not reach all the way to the orbit of the Moon! Then, the orbit of the Moon about the Earth could be a consequence of the gravitational force, because the acceleration due to gravity could change the velocity of the Moon in just such a way that it followed an orbit around the earth. Source: http://csep10.phys.utk.edu/astr161/lect/history/newtongrav.html

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The Falling Moon l Newton’s First law: –An object (the moon) will remain in motion in a straight line unless acted on by an outside unbalanced force (gravitational attraction) l The force that pulls an apple to the ground also keeps the moon in orbit.

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The Falling Earth l Newton’s theory of gravitation confirmed the Copernican theory of the solar system. l A planets tangential speed allows the planets to orbit the sun without being pulled into it.

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Newton’s law of Universal Gravitation

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The Gravitational Constant Henry Cavendish 1798 He used a device with two objects on a rod that was hung on a wire. These masses were attracted to two larger objects, twisting the rod slightly. The measurement of the masses, distance between them and the torque on the wire allowed G to be determined.

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The Universal Gravitational Constant – A G-thing l G is a constant of proportionality. l The magnitude is the force exerted by two 1-kg masses 1 meter apart. l G = 6.67 x 10 -11 Nm 2 /kg 2

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Weight and Mass

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Gravity and Distance: The Inverse Square Law l A quantity varies as the inverse square of its distance from its source l A localized source spreads evenly throughout the surrounding space.

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The Weight of an Apple?

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Gravity and Orbits l Centripetal acceleration –a c = v 2 /r l Centripetal Force –F c = ma c l The force in circular motion is directed towards the center - centripetal

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Why is the Earth round? l Because of gravitation – earth attracted itself together. l The deviation of a planet from its normal orbit is called a perturbation. It is caused by other planets.

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Reviewing l Objects orbiting around the Earth are actually falling toward Earth but have great enough tangential velocity to avoid hitting the earth. l Everything pulls on everything else with a force that depends on the mass of the objects and distances between them. l Gravitation decreases according to the inverse square law.

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Geosynchronous Orbits

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GPS

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