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Universal Gravitation

Date post: 26-Feb-2016
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Universal Gravitation. Recap. You’ve been exposed to basic F g Standing on Earth, you experience gravitational force. Jumping, you still experience it. It slows you down until you reach the peak of your motion, then it pulls you down faster and faster. - PowerPoint PPT Presentation
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Universal Gravitation
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Page 1: Universal Gravitation

Universal Gravitation

Page 2: Universal Gravitation

Recap•You’ve been exposed to basic Fg •Standing on Earth, you experience gravitational

force.• Jumping, you still experience it. It slows you down

until you reach the peak of your motion, then it pulls you down faster and faster.

Page 3: Universal Gravitation

•Gravity provides an acceleration on your body while in the air. (g- the ACCELERATION due to gravity)

•The value for g on Earth is 9.8 m/s2, regardless of mass. Regardless of mass. Regardless of mass. Regardless of mass? Yes, regardless of mass.

Page 4: Universal Gravitation

Kepler’s 3 Laws• Johannes Kepler: German mathematician and

astronomer.•Developed 3 laws to explain the planetary orbits

about the Sun.•Developed from years of data collection by his

Danish teacher, Tycho Brahe.

Page 5: Universal Gravitation

Kepler’s 3 Laws

Kepler (German) Brahe (Danish)

Page 6: Universal Gravitation

•Law of Ellipses: the paths of the planets are elliptical in shape, with the center of the sun being located at one focus.

•Law of Equal Areas: an imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal time intervals.

•Law of Harmonies: the ratio of the squares of the periods of any 2 planets is equal to the ratio of the cubes of their avg distances from the sun.

Page 7: Universal Gravitation

•They provided a what, but not a why•Kepler believed the planets were “magnetically”

driven by the sun to orbit elliptically.• Isaac Newton hates not having explanations for

things.

Page 8: Universal Gravitation

•Newton wanted to know why the planets orbit the sun elliptically, but the moon has a circular orbit around the Earth.

•And, both circular and elliptical paths were departures from inertial straight line paths.

•What force is causing them to change direction (accelerate)?

Page 9: Universal Gravitation

•According to legend, it all came together for him in an apple orchard at age 24.

•Newton was able to relate the cause for heavenly motion (the orbit of the moon around the Earth) to the cause for Earthly motion (why things fall).

Page 10: Universal Gravitation

Newton’s Mountain

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Page 12: Universal Gravitation

•His dilemma now was to explain why the moon doesn’t come crashing in.

•He needed to show that gravity became weaker over a distance.

Page 13: Universal Gravitation

•Newton knew things on Earth accelerated at 9.8 m/s2.• It had also been measured that the moon accelerates

towards Earth at 0.00272 m/s2.•Why does the moon accelerate at a MUCH slower

rate?

Page 14: Universal Gravitation

•Solved the riddle by looking at the distance from the center of the Earth.

Page 15: Universal Gravitation

•The moon is 60x further from the center of the Earth. It also experiences 3600x less gravitational acceleration.

• (602 = 3600).•Gravity must follow an inverse square law.

Page 16: Universal Gravitation
Page 17: Universal Gravitation

•The force of gravity is inversely related to the square of the distance.

• I.e., the further away you get, the less gravitational force.

Page 18: Universal Gravitation

Law of Universal Gravitation•Newton goes into the HOF, not for discovering

gravity, but for realizing it’s UNIVERSAL.•All objects have a gravitational force of attraction

between them.

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•Lord Henry Cavendish discovered the value of the constant G (universal gravitation constant) in 1798, nearly 100 years after Newton.

•G = 6.673 x 10-11 Nm2/kg2

Page 20: Universal Gravitation

Fg = Gm1m2

d2

Page 21: Universal Gravitation

Example 1•Determine the force of gravitational attraction

between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is standing at sea level, a distance of 6.38 x 106 m from earth's center.

Page 22: Universal Gravitation

•Determine the force of gravitational attraction between the earth (m = 5.98 x 1024 kg) and a 70-kg physics student if the student is in an airplane at 40000 feet above earth's surface. This would place the student a distance of 6.39 x 106 m from earth's center.

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•We know that Fg = mg.•We know that Fg = Gm1m2

d2

So, m1g = Gm1m2

d2

Page 25: Universal Gravitation

g = Gmplanet

R2

Where R is the radius of the planet

Page 26: Universal Gravitation

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