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Universal�Gravitation

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  • contrast gravitational force from gravitational field.
  • develop an equation that calculates the force of gravity between any two masses.

I can . . .

  • predict the period of an orbiting body based on the distance. �(Kepler's 3rd Law)
  • explain the difference between gravitational mass from inertial mass.

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Johannes Kepler

(1571 – 1630)

1609

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Ellipse (2)

Circle (1)

Earth’s Orbit (0.967)

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Artist: John Vanderbank

Sir Isaac Newton�(1642 – 1727)�1685

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Law of�Universal�Gravitation

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http://www.spiritoftrees.org/folktales/vaughan/harper_in_fairyland.html

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http://www.ou.edu/prometheus/pics/pages/Newton-1687-tp.html

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Distance = 1 2 3 4

Gravity = 1 1/22 1/32 1/42

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How fast must the moon orbit the earth?

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.00136 m

384,000,000 m

384,000,000 m

How fast must the moon orbit the earth?

 

 

 

 

 

 

 

 

How much time must it take to orbit the earth?

 

 

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Period of Revolution = 27 days, 7 hours, 43 minutes, 11.5 seconds

Full Moon to Full Moon = 29 days, 12 hour, 44 minutes, 2.9 seconds

http://www.lapalmamiel.com/tiempo/tiempo.htm

 

 

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Let’s find an�EQUATION �that relates:

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Distance, Mass, and Force of Gravity

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Gravitational Force is�INVERSELY proportional�to the SQUARE of the Distance

 

 

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9.8 Newtons

Gravitational Force is�DIRECTLY proportional to the Mass

 

19.6 Newtons

2 kg

1 kg

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Earth

Moon

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Earth

Venus

 

 

 

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http://www.cornillot.com/images/graphics/Planets/jupiter.jpg

 

 

Jupiter

Venus

 

 

 

 

 

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x

y

1

3

2

6

3

9

y ∝ x

y ≠ x

y = 3·x

 

 

 

 

 

 

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Henry Cavendish�(1731– 1810)�1798

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http://isites.harvard.edu/fs/docs/icb.topic229303.files/images/Cavendish51_800x532.jpg

How could this apparatus be used to measure “G”?

Photo by Clive Grainger

 

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Mass of Earth� �5,975,800,000,000,000,000,000,000 kg�

?

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1 kg

 

 

 

 

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Aristarchus of Samos�(born c. 310 bce—died c. 230 bce) 

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Solar Eclipse

Lunar Eclipse

Aristarchus of Samos�(born c. 310 bce—died c. 230 bce) 

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θ

 

S = 500 Miles

θ

Eratosthenes of Cyrene�(born c. 276 bce,— died c. 194 bce)

Cyrene

Alexandria 

 

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1846

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Uranus

Neptune

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0.80 meters

68 kg

68 kg

Find the gravitational force between these two people.

5.1 x 10-7 Newtons�0.00000051 Newtons

http://netdna.webdesignerdepot.com/uploads/2008/11/hand-1.jpg

1 kg (10N)

100g (1N)

1g (.01N)