•Gravitation •Planetary Motion •Laws of Gravitation

8/14/2019 Gravitation Planetary Motion Laws of Gravitation

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Gravitation PlanetaryMotion Laws of Gravitation


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GravitationGravitationGravitation is the namegiven to the force ofattraction between any twobodies of the universe, wasdiscovered by Newton in1665.


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The constant of proportionality G isknown as the universalgravitational constant.It is termed a "universalconstant" because it isthought to be the sameat all places and all

times, and thusuniversallycharacterizes theintrinsic strength of thegravitational force.

Laboratoryexperiments haveyielded a value for G of G = 6.67 10 11 Newton. (m 2/kg 2)


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Law Of UniversalGravitation

The law of universalgravitation accounts forplanets not falling into the Sunnor the Moon crashing into the

Earth.


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= 2 21r

mmG Force

v

m 2Now suppose Earthprovides pull insteadof string and arm

m1

=r

vm Force

2

2


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= 2 21r

mmG Force

=r

vm Force

2

2

= 2

21

2

2

r

mmG

r

vm

r

Gmv 12 =

(Force needed to keep it in orbit)(Force that can be provided)


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r

Gm 12v =

G = 6.7 x 10 -11 N .m 2/kg 2

m 1 = 2 x 10 30 kg

Mars Orbital velocity = 24 km/s Distance from Sun = 228 x 10 9 km

Earth Orbital velocity = 30 km/s Distance from Sun = 150 x 10 9 km


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o ge some ng n or , weneed a special horizontal

velocity The law of universalgravitation accounts for planets not falling into theSun nor the Moon crashinginto the Earth

Paths A, B, and C do nothave enough horizontalvelocity to escape Earthssurface whereas Paths D,E, and F do.

Path E is where thehorizontal velocity is exactlywhat is needed so its orbitmatches the circular curveof the Earth


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Keplers Laws of PlanetaryMotion

Using precise measurements of thepositions of the planets in the skycollected by Tycho Brahe, JohannesKepler deduced three laws of planetarymotion:

1. The orbits are ellipses.

2. Planets move faster when closer to the Sun andslower when farther away.3. Planets farther from the Sun take longer to

orbit.


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Orbits are ellipses


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Planets move faster whencloser to the Sun


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Planets farther from the Suntake longer to orbit

•Gravitation •Planetary Motion •Laws of Gravitation

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