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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
