5 gravitation
DESCRIPTION
5 Gravitation. The Milky Way galaxy and the black hole. www.ifa.hawaii.edu/~barnes/ast110_06/bhaq.html. 5 - 1 The world and the gravitational force. The Local Supercluster The Local Group The Milky Way and the Andromeda galaxy Cluster: Hydra and Centaurus. - PowerPoint PPT PresentationTRANSCRIPT
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The Milky Way galaxy and the black hole
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www.ifa.hawaii.edu/~barnes/ast110_06/bhaq.html
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5-1 The world and the gravitational force
•The Local Supercluster•The Local GroupThe Milky Way and the Andromeda galaxy Cluster: Hydra and Centaurus
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5-2 Newton's law of gravitation
221
rmmG F
Newton (23) —1665
22-11 /kgmN106.67=G
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Cavendish’s experiment
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Density Profile
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14-3 Gravitation and the principle of superposition
FdF
FFFFF=F
1
n
2=i1i1n1413121
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例 5-1 A discrete system (5 particles)
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例 5-2 A particle and a uniform rod
LM
drdmdm
rGmdF ,2
1 1
NdLd
MGmddLL
MGmrL
MGmrdr
LMGmdr
LM
rGmdFF
dLd
dL
d
dL
d
101
11
21
21
11
100.3)(
]11[]1[
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14-4 Gravitation near earth’s surface
22 rGM,ama,F
rMm GF gg
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Three reasons that 1. Earth is not
uniform.2. Earth is not a
sphere. 3. Earth is rotating.
gag
22
2
/034.0)2(
F
smRT
Rga
mamgma
maNma
g
g
g
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例 5-3 A pulsar %031.0)2( 2
gg
g
aR
Taga
211 /102.9 smag
例 5-4 The difference in ag (a) In the vicinity of
Earth r m 6 77 106. dr
rGM2da ,
rGMa 3
Eg2
Eg
263
Eg /1037.4 )70.1(
rGM2da smm
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(b) A black hole – The tidal force
hh RrmR 229,1095.2 4
2
3E
g
/5.14
)70.1(r
GM2da
sm
m
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5-5 Gravitation inside EarthA uniform shell of matter exerts no net gravitational force on a particle inside it.例 5-5
Express delivery
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KrrmGr
rGmr
MGmF
rVM
)3
4(
34
34
2
3
2
3
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5-6 Gravitational potential energy
dxxFdxxFxdxF
xdxFWU
rGMmU
R
)( ))(180)(cos()(
)(
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RGMm
xGMmdx
xGMmU
dxx
GMmxdxF
RR
][
)(
2
2
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Potential energy and force
2)(r
GMmr
GMmdrd
drdUF
Escape velocity
RGMv
RGMmmvUK
2
0)(21 2
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Some Escape Speeds
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例 5-6 Asteroids
skmvR
GMmmvR
GMmmv
UKUK
f
if
iiff
/16102
121 22
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5-7 Planets and Satellites: Kepler’s Laws1. The law of orbits.
elliptical orbits eccentricity semimajor(semiminor) axis
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2. The law of areas.
22
2
21
21
dt
21
rdtdrdA
drdA
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constant2dt
))((
))((2
mLdA
mrrmr
mvrrpL
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3. The law of periods.
32
2
222
)4(
)2())((
rGM
T
rT
mrmr
GMm
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例 5-7 Finding the mass:
)4( 2
32
GTrM
例 5-8 Comet Halley
97.0 ,
103.52
2 ,)4
(
12
3/12
2
eRaea
mRaR
aRRGMTa
p
pa
pa
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例 5-8 A binary system and a black hole
312
2
221
32
21
21
12
1221
4)(
,
))((
rGTmm
mmmrmr
rmr
mGmF
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holeblack a - 947.3109.6
2)6( ,2
2
30
3
22
321
s
s
S
MmMkg
GTv
mMm
vrT
312
2
221
32
21
21
12
1221
4)(
,
))((
rGTmm
mmmrmr
rmr
mGmF
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14-8 Satellites: Orbits and Energy
The potential energy r
GMmU
rvm
rGMm 2
2
The kinetic energy
rGmmmvK
221 2
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The total energy
orbit)(circular 2
2
Kr
GMmE
rGMm
rGMmUKE
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The elliptic orbits:
orbit) l(elliptica 2
orbit)(circular 2
aGmmE
Kr
GmmE
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5-9 Einstein and Gravitation• General/special theory of relativity
• Principle of equivalence: gravitation and acceleration are
equivalent.
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Gravitation is due to a curvature of spacetime that is caused by the masses.
Curvature of Space
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敬請期待物理 VI– 流力