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phy2048 lecture26

# phy2048 lecture26 - 13-1 What Is Physics 13-2 Newton’s...

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Unformatted text preview: 13-1 What Is Physics? 13-2 Newton’s Law of Gravitation13-3 Gravitation and the Principle of Superposition13-4 Gravitation Near Earth’s Surface13-5 Gravitation Inside Earth13-6 Gravitation Potential Energy13-7 Planets and Satellites: Kepler’s Laws13-8 Satellites: Orbits and Energy13-9 Einstein and GravitationChapter 13:GravitationChapter 13 Homework4, 5, 14, 17, 24, 26, 29, 35, 48, 55, 60, 63Examples: GravitySample Problem 13-2.Known: m1, m2= m3=m4= m5, a, θFind net force on m1?Gravitation Near Earth’s Surface2EE2ERMGgmgrmMGF≈==Sample Problem 13-4.Gravitation Inside EarthrRmMGF3EE=ME= 5.98×1024kgRE= 6.38×106mGravitational PotentialrrMmGFˆ2-=rMmGrMmGdrrMmGsdFWUrr-==⋅-=-=∫∫2drsdr=⋅ˆ⇒=∞=∞i.e.,TakeUrrMmGU-=EEEfor )()(RhmghRUhRU<<+=+MdrrˆFsdSample Problem 13-5. AsteroidKnown: vi= 12 km/s at ri= 10REFind vfat RE? (16 km/s)Gravitational Potential Near Earth’s SurfaceSum of Gravitational PotentialM1M2mr1r2r12bound systemunbound systemE= 0km/s2.1122:SpeedEscapeEEEe===gRRGMvEEscape SpeedEnergy of Satellites in Orbits...
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phy2048 lecture26 - 13-1 What Is Physics 13-2 Newton’s...

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