Download - Gravitation - P2, week 1
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7/30/2019 Gravitation - P2, week 1
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Force,Work,Energy,Power
WhenForceisappliedthetotalenergyofobjectschanges YoudoWorkonanobjectifyouapplyaforceonitoversomedistance.
Energyisthecapacitytodowork Energyisconserved
Poweristherateatwhichworkisbeingdone
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NewtonsLawsofmotion
1stLaw:Everyobjectcon@nuestobeatrestortomovewithuniformvelocityunlessactedonbyanetforce
2ndLaw:Therateofchangeofmomentumofanobjectispropor@onaltothenetforceac@ngonitF=ma
3rdLaw:ac@[email protected],theyexertequalandoppositeforcesononeanother
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Field:aregionofspacewhereaforceisac@ve Weusefieldstodescribeallcaseswheretwo(ormore)objectsseparatedinspaceexertforcesoneachother
GravitationalFields
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LawofUniversalGravitation
NewtonsLawofUniversalGravita
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FromNewtons2ndLawandNewtonsLawofUniversalGravita@onwehave
GravitationalFieldStrength
F=mg =GmM
r2 g =
GM
r2
4
Insidetheearth,g
varieslinearlywith
distance(1/r)
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Gravita@onalpoten@alEnergyUatapointPistheworkdoneinbringinganobjectofmassmfrominfinitytothat
pointP
GravitationalPotentialEnergy
U= W = F(x) dx
r
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F(x) dx =GmM
x2dx
U=GmM
x2
r
dx = GmM
x
$
%&'
()
r
= GmM
r
NewtonsLawof
Gravita@on:
so
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Thegravita
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Escapevelocity
Gravita@onalpoten@alenergyonsurface
Toescape,ini@alkine@cenergymustbeatleastequaltothepoten@alenergyonsurface,so
URE
= GmM
RE
1
2mv
esc
2G
mM
RE
= 0
vesc=
2GM
RE
=11.2km / s
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PlanetsandSatellites
Asatelliteorbi@ngtheearthhasatangen@alvelocityandaninwardaccelera@on
F=GmM
r2=
mv2
r
=mg
T=2r
v= 2
r3
GM
v =GM
r
8period
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PlanetsandSatellites
Asatelliteorbi@ngtheearthhasatangen@alvelocityandaninwardaccelera@on
KE=1
2mv
2=GmM
2r
PE= GmM
r
KE+PE= GmM
2r
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KeplersLaws
Kepler(1571-1630)wasaGermanmathema@cianandastronomer
UseddatacollectedbyTychoBrahe(1546-1601)toarriveatthreelaws
describingplanetarymo@on
1.TheLawofOrbits:Allplanetsmoveinellip@calorbits,withthesunatonefocus
2.TheLawofAreas:Alinethatconnectsaplanettothesunsweepsoutequalareasinequal@mes
3.TheLawofPeriods:Thesquareoftheperiodofanyplanetispropor@onaltothecubeofthesemi-majoraxisofits
orbit
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Keplers3rdLaw
ThesquareoftheperiodTofanyplanetispropor@onaltothecubeofthesemi-majoraxisrofitsorbit
Wemaywritethisasr3/T2=constant Thisra@oisthesameforallplanets ForaplanetinacircularorbitaroundtheSun:Fcentr =
mv2
r=G
mM
r2= Fgrav v =
GM
r
v =2r
T=
GM
r
r3
T2=
GM
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ToDo
Readchapter12fromthebook[p.224-p.235gravita@onalfields]
HomeworkAssignmentwk1:[email protected],12.4,12.6,12.8,12.13
Handitinnolaterthan4:00pmnextWednesday(16Jan)-LTEWORKWILLNOTBECCEPTED
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