7/30/2019 Gravitation - P2, week 1

1/12

Force,Work,Energy,Power

WhenForceisappliedthetotalenergyofobjectschanges YoudoWorkonanobjectifyouapplyaforceonitoversomedistance.

Energyisthecapacitytodowork Energyisconserved

Poweristherateatwhichworkisbeingdone

1

7/30/2019 Gravitation - P2, week 1

2/12

NewtonsLawsofmotion

1stLaw:Everyobjectcon@nuestobeatrestortomovewithuniformvelocityunlessactedonbyanetforce

2ndLaw:Therateofchangeofmomentumofanobjectispropor@onaltothenetforceac@ngonitF=ma

3rdLaw:ac@on-reac@on.Whentwoobjectsinteract,theyexertequalandoppositeforcesononeanother

2

Field:aregionofspacewhereaforceisac@ve Weusefieldstodescribeallcaseswheretwo(ormore)objectsseparatedinspaceexertforcesoneachother

GravitationalFields

7/30/2019 Gravitation - P2, week 1

3/12

LawofUniversalGravitation

NewtonsLawofUniversalGravita

7/30/2019 Gravitation - P2, week 1

4/12

FromNewtons2ndLawandNewtonsLawofUniversalGravita@onwehave

GravitationalFieldStrength

F=mg =GmM

r2 g =

GM

r2

4

Insidetheearth,g

varieslinearlywith

distance(1/r)

7/30/2019 Gravitation - P2, week 1

5/12

Gravita@onalpoten@alEnergyUatapointPistheworkdoneinbringinganobjectofmassmfrominfinitytothat

pointP

GravitationalPotentialEnergy

U= W = F(x) dx

r

5

F(x) dx =GmM

x2dx

U=GmM

x2

r

dx = GmM

x

$

%&'

()

r

= GmM

r

NewtonsLawof

Gravita@on:

so

7/30/2019 Gravitation - P2, week 1

6/12

Thegravita

7/30/2019 Gravitation - P2, week 1

7/12

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

7

7/30/2019 Gravitation - P2, week 1

8/12

PlanetsandSatellites

Asatelliteorbi@ngtheearthhasatangen@alvelocityandaninwardaccelera@on

F=GmM

r2=

mv2

r

=mg

T=2r

v= 2

r3

GM

v =GM

r

8period

7/30/2019 Gravitation - P2, week 1

9/12

PlanetsandSatellites

Asatelliteorbi@ngtheearthhasatangen@alvelocityandaninwardaccelera@on

KE=1

2mv

2=GmM

2r

PE= GmM

r

KE+PE= GmM

2r

9

7/30/2019 Gravitation - P2, week 1

10/12

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

10

7/30/2019 Gravitation - P2, week 1

11/12

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

42 11

7/30/2019 Gravitation - P2, week 1

12/12

ToDo

Readchapter12fromthebook[p.224-p.235gravita@onalfields]

HomeworkAssignmentwk1:ques@ons12.1,12.4,12.6,12.8,12.13

Handitinnolaterthan4:00pmnextWednesday(16Jan)-LTEWORKWILLNOTBECCEPTED

12