Wecanimaginethatthiscomplicatedarrayofmoving
thingswhichcons6tutes"theworld"issomethinglikea
greatchessgamebeingplayedbythegods,andweare
observersofthegame.Wedonotknowwhattherules
ofthegameare;allweareallowedtodoistowatch
theplaying.Ofcourse,ifwewatchlongenough,we
mayeventuallycatchontoafewoftherules.Therules
ofthegamearewhatwemeanbyfundamental
physics...
-RichardFeynman
Polarbears
aroundan
icehole
Thegameisinthenameofthegame–polar
bearsaroundanicehole–inventedinthedaysof
GhengisKhan.Aclueforyoutokeepyoutrue–
likepetalsaroundarose,youcancounteach
bear’snose.Howmanypolarbearsdoyousee?
hCp://www.btwaters.com/probab/dice/dicemain3D.html
Refiningyourthinking…
•  Youmayfeelfrustratedasyoutrytofigurephysicsout.
Refiningyourthinking…
•  Youmayfeelfrustratedasyoutrytofigurephysicsout.
•  That’sokay.Physicsishardtounderstandun6lyouknowthe
“rulesofthegame.”But,onceyoudiscovertherules,physics
oPenseemseasyandyoumaybesurprisedthatothersdon’t
understand.
Refiningyourthinking…
•  Youmayfeelfrustratedasyoutrytofigurephysicsout.
•  That’sokay.Physicsishardtounderstandun6lyouknowthe
“rulesofthegame.”But,onceyoudiscovertherules,physics
oPenseemseasyandyoumaybesurprisedthatothersdon’t
understand.
•  However,rememberthatyoudidn’talwaysunderstand.
Refiningyourthinking…
•  Youmayfeelfrustratedasyoutrytofigurephysicsout.
•  That’sokay.Physicsishardtounderstandun6lyouknowthe
“rulesofthegame.”But,onceyoudiscovertherules,physics
oPenseemseasyandyoumaybesurprisedthatothersdon’t
understand.
•  However,rememberthatyoudidn’talwaysunderstand.
•  Whenyoudiscovertherulesandunderstandwithoutsomeone
justtellingyouthe“answer”,youareexcited.Thejourneyto
understandingisveryimportant.So,nooneisgoingtotellyou
theanswer,butwe’reallheretosupporteachotheronour
journeys.
Refiningyourthinking…
•  Youmayfeelfrustratedasyoutrytofigurephysicsout.
•  That’sokay.Physicsishardtounderstandun6lyouknowthe
“rulesofthegame.”But,onceyoudiscovertherules,physics
oPenseemseasyandyoumaybesurprisedthatothersdon’t
understand.
•  However,rememberthatyoudidn’talwaysunderstand.
•  Whenyoudiscovertherulesandunderstandwithoutsomeone
justtellingyouthe“answer”,youareexcited.Thejourneyto
understandingisveryimportant.So,nooneisgoingtotellyou
theanswer,butwe’reallheretosupporteachotheronour
journeys.
•  Beingtoldthe“answer”atmostgivesyouoneanswerthatyou
didn’tknow.Learningtothinkcri6callyandarriveattheanswer
withsupportdevelopsaskillthatyouwillusetofindmany
answers.
Reasoning:OrderofMagnitude
Theorderofmagnitudeofaquan6tyis
itssizetothenearestfactorof10.For
example,theorderofmagnitudeofthe
sizeofanatomis10−10m.
hCp://htwins.net/scale2/
Reasoning:OrderofMagnitude
Whataretheordersofmagnitudeofthesizes
(inm)ofthesolarsystem,Sun,Earth,
Moon;
Reasoning:OrderofMagnitude
Whataretheordersofmagnitudeofthesizes
(inm)ofthesolarsystem,Sun,Earth,
Moon?
• solarsystem:diameterofPluto’sorbit,1013m
• diametersofSun:109m,Earth:107mand
Moon:106m.
diametersofSun:109m,Earth:107mandMoon:106m
HowmanyEarths,linedupsidebyside,couldbe
lineduponthediameterofthesun?
HowmanyEarthswouldfitinsideoftheSun?
HowmanymoonswouldfitinsideoftheSun?
A.  Onehundred
B.  Onethousand
C.  Onemillion
D.  Onebillion
E.  Noneoftheabove
diametersofSun:109m,Earth:107mandMoon:106m
HowmanyEarths,linedupsidebyside,couldbe
lineduponthediameterofthesun?
HowmanyEarthswouldfitinsideoftheSun?
HowmanymoonswouldfitinsideoftheSun?
A.  Onehundred
B.  Onethousand
C.  Onemillion
D.  Onebillion
E.  Noneoftheabove
diametersofSun:109m,Earth:107mandMoon:106m
HowmanyEarths,linedupsidebyside,couldbe
lineduponthediameterofthesun?
HowmanyEarthswouldfitinsideoftheSun?
HowmanymoonswouldfitinsideoftheSun?
A.  Onehundred
B.  Onethousand
C.  Onemillion
D.  Onebillion
E.  Noneoftheabove
diametersofSun:109m,Earth:107mandMoon:106m
HowmanyEarth,linedupsidebyside,couldbe
lineduponthediameterofthesun?
HowmanyEarthswouldfitinsideoftheSun?
HowmanymoonswouldfitinsideoftheSun?
A.  Onehundred
B.  Onethousand
C.  Onemillion
D.  Onebillion
E.  Noneoftheabove
Reasoning:Scaling
Youwanttodrawapictureofthesunand
theearth,toscale,onasheetofpaper.Tofit
itonthepaperyoustartbyrepresen6ngthe
diameteroftheearth’sorbitaroundthesun
byadistanceof25cm.
Howlargedoyouhavetodrawthe
diametersofthesun,theearth,andthe
orbitofourmoon?
•  diameterofPluto’sorbit,1013m;
•  diameterofEarth’sorbit,1011m
•  diametersofSun:109m,Earth:107mandMoon:106m.
•  So,sincetheordersofmagnitudearesovaried,focusonlyonthe
ordersofmagnitude.
OnthescaledrawingRES=25cm(dES’~10-1m),thescalefactorf=dES’/
dESis10-12;so:
•  dPS’=f*dPS=10-12*1013m~10m;
•  dS’~10-3m(1mm);
•  dE’~10-5m(10microns);
•  dm’~10-6m(1micron);
•  diameterofPluto’sorbit,1013m;
•  diameterofEarth’sorbit,1011m
•  diametersofSun:109m,Earth:107mandMoon:106m.
•  So,sincetheordersofmagnitudearesovaried,focusonlyonthe
ordersofmagnitude.
OnthescaledrawingRES=25cm(dES’~10-1m),thescalefactorf=dES’/
dESis10-12;so:
•  dPS’=f*dPS=10-12*1013m~10m;
•  dS’~10-3m(1mm);
•  dE’~10-5m(10microns);
•  dm’~10-6m(1micron);
•  diameterofPluto’sorbit,1013m;
•  diameterofEarth’sorbit,1011m
•  diametersofSun:109m,Earth:107mandMoon:106m.
•  So,sincetheordersofmagnitudearesovaried,focusonlyonthe
ordersofmagnitude.
OnthescaledrawingRES=25cm(dES’~10-1m),thescalefactorf=dES’/
dESis10-12;so:
•  dPS’=f*dPS=10-12*1013m~10m;
•  dS’~10-3m(1mm);
•  dE’~10-5m(10microns);
•  dm’~10-6m(1micron);
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
weight1000(103)
volume1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
weight1000(103)
volume1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
weight1000(103)
volume1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
weight1000(103)
volume1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
weightsupportedbylegbones1000(103)
pressureonlegbones
=weight/crosssec6onofbone10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
pressureonlegbones=weight/crosssec6onofbone
10(101)
foodrequirement100(102)
SCALING
Consideragiant,similartoyou,butwithlinear
dimensionsthatareeach106mesaslarge.
Whatarethefactorsbywhicheachofthe
followingislargerthanforyou?
lengthofleg10(101)
surfacearea100(102)
volume1000(103)
weight1000(103)
crosssec6onoflegbones100(102)
pressureonlegbones=weight/crosssec6onofbone
10(101)
foodrequirement100(102)
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
Firstaskyourself,howdothevolumesofthe
planetscomparetothevolumeofthesun?
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Takingtheearthasanaverage-sizedplanet,its
radiusis~100Rmessmallerthanthatofthe
sun.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Takingtheearthasanaverage-sizedplanet,its
radiusis~100Rmessmallerthanthatofthe
sun.
• SoVSun/VEarth=(100)3,or1million.Evenifyou
addupthecontribuRonsofalltheplanets,their
volumesaresRllonly~.0001%thevolumeof
theSun,sowecanignoretheircontribuRon.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystemis
occupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Takingtheearthasanaverage-sizedplanet,its
radiusis~100Rmessmallerthanthatofthesun.
• SoVSun/VEarth=(100)3,or1million.Evenifyouadd
upthecontribuRonsofalltheplanets,their
volumesaresRllonly~.0001%thevolumeofthe
Sun,sowecanignoretheircontribuRon.
Wehavethussimplifiedthisques1on.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Pluto’sorbithasameanradiusof6x1012m.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Pluto’sorbithasameanradiusof6x1012m.
• TheraRoVSun/Vsolarsystemis1.2x10-4.TheraRo
ofthevolumesisthecubeofthisnumber,or1.6
x10-12,or.0000000000016.
Reasoning:OrderofMagnitude
Whatfrac6onofthevolumeofthesolarsystem
isoccupiedbythesunandtheplanets?
• Thesun’sradiusisabout7x108m.
• Pluto’sorbithasameanradiusof6x1012m.
• TheraRoVSun/Vsolarsystemis1.2x10-4.TheraRo
ofthevolumesisthecubeofthisnumber,or1.6
x10-12,or.0000000000016.
• Whichmeansthatthemassiveobjectsinthe
solarsystemoccupyon.00000000016%ofthe
spaceinthesolarsystem!
Somebenchmarkmeasures
• 
• 
• 
• 
• 
• 
• 
• 
1cm≅lengthoftopsegmentofpinky
1m≅distancefromnoseto6poffinger
100m≅straightpartofarunningtrack
1km≅halfamile
1ms≅dura6onofabathimngaball
1,000sec≅20minutes
100,000sec≅2weeks
1year≅πx107sec