Q4_Week_Modern Astronomy.pdf. Kepler's Law of Planetary Motions

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2. Modern Astronomy

3. Tycho Brahe
✓aDanishastronomer
and nobleman who
made accurate
observationsofthe
movement ofcelestial
bodiesinanobservatory
builtforhimbyKing
FrederickIIofDenmark
in1576.

5. Kepler’s Law of Planetary Motion
A.Law of Ellipses
✓planets are orbiting the sun in a path described as
an ellipse

6. Kepler’s Law of Planetary Motion
B. Law of Equal Area
✓when an imaginary line is drawn from the center of
the Sun to the center of a planet, the line will sweep
out an equal area of space in equal time intervals

7. Kepler’s Law of
Planetary Motion
C. Law of Harmonies
✓the square of a planet’s orbital
period (T
2
) is proportional to the
cube of a planet’s average
distance from the Sun (R
3
). It
states that that the ratio of the
squares of the periods of two
planets is equal to the ratio of
the cubes of the average
distances of these two planets
from the Sun

9. SampleProblem
AccordingtothenotebyKepler,Mars
hasaperiodofabout687dayswhichis
1.88years.Determine themean
distanceofMarsfromtheSunusingthe
Earthasareference.TheEarth’smean
distanceis1.496X10
8
km.

10. SampleProblem
Jupitertakes11.86yearstocomplete
onerevolution.Whatisitsdistancefrom
thesuninkm?(TheEarth’smean
distanceis1.496X10
8
km.)

11. SampleProblem
Jupitertakes11.86yearstocomplete
onerevolution.Whatisitsdistancefrom
thesuninkm?(TheEarth’smean
distanceis1.496X10
8
km.)

12. The Aristotelian and
Galilean Conceptions of
Vertical, Horizontal and
Projectile Motions

14. HORIZONTAL MOTION

15. VERTICAL
MOTION

16. PROJECTILE MOTION

17. I.Aristotle’s
Concept
1.Vertical Motion-
Verticalmotionisreferred
toasnaturalmotion.Ina
naturalmotion,theobject
willmoveandwillreturnto
itsnaturalstatebasedon
theobject'smaterialor
composition-earth,water,
air,andfire.

18. I.Aristotle’s
Concept
2.HorizontalMotion-An
objectmovinginaviolentmotion
requirespushorpulltomaintain
horizontal motion. Motion
continuesonlysolongasthereis
anappliedforcetoanobject.
Whentheforceisremoved,
motionstops.

19. I.Aristotle’sConcept
3.ProjectileMotion-Aristotle
believedthattheprojectilemotionof
anobjectisparalleltotheground
untilitistheobject'stimetofallback
intotheground.Animpetuswillbe
keptbytheobjectuntilsuchtime
thattheinitialforceisforgotten,and
theobjectreturnstoitsnaturalstate
tostopmovingandfalltotheground.
Heviewedprojectilemotionasnatural
andviolentmotion.Hesaidthat
heavyobjectsfallfasterthanlight
ones

20. I.Galileo’sConcept
1.VerticalMotion-Inthe
absenceofaresistance,
objectswould fallnot
dependingontheirweight,but
inthetimeoffall.Also,ifthe
objectencounteredaresistive
forcefromafluidequalor
greaterthanitsweight,itwill
slowdownandreachesa
uniform motion untilit
reachesthebottomandstops.

21. II.Galileo’sConcept
2.HorizontalMotion-Anobjectinmotion,ifunimpeded,will
continuetobeinmotion,andanexternalforceisnotnecessaryto
maintainthemotion.IftheEarth’ssurfaceisveryflatandextended
infinitely,objectsthatarepushedwillnotbeimpeded.Thus,the
objectswillcontinuetomove.

22. II. Galileo’s Concept
3.ProjectileMotion-aprojectileisacombinationofuniform
motioninthehorizontaldirectionanduniformlyacceleratedmotioninthe
verticaldirection.Ifitisnotimpeded,itwillcontinuetomoveeven
withoutanappliedforce.

23. Galileo'sExperimentationtoprovehis
Ideasaboutmotion
.
ExperimentI:
Galileodroppedtwodifferent
weightsofcannonballtothe
LeaningTowerof
Pisaandtheyfellatthesame
timebutcouldnotmeasure
thedistancetravelled
thereforeheproceededto
anotherexperimentation.

24. Galileo'sExperimentationtoprovehis
Ideasaboutmotion
.ExperimentII:
•Galileousedtheinclinedrampinorder
tomeasuretheaccelerationofan
object.Heusedarollingballto
measurethechanges.Hemeasured
thatobjectsacceleratesatthesame
timeregardlessoftheirsizeandmass.
•Speedisthedistancetraveledbyan
objectdividedbythetimetakento
travelthedistance
•Aballrollingdownaninclinedplane
increasesitsspeedbythesamevalue
aftereverysecond

26. FreeFallandGravity.
•Freelyfallingbodiesundergoconstantaccelerationinwhichit
isreferredtoasfreefall.Thefreefallaccelerationrepresenta
symbolgwhichmeansgravity.
•Atthesurfaceoftheearth,gravity(g)isapproximately9.8
m/s2.
•Gravityleadstheobjecttoaccelerateinaconstantrate.

27. Understanding Newton’s First
Law of Motion

29. Inertia
•Resistschangeinmotion

30. GalileoandInertia
Galileodevelopedthefirstconceptoflawsof
motion:
1.Developedtheconceptofmotionintermsof
velocitybyusinginclinedplanes
2.Developedtheideaofforcethatcausemotion
3.Determinedthatthenaturalstateofan
objectisrestoruniformmotion
4.Developedtheideathatobjectresistmotion,
inertia

33. IsaacNewtonandhisFirstLawof
Motion
“Anobjectatreststaysatrestandan
objectinmotionstaysinmotionwiththe
samespeedandinthesamedirection
unlessacteduponbyanunbalanced
force.”

34. MassandInertia
✓Anobject’sinertia
dependsonitsmass.
✓Anobjectwitha
greatermasshasa
greaterinertiaand
anobjectwitha
lessermasswillalso
havealesserinertia.

35. ThreeTypesofInertia
1.Inertiaofrest-anobjectwillstayinplaceunless
somethingorsomebodymovesit.Example:aplate
onthetable
2.Inertiaofmotion-anobjectwillcontinueatthe
samespeeduntilaforceactsit.Example:a
rollingball
3.InertiaofDirection-anobjectwillstaymovingin
thesamedirectionunlessaforceactsonit.
Example:amovingcarturningright

36. Forces
Friction-aforcethatopposesmotionbetweenany
surfacesthataretouching.
BalancedandUnbalancedForces
Balancedforce–forceinwhichthenetforceequal
tozero
Unbalancedforce–netforcenotequaltozero.It
aforcethatcausesacceleration.