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1The Scientific Method• The Scientific Method is theprocedure scientists use toconstruct their ideas about how theUniverse works.– Start with a hypothesis – a testableidea of how something works– Test the hypothesis!– If the test fails, modify or abandonthe hypothesis, and retest.• Hypotheses that pass many yearsof testing become Laws(mathematical) or Theories(described using words).•A Model is a complexdescription of physicalphenomena incorporatingmany laws and/or theories–Ex: The Celestial Sphere–Ex: Universal GravitationHypothothesisTheory or LawTests/observations Models/predictionsFacts/observables2Why is it impossible toprove a theory?• A theory is not a fact. Only facts can be proven.• * A theory is only supported by observations, a single contraryobservation can disprove it.• Theories can be proven! Once it is proven it is called a fact.• It is not possible for humans to observe evrything about theuniverse, if they could they could prove a theory. (this one can alsobe argued as true)The scale of things (reduced 1:10 billion)140mm(14 cm)Mars0.7mm23mVenus1.2mm11mEarth1.3mm15mJupiter14.3mm78mSaturn12mm143mUranus5.2mm287mNeptune4.8mm450mPluto0.2mm590mMercury0.5mm6mAsteroid Belt3Scale Models of the Universe• Scale model #1• Sun - a basketball in my hand• Earth - at the back of the room• Pluto - at the State Capital Building (edge of solar system)• Nearest star - Hawaii-- now, even smaller --• Scale model #2• Sun - a speck of dust in my hand• Nearest star - at the back of the room• Center of Milky Way - Chicago• Nearest galaxy - opposite side of the Earth4The Celestial Sphere II• Important Terms– Zenith: The point directly overhead on thecelestial sphere (CS)– Nadir: The point opposite the zenith on the CS– North or south celestial pole: The point aroundwhich the stars appear to rotate– Celestial Equator: An extension of the Earth’sequator expanded out to the surface of the CS.– Horizon: The lower edge of the visible CSThe Annual Motion of the Sun• As the Earth revolves around(orbits) the Sun, the Sunappears to move through 13constellations on a belt aroundthe celestial sphere called theecliptic• When the sun’s glare blocks aparticular constellation fromview, we say that the Sun is“in” that constellation• As this motion repeats itselfafter one year, it is called theSun’s annual motion• The motion of the stars isrecorded as sidereal time• Sidereal day is 1/356 shorterthan a solar day (4 minutes).5The Motion of the Planets• Because the planets’orbits all lie in more orless the same plane, thepaths of the planetsthrough the sky all lieclose to the ecliptic,appearing to movethrough the constellationsof the zodiac• Only Pluto seems tomove far from the eclipticGeocentric Models• Models in which everythingrevolves around the Earthare called Geocentricmodels.• From earliest Greek times,this kind of model was usedto describe the heavens• Planets and stars residedon their own spheres, eachtipped slightly relative toeach other. Thisreproduced the motion ofthe planets and Sunthrough the sky.• Did not explain retrogrademotion!6Kepler’s First Law• Planets move in ellipticalorbits with the Sun at onefocus of the ellipse– Developed a heliocentric(Sun-centered) model– Did not agree with theancients (or Brahe!)– The shape of the ellipse isdescribed by its semi-major and semi-minoraxes.7Kepler’s Second Law• The orbital speed of aplanet varies so that a linejoining the Sun and theplanet will sweep out equalareas in equal timeintervals• That is, planets movefaster when near the Sun,and slower when fartherfrom the Sun• Explained the non-circularbehavior of the planets!Kepler’s Third Law• The amount of time a planet takesto orbit the Sun (its period) P isrelated to its orbit’s size, a, byP2 = a3• Kepler’s Laws describe the shapeof a planet’s orbit, its orbitalperiod, and how far from the Sunthe planet is positioned.• These were empiricalrelationships, found fromobservation rather than the logicof the ancients.8Newton’s First Law• An object in uniform motion willstay in motion, an object at restwill stay at rest.• If an object’s velocity is notchanging, either there are noforces acting on it, or the forcesare balanced and cancel eachother out– Hold a ball out in your hand, and notethat it is not moving– Force of gravity (downward) isbalanced by the force your handapplies (upward)!• Note: Velocity has a speed (I.e. 60mph) and a direction (I.e.NW).• If an object’s velocity is changing,there must be forces present!– Dropping a ball– Applying the brakes in a car• This change can be either speed ordirection or BOTH!150 HP150 HPSame Horse power, which accelerates faster, why?9Newton’s Second Law• The force (F) acting on an objectequals the product of its acceleration(a) and its mass (m)• F = m × a• We can rearrange this to be:• a = F/m• For an object with a large mass, theacceleration will be small for a givenforce• If the mass is small, the same forcewill result in a larger acceleration!• Though simple, this expressioncan be used to calculateeverything from how hard to hitthe brakes to how much fuel isneeded to go to the Moon!Newton’s Third Law• When two bodies interact,they create equal andopposite forces on eachother• If two skateboarders have thesame mass, and one pusheson the other, they both moveaway from the center at thesame speed• If one skateboarder has moremass than the other, thesame push will send thesmaller person off at a higherspeed, and the larger one offin the opposite direction at asmaller speed– Why?This works for planets, too!10Circular Motion• Tie a string to a ball andswing it around your head– Law of inertia says that theball should go in a straightline– Ball goes in a circle – theremust be forces!• Where’s the force?– It’s the tension in the string that ischanging the ball’s velocity– If the string breaks, the ball willmove off in a straight line (whilefalling to the ground)• Newton determined that this forcecalled Centripetal Force can bedescribed by the above equation:dVmFC2!=Conservation of AngularMomentum• Since angular momentum isconserved, if either the mass, sizeor speed of a spinning objectchanges, the other values mustchange to maintain the samevalue of momentum– As a spinning figure skater pulls herarms


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UW-Madison AST 103 - The Scientific Method

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