Monday, Sep. 15Syllabus, class notes, and homeworks are at:www.as.utexas.edu courses AST 301, LacyReading for this week: chapter 5The exam this Friday will cover ch. 1-4.Get a review sheet in back on your way out.The observing homework is due this Friday. You shouldhave seen the Moon several times. Say what you saw ofthe planets (even if you didn’t see much).The Wednesday help session has been moved toGRG 424 at 5:00 (for the entire semester).Note the new time and place.Topics for last week and todayDescribe the models of Aristotle, Copernicus, and Kepler.How correct and how accurate was each? How dideach explain retrograde motion of the planets?State each of Kepler’s 3 laws and be able to use them tocompare speeds of different planets and of one planetat different points in its orbit.What arguments did Galileo make in favor of theCopernican model?State Newton’s 4 laws. Know what the words in eachmean. Apply them to the problem of falling balls.What did Newton add to our understanding of Kepler’slaws?Retrograde and prograde motionMars’ normal (prograde) motion is caused by itscounterclockwise motion around the Sun.Mars moves in the retrograde direction when the Earthpasses it up, making it appear to move in a clockwisedirection.Venus’ prograde motion is caused by the Earth’s motionaround the Sun. This causes a counterclockwiseapparent motion of Venus (and the Sun). Venus movesin the clockwise (retrograde) direction when it passes us.Kepler’s laws (or rules)1. The planets move on elliptical paths with the Sun at onefocus of the ellipse for each planet.2. The speed of a planet changes during its orbit, movingfastest when it is closest to the Sun and slowest when itis farthest from the Sun. A line from the Sun to the planet sweeps out equal areasin equal times.3. Different planets move at different speeds, with a planetin a smaller orbit moving faster than one in a larger orbit. The time for a planet to orbit the Sun depends on thesize of it orbit according to the rule:P2 = a3, where P is in years and a is in AUKepler’s 2nd lawA simpler, although not exact, way to state Kepler’s secondlaw is to say:The distance traveled by a planet in a given time isinversely proportional to the planet’s distance from theSun during that time.Or the speed of a planet is inversely proportional to itsdistance from the Sun.This means that if at one time a planet is twice as far fromthe Sun as at a second time, it is moving ½ as fast.Or: closer to Sun means faster. twice as close means twice as fast twice as far means ½ as fastProportional thinkingThe distance you travel in a day is proportional to your speed.This means that if you drive at 30 mph on Saturday and 60 mphon Sunday (and you drive for the same time on both days) youwill travel twice as far on Sunday.Written as an equation:distance on Sunday = speed on Sundaydistance on Saturday speed on SaturdayThe time to get someplace is inversely proportional to your speed.If you drive the same distance on Saturday and Sunday, but drivetwice as fast on Sunday, it will take you twice as long to getthere on Saturday.time on Sunday = speed on Saturdaytime on Saturday speed on SundayQuizIf the speed of the planet between A` and B` is 30 km/s,what is its speed between A and B?A. 10 km/sB. 28 km/sC. 32 km/sD. 90 km/s3 AU1 AU30 km/sQuizIn the figure below, given that the distance from the Sun topoints A and B is 3 AU, the distance to points A` and B`is 1 AU, and the distance from A to B is 0.5 AU, what isthe distance from A` to B` (along the orbit)?A. 0.5 AUB. 1 AUC. 1.5 AUD. 3 AU3 AU1 AU0.5 AUGalileoLived about 400 years ago, while Kepler lived.Made several observations and arguments whichsupported the Copernican model:Venus has phases like the Moon’s, which can only beexplained if it orbits the Sun, not a point between theEarth and the Sun.Jupiter has moons, which orbit it, not the Earth.The Moon has mountains, so is imperfect, like the Earth.More generally, Galileo argued for basing science onobservations and experiments, not pure thought.Newton’s theory of motionCommon experience tells us that you have to push on anobject to make it move and the harder you push thefaster it goes.If you stop pushing on an object it will stop moving.Newton realized that this is a result of a complicatedsituation involving friction.In a simple situation (like an object in space or a verysmooth ball rolling) the rules are different.And the rules for simple situations can be combined toexplain motion in complicated situations.Newton also realized that his laws of motion when appliedto the planets could explain Kepler’s laws.Newton’s laws of Motion1. If there are no forces acting on an object, if moving it willcontinue to move with constant speed and in the samedirection. If not moving, it will remain stationary.2. If a force is acting on an object, the object’s acceleration(the rate of change in its speed or direction of motion) isproportional to the force acting on it and is inverselyproportional to its mass.a α F / m3. If an object exerts a force on a second object, thesecond object necessarily exerts the same force on thefirst, but in the opposite direction.Definitionsspeed: distance traveled / time spent travelingacceleration: change of speed / time spent changing(can also be a change in direction of motion)force: how hard one object pushes or pulls on anothermass: is best defined by Newton’s 2nd law, but isproportional to the amount of matter in an objectvolume: the amount of space an object takes upfor a box: height x width x depthQuizIf I step on my brakes and slow down from 60 mph to 30mph, am I accelerating?A. yesB. NoBy scientists’ definition any change in speed is calledacceleration, whether an increase or a decrease.If I take my foot off of the gas and coast around a corner atconstant speed, am I accelerating?A. yesB. noA change in direction is also considered an acceleration,even if speed stays constant.QuizIf I push on my car for 5 seconds I can make it move at 2mph. If I pushed for an additional 5 seconds with thesame force, how fast would it then be going? Ignore allother forces acting on the car.A. 2 mphB. 4 mphC. 7 mphD. 10 mphQuizIf I push on my car for 5 seconds I can make it move at 2mph. If two identical cars were lined up bumper-to-bumper, how fast could I make them move by pushingfor 5 seconds?A. 0 mphB. 1 mphC. 2 mphD. 4
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