AST 301Introduction to AstronomyJohn LacyRLM [email protected] LiRLM [email protected] JeonRLM [email protected] site: www.as.utexas.eduGo to Department of Astronomy courses,AST 301 (Lacy), course websiteTopics for this weekWhat is a photon? What is an electromagnetic wave?How are the photon and wave pictures of light related?Make a sketch of an atom, showing its parts.How do the wave properties of electrons result in onlycertain electron orbits being allowed in an atom?How does the fact that only certain electron orbits canoccur result in photons of only certain wavelengthsbeing emitted?Describe emission and absorption line spectra and theconditions under which each occurs.Describe black body radiation and the relations betweentemperature and the power emitted and thewavelengths of light emitted.Describe the Doppler shift.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 a measure of the amount of matter in an objectand how much it resists being pushed aroundvolume: the amount of space an object takes upfor a box: height x width x depthNewton’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.Exam questionThese was the most common answers to question 6.Can both of these answers be right?Newton’s explanation of Galileo’s experimentIf the two balls that Galileo dropped from the leaning towerhad different masses, the force of gravity on them shouldhave been different. Why did they fall at the same rate?What if one ball had a mass of 1 kilogram and the otherhad a mass of 2 kg? The force of gravity on the 2 kg ballwas twice the force on the 1 kg ball and Newton’s 2nd lawsays that acceleration is proportional to the force on anobject.But Newton’s 2nd law also says that acceleration isinversely proportional to the mass of the object.Doubling the force and doubling the mass have oppositeeffects, resulting in the same acceleration for the twoballs.Newton’s law of gravityGravity is a attraction between any two objects.The force of gravity is proportional to the product of themasses of the two objects and is inversely proportionalto the distance between their centers.F α m1 m2 / d2orF = G m1 m2 / d2For objects near the Earth, d is the distance to the center ofthe Earth, not to the surface.QuizWhen the Apollo astronauts were on the way to the Moon,10 Earth radii away from the center of the Earth (1/6 ofthe way to the Moon), what was the force of gravity on a150 pound astronaut?A. 0B. 1.5 lbC. 15 lbD. 150 lbGalileo (and Einstein) just argued that all objects acceleratethe same under the influence of gravity. Newtonexplained that by saying that the force of gravity isproportional to mass, and acceleration is proportional toforce / mass.If the force of the Earth’s gravity on a 1 kg ball is 10Newtons, what is the force of the ball’s gravity on theEarth?A. much less than 1 Nt.B. 1 NtC. 10 Nt.D. much more than 10 Nt.Newton’s version of Kepler’s 3rd lawNewton’s laws can be used to derive Kepler’s 3rd law.A force is needed to cause a planet to move on a curvedpath. That force is the force of gravity of the Sun.By equating the force of the Sun’s gravity to the forceneeded to cause a planet to follow a curved path, we cancalculate the speed of the planet.The result is: v = (G MSun / a)1/2,where v is the average speed of the planet, MSun is themass of the Sun, and a is the average distance of theplanet from the Sun.Knowing the speed of the planet, we can calculate the timeit takes to orbit the Sun.The result is: P2 α a3 / MSunThe MathFon Earth = G MEarth MSun / r2aof Earth = Fon Earth / MEarth = G MSun / r2ain orbit = v2 / rfor aof Earth = ain orbit we need:G MSun / r2 = v2 / r, orG MSun = v2 r, or v2 = G MSun / rbut we also know that v = distance/time = 2πr / P, soG MSun = (2πr / P)2 r = 4 π2 r3 / P2, orP2 = (4 π2 / G MSun) r3, or P2 α r3(and for a circle, r = a, the semimajor axis)What is light?We need two ways of looking at light:It is an electromagnetic wave.We often think of radio waves this way.In fact they are just very long wavelength light.It is also a shower of particles called photons.x-rays are usually thought of as photons.They are very short wavelength light.For visible light we need both pictures.What is a wave?A moving disturbancelike a wave going around the stadiumor a wave in wateror a wave in a springFor all of these, no object moves with the wave.It is only the disturbance that is moving.Waves can be described by:wavelength – the distance between peaksperiod – the time between peaks passing a pointamplitude – the wave heightWhat is the relation between wavelength andperiod of a wave?Measure the wavelength and period of a wave in a spring,for several different frequencies.What is the relation between wavelength andperiod of a wave?In one period of a wave, one full cycle (peak through valleyand back to peak) passes by.That means that the wave has moved by one wavelength.Since speed is distance traveled / time spent, and a wavemoves a distance of one wavelength in a time of oneperiod, its speed must be:speed = distance / time = wavelength / period v = λ / pWe more often use frequency = 1 / period. Then:speed = wavelength x frequency v = λ x
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