Lecture notes (professor robert zinn) Planets And Stars (ASTR 110) PDF

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Lecture notes (professor robert zinn) Planets And Stars (ASTR 110) January-April...

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02 Jan 15 lecture notes Homework policy a. Homework handed out and posted on classes v2 at the beginning of class on Wednesdays b. Policy also on classes v2 c. Problems will be similar to the ones in the textbook but not identical i. Textbook has answers to many of the problems ii. many will be numerical d. problems on test similar to ones in textbook and problem sets i. same principles ii. equations will be there but must understand which ones to use e. Wednesday start of class when assignments due, hand in assignments in boxes i. if passed in at end of class, considered late f. solutions will be posted on classes v2 g. need to show work, show how you arrived at your answer h. need to put down UNITS for all numerical values i. ex: what is the mass of the sun? ii. 2 x 10^30 and 1—incorrect iii. 2 x 10^30 kg and 1 solar units—correct i. No copying others’ works, but can work with others j. Post questions on classes v2 forum i. Teaching fellows will stop answering at Tuesday 10 PM k. Needs to be neat, try to box your final answers, stapled 2. Small angle formula a. Aka skinny triangle formula b. To relate the angular subtended by something ( how big and far away it is) c. S=arc length d. Α=degree of angle e. D=diameter f. d=distance g. S=α*d h. 1 degree = 60 arc minutes i. 1 arc minute=60 arc seconds j. 1 radian=206265 arc seconds k. D=αd/206265 but α must be in arc seconds l. Read box 1-1 in book for more 3. Celestial sphere a. Path of the sun through the sky aka ecliptic b. 23.5 degrees btwn it and the equator i. Intersect at autumnal and vernal equinox ii. Reason why we have seasons

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Winter solstice=dec 21 North pole never sees sun c. Summer solstice=jun 21 i. Sun almost goes thru zenith ii. South pole never sees sun d. Must be between two tropics in order to see sun go through zenith Earth spins like a top a. Fatter around equator b. Means that the gravitational attraction of sun and moon c. Earth’s axis of rotation changes direction d. 23 hours and 56 minutes in a day i. Earth rotates 23 hours and 56 minutes relative to stars Pole of the earth moves through the sky a. Right now close to Polaris b. Thuban used to be north star thousands of years ago The moon’s diameter is 27% of the earth’s a. Moon is about 30 earth diameters from the earth Diagram explaining phases of the moon a. Moon shines because it’s large and a lot of light reflected off of it b. New moon i. Moon in same direction as the sun ii. Only see a crescent c. Moves counterclockwise i. Crescent appears to grow d. First quarter moon i. See half e. Full moon i. See entire moon f. Takes 29.5 between full moons i. Not the orbital period of moon around earth ii. Combination of moon’s orbit around earth and earth’s orbit around the sun 1. Relative to only stars, takes 27 days g. Moon used to keep time i. Early calendars used lunar calendar ii. Week about the time btwn quarter moon and full iii. But days of the week comes from names of planets and sun Another diagram of moon a. We only see one face of the moon b. If moon didn’t rotate, we would see both sides c. Consequence of tightly locked revolution d. Rotation equals period of revolution e. Moon must rotate once as it rotates around the earth iii.

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Diagram of earth and sun orbiting sun a. Moon’s orbit inclined by 5 degrees to the plane of the earth’s orbit around the sun (ecliptic) b. Intersection of two planes is a line i. Called the line of nodes c. Only when the moon is passing thru the line of nodes when there is a new moon or full moon do we get eclipses i. New moon—total solar eclipse ii. Full moon—lunar eclipse d. Otherwise, plenty of space for shadow to not strike the earth The moon is about 30 earth diameters from the earth a. Su is about 12000 earth diameters from the earth b. Sun’s diameter is about 109 times the earth’s diameter c. Red moon i. Red light has longer wavelengths ii. Pass thru atmosphere easier so astronomical objects look redder from earth Timeline of lunar eclipse a. When you see the moon going into a lunar eclipse i. See line curved ii. Because of earth’s shadow Picture of eclipse of sun a. Can see outer atmosphere of sun Moon’s orbit is not a perfect circle a. Apogee—moon at its farthest point from the earth b. Perigee—moon at its closest point from earth If solar eclipse when apogee, moon doesn’t completely cover sun Greek astronomy in brief a. Aristotle: 384 to 322 BC i. His writings had an enormous impact for about 1500 years ii. Student of plate iii. Contemporary of Alexander the great b. Cosmology of Aristotle :Geocentric cosmology i. Earth experiences changes==earthquakes, volcanoes, weather, etc ii. Heavens are on the contrary unchanging iii. Earth is stationary 1. Moon sun and planets are on the nested transparent spheres that move at a constant rates around the earth a. Means all the spheres have the same center (around the earth) 2. Starts are fixed on the outermost sphere 3. Earth and the unchanging heavens are separated at the sphere of the moon iv. Changes on the earth occur when any of the 4 elements (earth, air, fire

and water) are out of their natural place v. Moon, sun , planets, and starts do not change b/c they are made of a substance

already in its natural place 1. Fifth element, quintessence, is the perfect unchanging form of matter vi. motion of objects in the heavens (so perfect( is uniform in rate and on circles vii. because comets appear in the sky were none was seen before, they must be in the sphere of the earth and not in the heavens 1. hence, closer to the moon 2. really, they are beyond the moon viii. one notable success 1. Aristotle and other Greek astronomers said that the earth was sphere a. Different starts are seen in the sky when one moves north of south of the earth b. Lunar eclipse 16. Stellarium

Looking at Mars to see how it moves relative to stars Mark where mars is relative to a picked star and measure the angle between them c. Mars used to be close to pollux, moves toward regulus i. Mars has moved toward the west, then back to the east 1. How to explain using uniform motion? 2. All the planets do this

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Aristotle 384-322 BC a. Writings had an enormous impact for ~1500 yrs. Student of plate. Contemporary of Alexander the great Cosmology of Aristotle: a. Earth experiences changes: earthquakes, volcanoes, weather, etc b. Heavens are on the contrary unchanging c. Earth is stationary. Moon, son, and planets are o the nested transparent spheres that move at constant rates around the earth. Stare are fixed on the outermost sphere. Earth and the unchanging heavens are separated at the sphere of the moon. d. …same as last class notes… e. …because omets appear in the sky where none was seen before, they must be in the sphere of the earth and not in the heavesn (hence, closer to the moon) One notable success a. Aristotle and other greek philosophers said that the earth was a sphere i. Different starts are seen in the sky when one moves north or south on the earth ii. During a lunar eclipse, the shadow that the earth casts on the moon is curved b. Math becomes a tool by which you can apply to the heavens The motion of mars on the sky in 2011-2012 a. Movie i. Shows path of mars—goes east and then curves back to the west on 1/1/2010, then curves around to the west again 3/1/2010 ii. Direct motion 1. Planets move relative to the stars west to east iii. Retrograde motion 1. east to west b. motion difficult to explain in geocentric view c. direct retrograde direct motion d. all planets do this Ptolemy 127-151 AD a. Last of the great greek astronomers b. Book on astronomy, the almagest, was the book in astronomy for about 1000 yrs c. Ptolemaic system was geocentric and based on the deferent and epicycle, which had been invented earlier by the greek astronomer Hipparchus d. System did an excellent job of predicting planets for thousands of years Large circle around earth—deferent a. Epicycle is circle around planet b. Explains retrograde motion in geocentric system c. Planetary motion as modeled by combination of circular motions d. As seen from earth Copernicus started the revolution in 1543

1473-1543 AM Contemporary of Columbus, Michelangelo, da vinci c. Basic ideas of the cosmology of Copernicus i. Sun and NOT the earth is at the center of the universe ii. Earth rotates once on its axis once in approx 24 hours. Earth is a planet, and it and the other planets revolve around the sun on circular orbits 1. This explained the retrograde motions of the planets iii. Distance from earth to the sun must be very small compared to the distances of the stars from the Sun d. Found that Ptolemaic system did not fit with earth as its center e. Did not throw out idea of circular orbits though f. Realized that if the earth is in motion and goes around the sun, if the suns were close to the sun, we would be able to perceive motion of stars i. Thus, stars are far g. Had a few followers Shortcomings of the Copernicus model a. Kept the old idea that heavenly bodies had to move at a uniform rate on circles b. Therefore, to make his model fit the observations, he too had to use deferents and epicycles c. His model was no less complicated than ptolemy’s, and it did not predict the positions of the planet with greater accuracy Heliocentric model provided a simple explanation of retrograde motion a. Earth inside mars’ orbit b. Earth travels around sun more rapidly than mars c. Earth overtakes and passes this slower-moving planet d. Mars appears for a few months to fall behind and move backward with respect to the background of stars e. Earth in motion, mars in motion Tycho Brahe 1546-1601 a. Contemporary of Shakespeare b. Built the worlds’ best observatory and made the most accurate measurements of the stars and planets before the invention of the telescope c. Shows technology contributes a lot to knowledge of astronomy Using triangulation, Tycho determined that a comet was more distant than the moon a. The heavens therefore were not changing b. Apparent position changes (in diagram, after 12 hours) because your position changes while looking at the object c. Made a baseline, construct triangle d. People had thought moon and beyond = heavens i. Comets thought to be too irregular, too changing to be in heavens ii. Aristotle was wrong Kepler a.

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Discovered that orbits of the planets are ellipses 1571-1630 c. Tycho hired Kepler as his assistant shortly before his death d. Kepler was a mathematician and unlike tycho not an observer e. On tycho’s death, kepler “inherited’ tycho’s observations of the planets and used to the revolutionize astronomy f. If the model didn’t fit the observations, kepler would throw out the model Kepler’s 3 laws of planetary motion *IMPORTANT* a. Planets orbit the sun on elliptical orbits i. Sun is located at one of the 2 foci of the ellipse ii. Other focus is empty b. Line joining a planet and the Sun sweeps out equal areas in equal time (conservation of angular momentum) i. Planet moves fastest when closest to the sun (perihelion) 1. January ii. Slowest when farthest from the sun (aphelion) 1. July c. Square of the sidereal period of a planet is proportional to the cube of the semimajor axis of its orbit i. P2=k*a3 ii. If P is in years and a is in AU, k=1 P2=a3 iii. Avg distance from earth to sun is semimajor axis iv. *only for things orbiting around the sun Semimajor axis (a) and eccentricity (e) specify the size and shape of the ellipse a. Major axis is long “diameter” of ellipse i. Semimajor axis is half that ii. Foci located on major axis b. e=0 is a circle (one focus) c. e=0.99 is a very oblong ellipse i. foci almost on ellipse the ellipse a. distance between focus and center is e*a i. e is eccentricity b. “a” is half of long diameter c. minor axis labeled “b” (half of short diameter) eccentricity of planets a. mercury 0.206 b. venus 0.007 c. earth 0.017 d. mars 0.093 e. Jupiter 0.048 f. Saturn 0.053 a.

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Uranus 0.043 Neptune 0.010 Animation of kepler’s 1st and 2nd laws a. Kepler found by using his three laws, he was able to calculate the apparent motions of the planets Galileo a. First to view the sky with a telescope and record what he saw b. 1564-1642 c. Contemporary of Kepler, Descartes, Rembrandt… d. Saw craters on the moon e. Discovers the phases of venus f. Discovers there are four things orbiting Jupiter g. Realized sun is rotating Galileo’s observations of the phases of venus verified the heliocentric model a. Notice when venus is a thin crescent it has also a large angular size b. Units should be in arcsec (“) c. New α=58” d. Full α=10” e. Half α=24" f. Geocentric model could not explain the large variation in the angular size of venus i. Would show very little change in angular size Modern photo of Jupiter and its 4 brightest moons Sketches of Jupiter and its moons in 1620 Galileo’s trial and house arrest a. 1616, Galileo ordered by church not to teach the Copernican model which was thought to be inconsistent with holy scripture and therefore church doctrine b. 1632, Galileo published in Italian (not latin) book –dialogue concerning the two chief world systems—in which three men debate the models of the cosmos i. Scholars used latin, using Italian showed he was trying to reach to masses ii. the brilliant salviati (Galileo) argues strongly in favor of the Copernican model iii. initially neutral sagredo quickly swayed by the arguments of salviati iv. simple-minded simplicio argues in favor of the geocentric picture, ideas of Aristotle et al, and looks foolish c. church leaders, including pop urban VIII, were not amused d. Galileo put on trail, made to recant the Copernican model, ordered never to teach it and placed under house arrest of the remainder of his life e. Book is banned in catholic countries, which made it a ‘best seller’ elsewhere f. Even today, his trial is mentioned as evidence that religion, in particular the roman catholic church, is fundamentally opposed to science. g. This is a gross distortion g.

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Slide looking at a. Hot—glows deep red b. Hotter—glows reddish-orange c. Even hotter—glows yellowish-white i. Has approx the same amount of radiation all around d. Thermal radiation: radiation given off by objects that have some heat Blackbody a. Don’t confuse with black hole b. A blackbody absorbs all radiation that strikes it i. No reflection c. Blackbody emits radiation at ALL wavelengths unless its temperature is 0 Kelvin (absolute zero) d. Distribution of radiation with wavelength depends only on the temperature of the blackbody e. A hotter blackbody emits more radiation per unit surface area at every wavelength than does a cooler blackbody Blackbody curves for different temperatures a. Show how the energy leaving is distributed as a function of wavelength b. Have characteristic shape c. Intensity=energy, per second, per sq meter, per nanometer d. Have different shapes depending on temperature e. Wavelength (x-axis, nm) v. intensity (y-axis) f. Hotter black body emits more radiation per unit surface area at all wavelengths i. Curves do not intersect g. Peak of temperature curves shifting to shorter wavelengths (to left) The sun and most stars are approximately blackbodies a. Blackbody curve at 5800 K is approximately the same as the Sun’s intensity curve b. Very rare that you say a star is not like a blackbody c. But ARE NOT EXACTLY blackbodies d. Or else we wouldn’t know what the composition is The solar spectrum is not continuous and therefore the sun is not a blackbody a. However, for many problems one can approximate a star by a blackbody b. Some gaps in spectrum due to iron, sodium, hydrogen, etc Radiation laws for blackbodies a. Much less complex that non-blackbodies b. Wien’s Law i. The maximum of the blackbody curve (λmax) depends only on the temperature 1. λmax=constant/T=(0.0029 K m)/T ii. λmax= wavelength of maximum emissions in meters 1. Measures the peak on intensity curves

T=temperature in Kelvin *temperature in this class always in Kelvin Blackbodies laws continued a. Stefan-blotzmann law i. F=σT4 ii. F= energy flux, Watt/sq. meter, W m-2 iii. 1 watt=1 joule/sec iv. σ=a constant=5.67x10-8 W m-2 K-4 v. T=temperature in Kelvin vi. F is the area under these curves Luminosity a. Luminosity (L) is the rate at which electromagnetic radiation is emitted from an object i. Measured in Watts b. If F, the flux of radiation, is constant over the object i. L=(Surface area)F c. And if the object is spherical (like a star), i. L=4πR2F ii. R is radius d. And if the object is a blackbody i. L=4πR2σT4 The flux of solar radiation at 1 AU is the “solar constant”—F=1370 W m-2 a. AU is average distance between Earth and Sun b. Once the solar constant has been measured, the luminosity and the surface temperature of the sun can be determined c. Sun’s L=3.9x1026 W d. Sun’s T=5800 K Homework problem a. Sun in the center, spherical radiation b. Distance: d=1 AU i. 1.496x108 km c. Sphere d. Measure F of satellite on orbit i. F=solar constant=1370 W m-2 e. L=4πd2F=3.9x1026 W f. Homework hint, say you’re on Venus i. What’s their solar constant? ii. Radiation goes thru a smaller radiation sphere iii. Luminosity is the same, so fewer sq meters and larger solar constant Another picture of a sphere—the sun a. L=3.9x1026 W b. Amount of energy coming from one sq meter on surface of sun F i. F=L of sun/surface of sun iii.

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F=L/4πR 2 =σT4 approximately iv. T=5800 K v. R in meters Each element produces a different spectrum a. Experiment i. Add a chemical substance to a flame ii. Send light from the flame through a narrow slit, then through a prism iii. Bright lines in the spectrum show that the substance emits light at specific wavelengths only b. No two elements produce the same spectrum c. Some elements were discovered by this spectrum Chemists use spectroscopy to deduce the compositions of samples a. Astronomers use spectroscopy to deduce the composition of stars and other celestial bodies Kirchhoff’s laws a. Hot blackbody light goes thru prism i. Continuous spectrum ii. Blackbody emits light at all wavelengths b. Hot blackbody light goes thru cloud of cooler gas, then prism i. Absorption Line Spectrum 1. Atoms in gas cloud absorb light of certain specific wavelengths, producing ark lines in spectrum 2. Like continuous spectrum but with dark lines 3. At some wavelengths, less light 4. Change kind of gas and get different spectrum a. Lines in different locations ii. Emission line spectrum 1. Atoms in gas cloud re-emit absorbed light energy at the same wavelengths at which they absorb it 2. Different from absorption line spectrum because of different positioning of the prism to reflect only the cooler gas 3. These lines line up with the dark lines in the absorption line spectrum a. Exact same wavelengths 4. Mostly dark with those few lines c. Interior of the star is very hot ad emits like a blackbody d. What we call the atmosphere of the star is a cooler region e. Therefore, like the situation of a hot blackbody with a cooler gas in front Examples of absorption and emission line spectra a. The sun was once thought to be mostly iron (completely wrong) b. It does contain iron, but hydrogen is far more abundant c. Compared absorption spectrum of sun with emission spectrum of iron (in a lab on the iii.

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earth) For each emission line of iron, there is a corresponding line in the solar spectrum e...