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Astronomy 2022B Midterm Exam Review Notes (Lecture).docx

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Astronomy 2022A/B
Chris Racknor

Astronomy 2022B Exam Review Notes Christian/Jewish/Muslim view:  God created heavens and earth Greco/Roman mythology:  Hesiod- in the beginning there was only chaos, then Erebus and Night appeared who slept together, giving birth to the heavenly light Nordic/Germanic mythology:  No earth or heaven in beginning. Rivers flowed south and hardened into ice… Hopi people:  World was endless but the Creator, Taiowa, created Sotuknang who was his agent to establish nine universes Chinese mythology:  Pangu hatched from an egg and all of the light parts flew up and became the sky and heavy parts became the earth Creation story 2012:  In the beginning there was shifting foam of strings and space, time and energy unified within the foam.  The foam cooled and there was gravity, space time and then the universe What is science?  The human effort to understand better the history of the natural world, with observable physical evidence as the basis of that understanding  The scientific method: o Observations  induction  general principle  deduction  prediction  experiments  revision (this step makes science different from other approaches) Lecture 2 The universe is big:  Earth’s diameter: o 12756 km  Earth-Sun: o 150 000 000 km  Earth-Pluto o 6 000 000 000 km  Earth-nearest stars o 10 000 000 000 000 km  Earth-centre of our Milky Way galaxy o 200 000 000 000 000 000 km  Earth-Andromeda Galaxy (M31) o 20 000 000 000 000 000 000 km  Earth-edge of observable Universe o 100 000 000 000 000 000 000 000 km Universe/Cosmology  Cosmology- the study of the universe (cosmos) as a whole  Cosmogeny, cosmogenesis (soft g): birth, start  Cosmogony (hard g): infancy  Eschatology (ch=k): senility, last days  Cosmothanatos: death, end  For the most part we will use “cosmology” to encompass all of these phases Nature of the Universe  Earth is clearly flat, despite its hills and valleys  Sky is a dome- blue during the day with stars at night  Flat earth was a common assumption among early cultures (eg. Egyptian, Mesopotamian, Hebrew)  The Greeks were the first to introduce the (correct) idea of a spherical Earth  Aristotle was the most famous of the Greek advocates for this idea  Eratosthenes (c. 240 BC) actually measured the Earth’s diameter to within 2% with no modern tools o Heard a report that at noon on the longest day of the year, shadows of columns disappeared in Egypt (indicating that the sun was directly overhead) o He postulated that a curved Earth was required and computed the diameter of the earth to a few percent His reasoning: o If the sun is far away, the light arrives almost parallel to itself at Earth o So if the sun’s rays produce no column shadows in Syene but column shadows in Alexandria, the columns at Alexandria must be tilted in respect to those at Syene o His argument was fundamentally flawed Round Earth  We don’t fall off the earth because earth’s gravity pulls things towards its centre Aristotle  Incorrectly believed that the earth was the centre of the universe and the planets/sun moved around the earth  Believed that if the earth moved, there would always be a howling wind  All of the stars seem to spin on a single sphere which we see from the inside  Because of the planets, the stars seemed to be fixed to a sphere which rotates around the earth  Aristotle’s universe required one sphere per planet (plus one for the sun and moon) to explain what was seen Planets  It’s hard to see the sun’s motion against the background stars in the daytime  If you watch the sun rise/set, you can determine which constellation the sun is in o It changes during the year o The constellation the sun is in on your birthday determines your astrological sign  The moon’s motion against the stars is the fastest/easiest to see o Moves its own width every hour o Its motion can easily be seen after just 15-20 minutes Wandering planets  Over a single night, the planets seem to follow the same fixed rotation as the stars o Over days and weeks- they can be seen to move slowly relative to the stars around them  Planets’ motion is confined to a band of twelve constellations on the sky, called the zodiac Ptolemy  Believed that the sun. moon and planets circled the earth (Aristotle)  He improved it to account for the fact that planets sometimes appear to travel backward across the sky (retrograde motion) o Retrograde motion could easily be explained by having the sphere carrying a planet slow to stop, reverse its motion, and then resume spinning forward again  Ptolemy proposed (incorrectly) that each planet moved in a small circle (epicycle) as it was orbiting the earth Problems with Ptolemy’s epicycle model:  Model was clunky and complicated- epicycles upon epicycles were required to match the observed motions reasonably well but only gave good predictions for a short time  Model couldn’t fix observations in the long term Copernican theory  Planets move around the sun, not the earth  Heliocentric universe- sun centred  Geocentric universe- earth centred Pros:  Simple  Naturally explains why inner planets never travel far from the sun  Provides natural explanation for the seasons  Provides natural explanation of retrograde motions without relying on epicycles Cons:  Couldn’t predict positions of planets  Couldn’t explain earth moving without wind being felt  The planets circled the earth because they were pure (keeping their distance) Fall of the Ptolemaic system  Tyler Brahe observed supernovas which contradicted the Ptolemaic and Aristotelian theories that an outer sphere contained all the stars and that it was perfect and unchanging  Galileo observed moons moving around Jupiter o Broke the Ptolemaic notion that things orbited because they avoided earth o He became an outspoken advocate of the sun-centred theory o The church opposed Galileo and science o Church insisted on a geocentric universe  Sir Isaac Newton postulated that all bodies exerted gravitational forces proportional to their mass and inversely proportional to the square of their distances between them o This theory predicted that elliptical orbits centred on the sun for the planets o His laws of motion also explained how the earth could move with no wind- the air simply moves along with the earth o Heliocentric system was vindicated Johannes Kepler  Proposed that planets move on slightly eccentric ellipses around the sun, not the earth What about the stars?  Galileo’s telescope could reveal previously unseen detail on the planets but showed nothing but a bright featureless dot for any star  Since the earth moved around the sun, the stars should undergo a motion called “parallax” which had never been observed Parallax  eg. Putting thumb up in front of face and closing one eye and alternating. The thumb moving is what is called parallax.  Star appears slightly shifted from different positions of the earth on its orbit  The farther away the star is (larder d), the smaller the parallax angle p  As earth orbits the sun, the position of a nearby star appears to shift against the background of more distant stars  Parallax is measured in arcseconds o 1 arcsecond of movement = 1 parsec away. o d=1/p o 1 parsec = 3.26 ly o 1 arcsecond = 1/1296000 of a circle  The only way to measure astronomical distances available to early scientists Stellar Parallax:  The first parallax for a star was only measured in 1838 by Friedrich Bessel  It revealed that the star 61 Cygni had a parallax of 0.0000872 degrees, putting it 3.15 parsecs or 10.3 light-years away  This is 160 trillion km, 650000 times further from the Earth than the Sun, and 30000 times further than any Solar System object.  The parallax of 61 Cygni is comparable to the apparent width of the tip of a ball point pen when seen at 300 meters  This star was later found to be one of the nearest of our neighbouring stars, first revealing that the scale of the Universe was truly vast… The stars  After the first stellar parallaxes, it was realized that stars were sprinkled through a vast empty space o From their brightness, they seemed similar to the sun (giant spheres of hot glowing gas) Distribution of stars:  It became clear that the Milky Way, a bright band visible across the night sky, was actually composed of many faint stars- became clear that stars were not randomly distributed and there are some in more directions than others The end of the stars:  Telescopes find that the stars don’t go on indefinitely  There is an edge to the group of stars that surround us  We call that group the Milky Way, more stars in some directions than others  The Greek name for the massive collection of matter is known as galaxies Where are we?  It was found that the Milky Way is flat and at some point, the number of stars in all directions of the MW plane was roughly the same Globular Clusters  Since GC are massive and fairly far away, they should feel the gravitational force of the entire galaxy and thus be orbiting the centre of our galaxy  Shapley found that GCs were not centred around our sun, but were off to one side Nebulae  Debate centred on mysterious faint cloud-like objects called nebulae  Some thought these were distant star clusters, that is other galaxies like our own Milky Way  Too far for parallax Spiral Nebulae:  Individual stars could not be resolved so they looked like fuzzy blobs with a spiral shape Shapley-Curtis debate  Shapely argued the nebulae were small nearby objects  Curtis argued that they were distant star clusters like our own galaxy  Observations by Edwin Hubble revealed it was made of individual stars  Nebulae are thus clearly distant galaxies, like our own Nebulae: conclusion  Some nebulae are distant galaxies and some are small nearby objects  Regardless, some were far away  Cosmos was now filled with vast star groups at incalculable distances Lecture 2 The universe  Einstein’s most famous equation, E= mc2 says that matter can turn into energy, and vice-versa  The Universe is composed entirely of two things: spacetime and matter-energy Einstein and space-time  Time and space do not stand apart (SR).  Objects in the space influence space itself (GR). Curved Space  GR abandons the idea of a flat static space that is simply a stage for matter and energy to do their thing and the idea that Gravity is just some magic influence. Instead, space is affected by the things in it  GR postulates (correctly as far as we can determine so far) that space responds to be presence of mass by curving. The more massive the object, the more curved is space, like a ball resting on a rubber sheet.  One of the strange properties of this curvature of space is that it is what causes gravity. Instead of thinking of a moon orbiting a planet because a force from the planet chains the moon to it, rather the moon simply rolls around in the bowl of curved space created by the planet’s mass. Conservation of mass-energy  It appears that, in all experiments we’ve done, the total amount of matter-energy in the Universe is constant  It may be stored or converted to different forms, but there is none that gets lost, nor is any new created. Hydrogen Fusion  Hydrogen atoms contain just one proton.  “Regular” Helium (4He) consists of two protons and two neutrons.  What the Sun does – through a complex process of fusions - is take 4 hydrogen atoms, and transform them into 1 helium atom.  A Helium nucleus has a slightly smaller mass than the combined mass of four hydrogen nuclei – a difference by about 0.7%.  So in making our helium nucleus, a tiny fraction of mass has been lost; this bit of mass has been converted into energy.  The energy is emitted in the form of gamma ray photons, and eventually will become sunlight. Einstein’s Equation  In order to use Einstein’s equation, we would have to “plug in” the stress-energy tensor which describes the position and mass of every bit of matter and energy in the Universe: an impossible task!  If the Universe is roughly uniformly filled with matter and energy (an assumption that seems correct but that we’ll re-examine later), then Einstein’s equation calculates that the space that the Universe is made of is either expanding or shrinking (depending on exactly how much matter and energy the Universe contains): it cannot be simply “sitting still”! Olber’s Paradox  If the universe were 1) infinite 2) unchanging 3) everywhere the same o Then, stars would cover the night sky Velocities of spiral nebulae  Slipher recognized that the spectra of spiral nebulae all exhibit a Doppler shift and fairly systematically a shift toward the longer wavelengths or a redshift  Hubble measured distances and redshifts for many galaxies and concluded: o The more distant a galaxy, the greater its redshift and hence the faster it moves away from us Cosmic Stretching  Even though the universe is stretching, doesn’t mean everything in it is stretching/expanding o Eg. Putting two coins on a rubber sheet. Stretching the sheet won’t stretch the coins.  The only things not bound together strongly enough to resist the expansion are neighbouring galaxies: their mutual gravity is just too weak.  That means any stretching of the Universe will only be revealed by a stretching of the distances between galaxies. Measuring speed with light  The light from the Sun (or from stars in a distant galaxy) is composed of different colours.  These colours can be revealed by water droplets (rainbow) or a glass prism into a spectrum.  The different colours correspond to different frequencies (or wavelengths) of light. Starlight  Spectra of stars are more complicated than pure colours o Characteristic lines, called absorption lines appear  These colours are absorbed by atoms in the outer layers of the stars Composition of stars  Each element absorbs a very specific pattern of light colours  From the relative strength absorption lines, one can infer the composition of stars The Doppler Effect  The light of a moving source is blue/red shifted by an amount that increases with increasing velocity. This is called the Doppler effect.  It doesn’t change the pattern of lines seen in spectra, but does shift the whole pattern.  Unshifted- stationary  Redshifted- moving away from us  Blueshifted- moving towards us  The further the Galaxy, the larger the redshift Hubble’s Law  Nowadays, the fact that more distant galaxies have higher redshifts is known as Hubble’s Law, and is one of the four pillars that current ideas of an expanding Universe rest upon.  The more distant a galaxy, the greater its redshift and hence the faster it moves away from us  v = H0x d o v= velocity o H0= Hubble’s constant o D= distance Expanding space/universe  Space is expanding, carrying galaxies along o Eg. Loaf of raisin bread expanding. Raisins are not expanding but moving along with the expanding bread. The Hubble Constant  Best value for the Hubble constant is about 22 km/s/million lightyears o For each million light-years, the velocity of galaxies increases with 22 km/s. o A galaxy 10 million light-years away will have a o velocity of 220 km/s o A galaxy that’s a billion light-years away, will have a velocity of 22,000 km/s.  The Hubble constant is a velocity per unit distance  Also expressed as 71 km/s/Megaparsec Age of the universe  It’s the inverse of the Hubble constant: t =01/H  So (1/H0) must be the age of the Universe Mass density  Gravity counteracts expansion and should slow the expansion rate  The more mass there is, the more gravity, and this the greater the expansion is slowed down Curvature and matter  Positive curvature produces a closed universe, where all space re-collapses to a single point  No curvature/negative curvature- a flat universe/open universe which will expand forever Critical Density -29  Precise calculations show that gravity can win if the density is higher thangram per cubic
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