AST201H1 Lecture 1: AST201 First half of term! Lecture 1 - 12

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Department
Astronomy & Astrophysics
Course
AST201H1
Professor
Bryan Gaensler
Semester
Fall

Description
AST201H1S: Stars & Galaxies Notes Lecture 1 – A very big mystery: the Dark Universe th (January 5 ) Aims: • Explain what the Hubble eXtreme Deep Field is, how it was produced, and what it tells us about the overall makeup of the universe • Describe the overall composition of the universe in terms of matter, energy, dark matter, and dark energy • Identify one piece of evidence for the existence of dark matter • Develop your willingness to ask “Why?” and “How do we know?” Hubble eXtreme Deep Field • Is an image of a small region of space in the constellation ‘Fornax’, containing an estimated 10,000 galaxies • How was it produced? - Hubble Space Telescope’ data accumulated from 2003 to 2004 • What does it tell us? - Reveals galaxies that date back 13.5 billion years ▪ Between 400 to 800 million years after Big Bang Overall Composition of the Universe • Normal Matter (4.9%) - Stars, Galaxies, Planets, Gas, Dust, etc. • Dark Matter (26.8%) • Dark Energy (68.3%) AST201H1S: Stars & Galaxies Notes Lecture 2 – Space, time and “space-time” th (January 10 ) • Velocity and Acceleration o Distinguish between velocity and acceleration o Apply the concepts of velocity and acceleration to describe the motion of objects o Translate descriptions of motion between the reference frames of different observers, such as a person on a moving train vs. a person on the ground • Speed of Light o Explain what it means for the speed of light to be “invariant” o Distinguish the invariance and the constancy of the speed of light • Time dilation o Use an example to show how the invariance of the speed of light gives rise to time dilation, using the example of the two observers on and off the train • Spacetime o Length Contraction o Explain how the invariance of the speed of light binds space and time together into “spacetime” Velocity and Acceleration Distinguish between velocity and acceleration • Velocity - The speed of an object in a given direction • Acceleration - Increase in the rate of speed of an object - The rate of velocity of an object in respect to time Application of velocity and acceleration to describe the motion of objects • We can only measure motion relative to a given frame of reference • E.g. the speed of a ball on a plane and on the ground, is different - Different in “different reference frames” AST201H1S: Stars & Galaxies Notes Speed of Light Explain what it means for the speed of light to be “invariant” Some unbreakable rules of light: • Light always travels at ‘c’ (in a vacuum) • No object with mass can ever reach or exceed light speed • The speed of light is the same in all reference frames - No matter the reference frame, the observable speed of light is always ‘c’ - Therefore, it is invariant Distinguish the invariance and the constancy of the speed of light Foundations of ‘Special Relativity’ • We can only measure speeds of objects relative to one another - The laws of physics apply equally to in all reference frames - But, the speed of light is invariant Q: Jackie is moving away from you at speed 0.9c. You shine a beam of light at her (at speed c, of course). How fast does Jackie measure the light to be moving? A: Light moves at the speed of ‘c’ because the speed of light is invariant AST201H1S: Stars & Galaxies Notes Time Dilation • Time flows at different rates for any two people in motion relative to one another • If someone is moving relative to you, their clock will appear to run slower to you - i.e. if they are on a moving train, and you are on the platform ▪ Their clock would appear slower to you, and vice versa ▪ “More time has passed for you than them” Use an example to show how the invariance of the speed of light gives rise to time dilation, using the example of the two observers on and off the train Train Case Case: Let’s look at motion on a train, from the perspective of two different observers. Person on the train throws a ball in the air. Train: • Person on the train says the ball went up 1 metre and came down 1 metre in 1 sec, for a speed of 2 metres/sec. Track: • Person on the tracks says that the ball went diagonally up 2 m and came diagonally down 2 m in 1s, for a speed of 4 m/s. Q: What do we usually say the two observers agree on about the ball’s motion? A: The time between throwing and catching Light Case Case: If we repeat the experiment with a laser beam bouncing off a mirror on the roof of the train, what do the two observers have to agree on? A: The speed of the light ray However: Because two observers moving relative to one another must agree about the speed of light, they must disagree about the time between events! AST201H1S: Stars & Galaxies Notes Spacetime Length Contraction • Observers in motion relative to one another also disagree about lengths and distances • If someone is moving relative to you, their lengths will all appear shorter to you o i.e. Someone on a train moving away will see their distances as longer than you see them. ▪ “they will appear shorter for you” Explain how the invariance of the speed of light binds space and time together into “spacetime” • Space and time are bound together - By the speed of light into a single entity called spacetime AST201H1S: Stars & Galaxies Notes Lecture 3 – Time Dilation and the Twin Paradox (January 12 )h • Time Dilation and the Twin Paradox • Explain the concept of time dilation and give real-world examples of its effects • Explain the Twin Paradox and its resolution o Length Contraction and the Twin Paradox Time Dilation and the Twin Paradox Time Dilation Review • Time flows at different rates for any two people in motion relative to one another • If something is moving relative to you, their clock will appear to run slower - i.e. “More time has passed for you than them” Length Contraction • Observers in motion relative to one another also disagree about lengths and distances. Q: Fritz is on Earth. Vera is flying past in a spaceship moving at 90% of the speed of light (0.9c). Which of the following best describes how they see each others’ clocks as Vera passes Fritz? A: The both see each other’s clocks running slower than their own AST201H1S: Stars & Galaxies Notes Twin Paradox • Time is based on a frame of reference - Observers of different reference frames will disagree on everything (distance, time, ages, etc.) - Like the Australia ‘up’ and ‘down’ example. Depends on who you are asking. • Each twin will claim the other’s clock is running slower to their own - Therefore, each expect the other one to be younger • The trick to resolving the paradox is to take careful account of the entire trip Q: Just before the end of the outbound trip, which twin is older? A: There is no definitive answer. It depends on who you are asking, which is why it is ‘relative’ • Turn-Around Point - Reference point changes - ‘Sudden Jerk’ before settling into new reference frame ▪ Time moves faster instantly - After settling into new reference frame, things go back to normal ▪ i.e. both see each other’s clock moving slower to their own E.g. Imagine you’re driving a car, fast, and you suddenly change into reverse. You experience a sudden jerk, before settling into your new reference frame. Explain the Twin Paradox and its resolution Q: On return, who has aged less. A: Zoomer (the one who changed reference points) • Stayer’s perspective - Constant reference point - Always saw Zoomer’s clock moving slower than his • Zoomer’s perspective - Changed reference points - Saw Stayer’s clock running faster when he turned around (at the turn-around point) AST201H1S: Stars & Galaxies Notes Length Contraction and the Twin Paradox • Observers in motion also disagree about lengths and distances • Stayer’s Perspective: - Constant reference point - Will see the distance as longer than Zoomers • Zoomer’s Perspective: - Changed reference point - Will see his distance as shorter than Stayer measurement Q: Someone on Earth would measure the star Vega to be 25 light years away. If you fly a spaceship to Vega at 0.999c, you will measure the distance to be: A: Much less than 25 light years Q: The person on Earth sees you travel 25 light years at 0.999c. They think your trip takes A: A little more than 25 years. (Because 25 light years / 0.999c) Q: YOU measure the distance between Earth and Vega as only 1 light year. Thus, at a speed of 0.999c, for you the trip to Vega takes only: A: About one year AST201H1S: Stars & Galaxies Notes Lecture 4 – Two ways to think about gravity th (January 17 ) • Name the four fundamental forces of nature - Rank them by relative strength, - Identify what role each one plays in the universe • Describe how forces are related to accelerations • Distinguish between Newtonian gravity a - and Einstein’s general relativity • Einstein’s Equivalence Principle - Explain it - Describe what it tells us about the nature of gravity • Spacetime - Describe how the presence of a mass deforms spacetime - Describe gravity in terms of spacetime curvature 4 Fundamental forces of nature • 1. Strong Nuclear force - Hold’s atomic nuclei together • 2. Electromagnetic - Makes atom cling to each other - Infinite range • 3. Weak Nuclear force - Breaks atoms apart • 4. Gravity - Makes masses attract to one another - Infinite range Q: Are stars on one side of our galaxy affected by the gravitational pull of stars on the other side? A: Yes Describe how forces are related to accelerations Q: Imagine a universe which is empty except for you and a baseball. You throw the baseball. If we ignore gravity, what will ultimately happen to the baseball? A: It will keep moving forever at a constant speed AST201H1S: Stars & Galaxies Notes Newton’s Gravity Distinguish between Newtonian gravity and Einstein’s general relativity Where G = Gravitational potential energy M = Object 1 mass m = Object 2 mass r = relative distance between two objects Q: If the distance between two stars triples, the force of gravity between them: A: decreases by a factor of 9 • First law: - Objects move at a constant speed and direction unless acted upon by an external force ▪ i.e. The moment the baseball loses contact with your hand, • It stops accelerating • Second Law: - Force = Mass x Acceleration ▪ i.e. after you throw the baseball, what will happen to you? • You will move in the direction opposite to the ball’s motion, but slower than the ball • Third Law: - If one body exerts a force on another, the other body will exert a force of equal strength but opposite direction. ▪ i.e. pressing on the force at ‘x’ force, the earth will press back at equal ‘x’ force • What keeps the moon in orbit around the Earth? - Equal forces on each other Q: If we could suddenly shut off gravity, what path would the Moon follow? A: It will go straight up AST201H1S: Stars & Galaxies Notes Einstein’s Equivalence Principle Explain it • The Equivalence Principle states that no experiment can distinguish a gravitational force from a corresponding acceleration of the whole reference frame. - i.e. ▪ The gravitational ‘force’ as experienced while standing on a massive body (i.e. Earth) ▪ Is actually the same as the force experienced by an observer in a accelerated frame of reference (away from any body of mass) Q: Imagine you’re in a spaceship, far from any object with mass. The spaceship is coasting upward at constant speed. You let go of a baseball at shoulder height. What happens to the ball? A: It will hover at shoulder height Q: Imagine you’re in a spaceship, far from any object with mass. The spaceship accelerates upward. You let go of a baseball at shoulder height. What happens to the ball? A: It falls downward toward your feet Describe what it tells us about the nature of gravity • Gravity and acceleration are: - Equivalent and indistinguishable • So, if acceleration bends light • Gravity must bend light too AST201H1S: Stars & Galaxies Notes Spacetime Describe how the presence of a mass deforms spacetime • General relativity does away with gravity - Replaces it with curved spacetime. ▪ i.e. Objects follow the straightest possible path through curved spacetime. • Matter curves Space - Space tells matter how to move Describe gravity in terms of spacetime curvature • General relativity replaces the force of gravity - i.e. freely-falling objects follow the straightest possible path through curved spacetime. AST201H1S: Stars & Galaxies Notes Lecture 5 – Black Holes: Cosmic Vacuum Cleaners? th (January 29 ) • Escape Speed o Define the term “escape speed” and explain how it changes with the mass of a body and the distance from that body o Describe what happens to bodies which attempt to orbit with speeds above and below the escape speed • Black Holes: Cosmic Vacuum Cleaners? • Schwarzschild radius o Define the term in terms of the escape speed and the speed of light. • Define the “event horizon” of a black hole • Explain why black holes are not “cosmic vacuum cleaners” Escape Speed Define the term “escape speed” and explain how it changes with the mass of a body and the distance from that body • v-orbital - Minimum speed to orbit: v = ‘v-orbital’ - Elliptical orbit: ‘v-orbital < v < ‘v-circular’ - Circular orbit: ‘v’ = ‘v-circular’ - Bigger elliptical orbit = ‘v-circular’ < v < ‘v-escape’ • v-escape - Escape velocity of an object - Where velocity is greater than the escape velocity Q: If I throw a ball with a speed just a little LARGER than the escape speed, what shape will its orbit be? A: It will be open (i.e. not a closed loop at all Q: If I throw a ball with a speed just a little SMALLER than the escape speed, what shape will its orbit be? A: Elliptical Q: If I throw a ball with a speed just a little larger than the circular speed, what shape will its orbit be? A: Elliptical AST201H1S: Stars & Galaxies Notes Q: What would happen to the escape speed if we kept crushing the Earth smaller and smaller? A: It will go up! Once the escape speed reaches c (the speed of light), nothing can get away from the crushed Earth! Black Holes: Cosmic Vacuum Cleaners? • An object with an escape speed of c or higher is a black hole - ‘A bottomless pit in spacetime’ - Singularity core ▪ Infinite density here Schwarzschild radius Define the term in terms of the escape speed and the speed of light. • The radius of the event horizon (i.e., the size of the black hole - The area in which nothing can escape from the black hole ▪ The velocity to escape is greater than the speed of light ▪ ‘V-escape’ > ‘c’ • R = 2xGxM / c^2 - 2 x Gravity x mass / light squared Q: If we add mass to a black hole, the black hole will A: Get Larger Define the “event horizon” of a black hole • Where the velocity to escape = the speed of light - ‘V-escape’ = ‘c’ • Like the border between two countries: - There is no physical object at the event horizon of a black hole ▪ Unless it is swallowing stuff Explain why black holes are not “cosmic vacuum cleaners” • Black holes exert gravitational energy on other objects as everything else also does. • Only things inside it’s event horizon get sucked in AST201H1S: Stars & Galaxies Notes Lecture 6 – Observational evidence for black holes th (January 24 ) • Observational evidence for black holes - Describe the observational evidence for the existence of black holes, including the black hole at the center of our galaxy • Distinguish between stellar-mass and supermassive black holes • Draw a diagram to explain gravitational lensing and relate it to observational evidence for the existence of black holes • Describe what would happen to Earth if the Sun was replaced by a 1 solar mass black hole Estimate the physical size of black holes of different masses (e.g. 1 solar mass, 25 solar masses, 1 million solar masses) Observational evidence for black holes Describe the observational evidence for the existence of black holes, including the black hole at the center of our galaxy Q: Which of the following would allow us to locate a black hole today? A: We could look for objects which appear to be orbiting an invisible object • Cygnus X-1 - 1973 - Astronomers discovered a star orbiting something small and dark - 15 times the mass of the Sun • This small dark thing was producing a lot of X-rays - How could that be? If nothing escapes the event horizon of a black hole? - The observable X-rays were being emitted by hot material just outside the event horizon Q: Why do we believe there is a black hole in Cygnus X-1? A: X-rays from a compact source suggests accession of hot gas into a black hole Distinguish between stellar-mass and supermassive black holes • Stellar-mass black holes - E.g. Cygnus X-1 - Form when very large stars die in huge explosions ▪ Called ‘Supernovae’ - Every galaxy probably has thousands or millions of stellar-mass black holes • Super-massive black holes - Much larger kind of black hole, AST201H1S: Stars & Galaxies Notes - Found only at the centers of galaxies • At the centre of our galaxy, this black hole has: - 4 million the mass of the Sun • Q: Which of the following would constitute the best evidence for a really huge black hole? • A: Many stars are seen orbiting something small which emits no light • Primordial black holes - The size of an atom or smaller - Would have just formed just after the big bang - No-one has ever seen one Draw a diagram to explain gravitational lensing and relate it to observational evidence for the existence of black holes Describe what would happen to Earth if the Sun was replaced by a 1 solar mass black hole Estimate the physical size of black holes of different masses (e.g. 1 solar mass, 25 solar masses, 1 million solar masses) Q: If we replaced the Sun with a black hole having exactly the same mass as the Sun, what would happen to Earth? A: Earth would continue to orbit as normal, but it would get very cold • At 25 solar mass, the earth would continue to orbit as normal • At 1 million solar mass, the gravitational pull would draw earth closer in orbit. AST201H1S: Stars & Galaxies Notes Lecture 7 – The Sun: An Ordinary Star – Part I th (January 26 ) • General Properties o Describe the general properties of the Sun in comparison to the Earth: ▪ Size, Mass, Distance • Solar Spectrum o Describe the main features of the solar spectrum: ▪ Continuous spectrum and Black Body spectrum ▪ Absorption lines • Atoms o Describe atoms in terms of their constituent particles: ▪ Protons, Neutrons, and Electrons • Explain how light generated by the Sun is absorbed to produce absorption lines • Explain how we can use absorption lines to determine the chemical composition of the Sun, or any celestial object General Properties • Size - Diameter is about 100 times Earth’s diameter • Distance - About 8 light minutes from earth ▪ i.e. we are seeing the sun as it was 8 minutes ago • Composition - Sun is made mostly of hydrogen, - A little helium - and tiny amounts of other elements Q: A light year is the distance light travels in one year through empty space. How far do you think the Sun is from Earth? A: Much less than 1 light year, 8 light minutes to be precise. AST201H1S: Stars & Galaxies Notes Solar Spectrum Describe the main features of the solar spectrum: What is light? • The sum of all colours = White (*white is not a colour in itself) - When you pass sunlight through a prism: ▪ It appears to separate into a perfectly smooth rainbow. • Light is a wave - Wavelength: ▪ A distance between two peaks (or troughs) - The wavelength of light determines its colour (and energy) ▪ Blue light = shorter wavelength - High energy (~400 nanometers) - ‘Decreasing wavelength’ ▪ Red Light = longer wavelength - Low energy (~700 nanometers) - ‘Increasing wavelength’ • All colours travel at the same speed = c AST201H1S: Stars & Galaxies Notes Continuous Spectrums • Sun ‘appears ‘to be a continuous spectrum - It has some of every colour of light AST201H1S: Stars & Galaxies Notes Blackbody Spectrums Opaque objects (things you can’t see through) emit a special kind of continuous spectrum • Every opaque object produces a blackbody spectrum - A spectrum that is continuous that goes up in the blue end and down in the red end • As you heat an opaque object, the spectrum goes up - It emits more light - The wavelength at which it emits the most light shifts to shorter wavelength ▪ i.e. If you heat up an iron bar, it willl eventually turn blue) AST201H1S: Stars & Galaxies Notes Absorption Lines • The Solar spectrum is not strictly continuous - Some specific shades of colours are missing from the sun ▪ Different stars have different spectra • Spectral lines - Missing colour lines in the spectrum • Composition: - These spectral lines tell us what the Sun and other stars are made of ▪ Particular colours that are missing in the spectrum tell us what material / element they are made of Q: Where do these lines come from? AST201H1S: Stars & Galaxies Notes Atoms Describe atoms in terms of their constituent particles: Protons, Neutrons, and Electrons Where do all these little lines come from? • Everything is made of atoms • An atom has different components: - Nucleus ▪ (in the middle made of protons + neutrons) - Electron ▪ Orbits the Nucleus ▪ Negatively charged Electrons • Electrons can only orbit in the orbitals allowed for that atom - At specific tracks / distances • The orbitals have different energies - Which decides the track it can orbit ▪ Low energy: - Orbit closer inside ▪ High energy - Orbit closer to the outside • Changing orbitals - Absorbing Light: ▪ Electrons can be forced to jump to a higher-energy orbital - Emitting Light: ▪ Electrons can drop to a lower-energy orbital • To transition between two orbitals: - An electron has to absorb or emit exactly the: ▪ Right energy ▪ / Wavelength ▪ / Colour of light - Has to be the exact shade of light / energy or else nothing happens that corresponds to the missing wavelengths AST201H1S: Stars & Galaxies Notes Explain how light generated by the Sun is absorbed to produce absorption lines • Absorption line are produced when a photon of just the right energy and wavelength is absorbed by an atom - Forcing it to jump to a higher energy orbit • The photon had energy equal to the difference of energy of the energy orbits - Because the energy levels in an element’s atoms are fixed - The size of the outward jumps made by the electrons are the same as the inward jumps - So, the pattern of the absorption lines are the same as the pattern of emission lines AST201H1S: Stars & Galaxies Notes Explain how we can use absorption lines to determine the chemical composition of the Sun, or any celestial object • Different chemical elements have different sets of orbitals - Orbitals do not have colours, only transitions between orbitals do • We can determine what a star, or any gaseous celestial object is made of by: - Matching it’s spectral lines to the spectra of substances we know of Q: If different elements have different orbitals, they must also differ in the: A: Colours / wavelength / energy of the light they can absorb Q: How might the spectrum change if we added atoms of a different chemical composition to the Sun’s outer layers? A: the spectrum would show additional absorption lines Q: To determine a star’s chemical composition, we would need to measure: A: the wavelength at which its spectrum shows absorption lines AST201H1S: Stars & Galaxies Notes Lecture 8 – The Sun: An Ordinary Star Part II th (January 30 , 2017) • Blackbody curve - Explain how we can use the shape of a celestial object’s blackbody curve to determine its temperature •
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