AST1002 notes - Professor Paul Sell; Discovering the Universe PDF

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Professor Paul Sell; Discovering the Universe...

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1/8/20 Chapter 1: a modern view of the universe (L2) -The Earth ● Diameter: 7920 miles ● Moon is 4x smaller than earth app. ● Moon is 30x the diameter of earth away ● Earth is 93 mil miles from the sun ● 93 million miles = 150 million km = 1 AU -The planets ● Pluto and Ceres - not ● To be a planet, you must: - Orbit sun - Have enough mass to shape into sphere (or nearly) - Have “cleared the neighborhood” around your orbit - definition of “planet” -New Horizons Probe ● To learn more about pluto and belt -outer planets few billion miles away from the sun on average -sirius is the brightest star in the sky -sun = red supergiant -Outside of our solar system ● Lightyear: distance that light travels in one year ● How far? 6 trillion miles ● Takes 8 min for light to go from sun to earth ● Light from sun to outer planets - few hours ● look-back time -Our Milky Way Galaxy ● ~100,000 lightyears big ● ~1,000 lightyears thin (like a pancake) ● Few hundred billion stars ● Would take a few thousand years to count the stars, one per sec 1/10/20 L3 -The universe is expanding -Hubble’s Law: they are all moving away from each other and the farther away ones are moving faster Night Sky: -certain stars are up in the same place at the same time each year -official star patterns = constellations -light pollution: the brightening of the night sky caused by street lights and other man-made sources -asterisms (not constellations) ex. The Dippers

-constellations: ● Road maps to the sky ● 88 official cons around the whole celestial sphere 1/13/20 L4 Our perspectives of the stars: ● The stars are projected onto the celestial sphere ● The stars are at different distances but they are so far away that we do not have good enough depth perception The spinning earth/celestial sphere ● The stars appear to move across the sky because the earth spins like a top on its axis under our feet ● That axis points to the north and south celestial poles - Polaris, a fairly bright star conveniently happens to be very close to the north celestial pole, no such star in south (north star) -What causes the seasons? The sun changes its height in the sky because the earth is tilted with respect to its orbit -The Zodiac: the projected line of the earth - sun against some constellations Two useful universal sky references: -the height of polaris from the horizon ● Starting reference point: at the north pole, polaris is straight overhead at 90 from the horizon 1. Adjust for latitude: the height of polaris = latitude -the height of the sun from the horizon at noon ● Starting reference point: the equator at equinox 1. Adjust for seasonal tilt +/- 23.5 2. Adjust for latitude: 90 - latitude ● Latitudes to know: - Equator: 0 - North pole: 90 - Gainesville: 29.7 Example: gainesville on the winter solstice = 90 - 29.7 - 23.5 = 36.8 To see the sun at zenith you have to be + or - 23.5 from equator Circumpolar ● You can always only see half of the sky ● But as the earth rotates, other parts come into view ● Stars near the south celestial pole are never visible from gville ● Stars near the north celestial pole are always visible from gville

1/15/20 L5 -Objects above the horizon are circumpolar -We measure sizes and separations between objects in the night sky using angles ● The angular distance from the zenith to the horizon is 90 ● An angle is how big/far apart something appears, not how big/far apart it is Theta = s1/d1 tan(th) = s2/d1 sin(th) = s2/d2 (theta = th) s1 ~ s2 when theta is small When theta is small, assume: 1) Th = sin(th) = tan (th) 2) d1 = d2 3) s1 = s2 -d is always large compared to s, so theta is always small! -What are the units of theta in Theta = s/d ● Radians! ● Radians are dimensionless, just a ratio of lengths ● 2pi radians in a circle ● 360 deg = 2pi radians ● 1 radian = 57.3 degrees 1 degree = 60 arcminutes 1 arcminute = 60 arcseconds 1/17/20 L6 Chapter 2: Discovering the Universe for Yourself -if you looked at the stars in the sky half a million years in the future, you would not be able to recognize it -planets in the sky are located very close to or on the ecliptic -the phases of the moon are caused by the relative position of the sun, moon, and earth -the moon’s phase changes over the course of its orbit which takes about 29.5 days (month) -there is a far side of the moon, but it’s not always the dark side -the moon always shows the same face to the earth -shadows do not cause the phases, but they do cause eclipses -to eclipse: to block out

-Solar eclipses: the moon lies directly between the sun and the earth and casts its shadow on a small part of earth blocking the sun from view in that area ● Penumbra: partial blockage ● Umbra: complete blockage -Lunar eclipse: the earth lies directly between the sun and the moon and casts its shadow on the moon ● Why do we see a red moon during a total lunar eclipse? Red light bends at a right angle; scattering -Why don’t we see eclipses very often? ● The orbits are not perfectly aligned ● The moon’s orbit is tilted with respect to Earth’s, thus the required alignment happens only infrequently L7 1/22/20 Chapter 3: The Science of Astronomy Can you view mercury or venus at midnight? no Can you view mars at midnight? Yes Is it possible to see the waning gibbous in the morning after the sun rises? Yes, it would be setting in the west How long is a day on the moon? 4 weeks (for the moon, one rotation is equal to one revolution) Solar eclipses: saros cycle - recurrence of time of eclipses (18 years, 11 ⅓ days) The Motion of the Sun, Planets, and Stars in the Sky: How can we use them? -

Year has 365 ¼ days because this is the number of times the earth rotates per revolution We introduce leap years and make other corrections to make even divisions A year has 12 months because the moon’s orbital period is 29 ½ days; unites the lunar and solar calendars (months have inconsistent numbers of days) A week has seven days because of the sun + moon + number of naked-eye planets visible to ancient cultures: Mercury, Venus, Mars, Jupiter, Saturn

-Greeks were the first people known to make models of nature without resorting to the supernatural -Early contributions: Aristotle ● Geocentric solar system ● “Earth” (a rock) sinks, so the earth must be at the center -Pythagoras

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Spherical earth

-Only a spherical body can cast a circular shadow for all alignments of the sun, earth, moon -Ptolemaic model: the most sophisticated geocentric model ● Sufficiently accurate to remain in use for 1500 years ● Arabic translation of Ptolemy’s work named Almagest (“the greatest compilation”) -Aristarchus  : heliocentric solar system -parallax (thumb test) L8 1/24/20 How was Greek  knowledge preserved throughout history? ● Muslim world preserved and enhanced the knowledge they received from greeks ● Al-Mamun’s house of wisdom ● Fall of Constantinople, eastern scholars headed to Europe Copernican Revolution ● Nicholas Copernicus: known for reviving the heliocentric model ● Better predicted motions ● Still clung to perfect circles in “the heavens” ● His perfect circle orbits did not match observations but observation quality was poor ● Tycho Brahe ● Still clung to geocentric model bc he couldn’t detect parallax ● Johannes Kepler: Kepler’s laws of the planetary motion ● Tycho’s precise measurements of the orbits could not be explained with circles - more generally… ● Ellipse: basically an elongated circle - A circle is just an ellipse with the foci at one center - Eccentricity: e = c/a -Planet = “wanderer” Kepler’s first law: the orbit of each planet around the sun is an ellipse with the sun at one focus Kepler’s second law: as a planet (or any orbiting object) moves around its orbit, it sweeps out equal areas in equal times Kepler’s third law: more distant planets orbit the sun at slower average speeds, obeying a precise mathematical relationship (for objects orbiting the sun): pyr^2 = aAU^3 - You are only allowed to use this formula if both of two conditions are met: - 1. p must be in years and a must be in AU - 2. The object must orbit the sun The Copernican Revolution (cont) ● Galileo Galilei: prodigy and arguably the greatest scientist of his time

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“Father of modern science” First to use the telescope to take observations of the heavens (did not invent it) Observed: moons of Jupiter, the sun’s imperfection and moon’s imperfection, all the phases of Venus

Science, pseudoscience, and conspiracy theories -astrology, tarot card readers, and psychics (pseudosciences) L9 1/27/20 Chapter 4: Making Sense of the Universe How we describe motion: - Speed = distance/time (units of m/s) - Velocity: speed and direction - Acceleration: any change in velocity; units of speed/time (m/s^2) Momentum and force - Momentum = mass x velocity - A net force changes momentum, which generally means an acceleration (change in velocity) - The rotational momentum of a spinning or orbiting object is known as angular momentum What is mass? - Mass: the amount of matter in an object - Weight: the gravitational force that acts on an object (mass x g) Isaac Newton: wrote the fundamental laws describing the motion of bodies ● Invented calculus to do it Newton’s first law: Newton’s second law: force = mass x acceleration (F=ma) Newton’s third law: whenever one body exerts a force on a second body, the second body exerts an equal opposite force on the first body -A Newton is a unit of force -Newton’s laws are the consequence of fundamental conservation laws in astronomy 1) Conservation of momentum -Acceleration doesn't always result when a force is applied. What matters is the sum of all the forces on the object or the net force

-Conservation of angular momentum: the total angular momentum of the system cannot change unless an external torque is acting

1/29/20 L10 Gravitational Theory · Aristotle: the physical laws that apply on earth do not apply to the heavens, heavier objects fall to the ground faster than lighter objects · Galileo: Nope! Except in some cases (leaf, feather), but the difference is air resistance · Newton: 20 years later, apple story

The Force of Gravity: · Greater masses, greater pull · Closer together, greater pull · Everything pulls on everything else · The universal law of gravitation tells us the strength of the gravitational attraction between the two objects · How to decrease your weight? - Decrease m - Decrease M (e.g., go to the moon) - Increase d (e.g., go to a mountaintop)

Why d^2? The d^2 is geometric, Fg does not just decrease in one dimension but in two The Acceleration of Gravity: -Why do all objects fall at the same rate? - F = ma  = GMm/d^2  -m cancels, so a does not depend on it -but a does depend on M and d^2 Understanding Orbits: so, if the earth is exerting a gravitational force on the moon, and the moon is exerting a force on earth, why aren’t they falling together? They actually are How do we know the masses of astronomical objects? · W  hat formulae do we know involve mass? · From orbits! -> Newton’s version of Kepler’s third law · How do we know the mass of the sun?

-when one mass is so much larger than the other, you can ignore it (again, only when adding/subtracting, not multiplying/dividing) Gravity (why it is so important) · · · ·

Causes

the earth to have an atmosphere Causes planets to orbit around the sun Caused a cloud of gas and dust to collapse to form the solar system ………..

Tides · Tides from the moon - F=GMm/d^2 - What is F at different d’s? · Moon and sun (spring and neap tides) - Spring tides occur at new moon and full moon - Neap tides occur at first and third quarter moon · What about tides from other objects? M is too small and d is too large 1/31/20 L11 Chapter 5: Light, The Cosmic Messenger -light is both a wave and a particle Traveling Waves - A comparison to sound - The speed of sound depends on the properties of the medium - In space, no one can hear you scream Is this true for light? How are light waves traveling (what medium)? ● They require no medium! ● Analogy to magnets What is light? ● We don’t notice the waves when they are short ● We do notice the waves easier when they are long What exactly is a light wave? ● Light is a small disturbance in an electric field which creates a small magnetic field, which in turn creates a small electric field, and so on… ● For this reason, we also call light electromagnetic radiation

-The disturbance of light is always measured to travel at the same speed in a vacuum, 300,000 km/s, and is a type of wave that doesn't need a medium to travel through -Nothing can travel faster than the speed of light (cosmic speed limit of information). Einstein found that anything with mass takes an infinite amount of energy to do so. Wavelength, frequency, and speed -If three waves all pass by at the same speed, the waves with the shorter wavelengths pass by more often Light is more than just a messenger, light is the primary means by which energy is transported throughout the universe. Think about how the sun warms us Sometimes it is more convenient to talk about light in terms of its energy Einstein won the 1921 Nobel Prize for calculating the energy of a photon Light and Color ● The wavelength of light is related to the color that we perceive with our eyes How to describe light -The number of photons versus the energy of photons How to describe the amount of light: energy and luminosity (power) ● E = energy per photon ● L = luminosity of a source Why are some lines fainter than others? ● The probability that the atom will emit a photon changes from line to line (requires quantum mechanics) ● Something (e.g. dust, gas) gets in the way to block or redirect the light 2/3/20 L12 -Light waves travel all at the same speed -shortest to longest wavelengths: gamma rays, x rays, uv, infrared, radio Continuous Spectra Blackbody: Ideal thermal emitter (object glows) ● A perfect absorber: no light is reflected so it appears black ● Light comes from the heat of an opaque object Two Blackbody Trends 1) Wein’s (Veen’s) Law 2) Stefan-Boltzman Law

Discrete Spectra -if we enlarged a Hydrogen atom until its nucleus was the size of a grape, its orbit would be the size of a football field The Atom ● Quantum mechanics tells us that electrons sometimes behave as particles and sometimes as waves ● Electrons don’t move on fixed paths about the nucleus like the planets about the sun ● Instead they can be thought of as inhabiting “probability clouds” called orbitals around the nucleus Electron Orbitals ● Electron orbitals are “quantized” - they exist only at particular energies ● The lowest energy orbital is called the ground state Absorption of a photon ● If a photon of exactly the right energy (corresponding to the energy difference between orbitals) strikes an electron, that electron will absorb the photon and move into the next higher orbital - The atom is now in an excited state Emission of a photon ● Conversely, if an atom drops from one orbital to the next lower one, it must first emit a photon with the same amount of energy as the orbital energy difference The Chemical Elements ● The number of protons (atomic number) in a nucleus determines what element a substance it ● Each element has a number of electrons equal to the number of protons Kirchoff’s Laws Doppler Shift: caused by waves compressing or stretching as the waves move toward or away from you (train example) L13 2/5/20 The sun’s surface temp is around 6000 degrees Kelvin. If it were to suddenly become hotter, where would most of its radiation be emitted? ● In the optical, uv, x ray, or gamma ray region depending on the temp change

If you took a spectrum of perfect blackbody emitting stars through a cold cloud, what would you see? ● A blackbody spectrum with absorption lines superimposed Telescopes ● Collect light ● Help us see smaller projected (in angle) objects ● Galileo was the first astronomer to use a telescope ● Light buckets; they collect photons like buckets collect rain water Two main types of optical telescopes: 1) Refractors ● Example: Yerkes Observatory ● 1 meter 2) Reflectors ● Very large telescopes (VLT) 8 meters each ● Keck Telescopes 10 meters each How much more sensitive are the 10 meter telescopes than the human eye (~1cm)? ● One million times (1000^2) ● But telescopes can take longer exposures and are more efficient, so this number actually grows to billions of times Why build large telescopes? ● Collecting area ● Resolution: there is a limit because the waves interfere with one another Varying resolution images ● Resolution reveals finer detail ● Magnification just makes the image bigger ● Generally, resolution is better but more difficult than magnification L14 2/7/20 Chapter 6: Formation of the Solar System Interferometry ● Equivalent to the collecting area of all the dishes added up together, but the angular resolution of the distance between the dishes Very Long Baseline Array (VLBA) ● The resolution of a telescope thousands of miles across

Why would it be useful to build a radio telescope on the far side of the moon (as opposed to building one here on earth)? ● Because the moon would always block radio waves ● There is no atmosphere on the moon - the atmosphere does not scatter radio light the way it does optical light (this makes it blue) Seeing the Universe Using More than just Light: -Other ways to see the universe through ● Neutrinos - a type of particle often referred to as a “ghost particle” because it rarely interacts with matter - From extreme processes in space: stellar explosions, fusion in the sun - Detected with a huge tank underground ● Cosmic rays - free charged particles: protons, electrons, etc. - From all kinds of energetic sources - Detected with specially-tuned telescopes ● Gravitational waves - waves caused by the extreme flexing of space itself - From extreme sources (black holes) - Detected by seeing the Dopler shift The Interstellar Medium ● In addition to stars, the Milky Way also contains lots of gaseous matter between the stars ● The gas in the above image is glowing red; dust absorbs or scatters away starlight, acting as a screen, so it shows up black Interstellar Dust ● More like the dust in a coal mine, mostly carbon and silicon grains (sometimes with coating water ice, ammonia, or methane) in an irregular configuration ● Dust grains come in a range of sizes but typically they are of order 500 nm Summary of cloud collapse: ● Collisions excite molecules that then radiate away the energy ● Temperature down means pressure down -> cloud can collapse L15 2/10/20 Chapter 6 and Chapter 7: Earth and the Terrestrial Worlds Where we left off: particles stick together due to condensation Hierarchical planet formation: 1) Planet seeds form by collisions of microscopic dust (=rock) and ice particles in the outer parts of the protoplanetary disk

2) Colliding particles stick together, making bigger particles. We call these bigger (~> 1km) “particles” planetesimals 3) Bigger planetesimals sweep up more particles than smaller ones 4) Some planetesimals grow massive enough to attract other particles by gravity (gravitational focusing) -> coalescence 5) The more particles they attract, the more massive they become, the more they attract, the more runaway growth! Inner vs Outer Planets Why are the outer planets more massive? ● Thy grow faster because they could accumulate not just rock, but also ice particles (and H and He at ~15 M) Exception: some strange things about our moon 1) No other terrestrial planets have moons (except for mars with captured asteroids 2) It is really massive compared to other moons - planets (via gravity) are generally moon (planetesimal) collectors - how could the earth catch it? How do we know the age of the solar system? ● isotopic - the ratio of different isotopes (same elements with different numbers of neutrons) ● carbon -14 dating ● This radioactive isotope of carbon (6 protons, 8 neutrons - imbalanced) radioactively decays (spontaneously changes) into nitrogen-14 (7 protons and neutrons - more balanced) ● Because th...