Notes from the whole semester
Notes from the whole semester

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School
University of California - Berkeley
Department
Astronomy
Course
ASTRON C12
Professor
Geoffrey Marcy
Semester
Fall

Description
Chapter 1; Our modern view of the universe Our place in the universe: Earth orbits the Sun. - The Sun is one of over 100 billion stars in the Milky Way Galaxy - Our galaxy is one of about 40 galaxies in the Local Group - The Local Group is one small part of the Local Supercluster o Which is a small part of the Universe. The universe began with the Big Bang and has been expanding ever since, except in localized regions where gravity caused matter to collapse into galaxies and stars. - The Big Bang produced hydrogen and helium, the rest of the elements have been produced by stars and recycled within galaxies from one generation of stars to the next i.e. we are “star stuff”. The age of the universe limits the extent of the observable universe. The universe is about 14 billion years old and so the observable universe extends to about 14 billion light years. Beyond that, it is back in time before the universe existed. 1 light year = 9.46 trillion km 1 AU = 149.6 million km Nearest (3) star system; Alpha Centauri – 4.4 light years away Giant cloud of stars; Orion Nebula – 1500 light years away Andromeda Galaxy – 2.5 million light years away Diameter of the Milky Way – 100 000 light years Scale of the universe: The observable universe contains approx. 100 billion galaxies and the total number of stars is comparable to grains of dry sand on all beaches on Earth. On a cosmic calander, human civilization is a few seconds old and human lifetime lasts only a fraction of a second. Spaceship Earth: Earth rotates on its axis once each day and orbits the Sun once each year. The axis tilt of the Earth is 23.5° to a line perpendicular to the ecliptic plane (Earth’s orbital path). It happens to point almost directly at Polaris (North Star) - Our Sun and other stars in the neighborhood orbit the centre of the Milky Way every 230 million years (entire galaxy is rotating). All galaxies beyond the Local Group is moving away, more distant galaxies are moving faster i.e. expanding universe. Chapter 2; Discovering the Universe for Yourself Patterns in the night sky: Stars and other celestial objects appear to lie on a celestial sphere surrounding Earth. We divide this into constellations with well- defined borders. From any location on Earth we see half the celestial sphere at any one time as the dome of our local sky. The zenith is the point directly overhead. The meridian runs from due south to due north through the zenith. Earth’s rotation makes stars appear to circle around the Earth. Stars whose complete circle lies above our horizon is circumpolar i.e. can be seen at all times. Others have circles that cross the horizon and rise in the east, sets in the west. - Constellations vary with latitude but not longitude. - Constellations vary with time of year as we orbit the Sun Cause of seasons = Earth’s axis tilt. Sunlight hits different parts of the Earth more directly at different times of the year. - Earth’s 26 000 year cycle of precession changes the orientation of the axis in space. The changing orientation of axis doesn’t affect season patterns but changes the identity of North Star and shifts locations of solstices and equinoxes in Earth’s orbit. Altitude of celestial pole in the sky = latitude Ecliptic; path the Sun follows as it appears to circle around the celestial sphere once a year. Angular size; angle it appears to span in your field of view. Angular size = physical size 360° 2π x distance Angular distance; angle that appears to separate a pair of objects in the sky. Solstices – two points at which sunlight becomes most extreme for the 2 hemispheres Equinoxes – two points at which the hemispheres are equally illuminated The Moon; Average distance from Earth = 380 000 km The moon rotates relative to a fixed point and so one side always faces the Earth. A new moon to the next takes 29.5 days. The times indicated in the picture depicts when the moon is at its highest point during each lunar phase. The moon is in synchronous rotation i.e. it rotates on its axis in the same amount of time that it takes to orbit the Earth. Eclipses Lunar – Earth lies directly between Sun and Moon i.e. full moon Solar – Moon lies directly between Earth and Sun i.e. new moon The shadow of the Moon/Earth consists of 2 distinct regions; umbra (sunlight completely blocked) and penumbra (sunlight partially blocked). Lunar eclipse; begins when Moon’s orbit carries it into Earth’s penumbra. - When perfectly aligned = total lunar eclipse. Moon becomes dark and eerily red during totality - When part of full moon passes through umbra = partial lunar eclipse - When moon passes only through Earth’s penumbra = penumbral lunar eclipse Solar eclipse; - If a solar eclipse occurs when the moon is relatively close to Earth, moon’s umbra touches small area of Earth’s surface (about 270km diameter) = total solar eclipse o Surrounding this region of totality (7000km in diameter) is the area that falls within the moon’s penumbral shadow = partial solar eclipse - If a solar eclipse occurs when the moon is relatively far from Earth, its umbra shadow may not quite reach Earth’s surface = annular eclipse Planetary motion Planets generally move eastward relative to the stars over the year, but for weeks-months they reverse course during apparent retrograde motion. This occurs when Earth passes (or is passed) by another planet in its orbit. Stellar parallax = slight apparent shifts in stellar positions over the year. As we view stars from different places in our orbit at different times of year, nearby stars should appear to shift back and forth against the background of more distant stars. Chapter 3; The science of Astronomy What ancient civilizations achieve in astronomy - Determining time of day o Egyptian obelisks o Phase of moon during different times o Time of constellations rising/setting - Marking the seasons o Stonehenge, Templo Mayor o Many city infrastructure e.g. roads run NSWE - Lunar calendar o Tracked lunar phases and used the lunar cycle as the basis of their calendar - Ancient structures and archeoastronomy Ptolemic model; Ptolemy’s model still placed Earth at the center of the universe. To explain apparent retrograde motion of planets, he applied an idea that each planet moves around Earth on a small circle that turns upon a larger circle. The larger circle is called the deferent and the smaller was called the epicycle. This remained in use for the next 1500 years. Copernicus, Tycho and Kepler challenges the geocentric model Nicholas Copernicus (1473-1543) - Tried Aristarchus’s heliocentric idea first proposed over 1700 years earlier - Recognized the much simpler explanation for apparent retrograde motion by a heliocentric system - Held the belief that heavenly motion must occur in perfect circles, forced to add complexities to his system, no more accurate, no less complex than Ptolemic model Tycho Brahe(1546-1601) - Observed Jupiter and Saturn and complied careful observations of stellar and planetary positions in the sky - Compiled naked-eye observations accurate to within less than 1 arcminute - Unable to detect stellar parallax, concluded that Earth remained stationary - Advocated a model where Sun orbits Earth while all others orbited the Sun Johannes Kepler(1571-1630) - Difficulties matching Mars data to circular orbit - Discovered that planetary orbits aren’t circles but an ellipse o Two foci o Major axis, semimajor axis o Varying eccentricity i.e. how stretched compared to a circle, whose eccentricity is zero Kepler’s Laws of Planetary motion 1. The orbit of each planet around the Sun is an ellipse with the Sun at one focus - A planet’s distance from the Sun varies during its orbit, closest at the perihelion and farthest from the aphelion. - The average of a planet’s perihelion and aphelion distances is the length of the semimajor axis. 2. As a planet moves around its orbit, it sweeps out equal areas in equal times - The planet moves a greater distance near perihelion than it does in the same amount of time near aphelion - The planet travels faster when it is nearer to the Sun and slower when it’s further from the Sun 3. More distant planets orbit the Sun at slower average speeds 2 3 - P = a - The fact that more distant planets move slower led Kepler to suggest that planetary motion might be the result of a force from the Sun Galileo - Refuted 3 objections; o Birds, falling stones and clouds should stay with Earth rather than falling behind as a moving object remains in motion unless a force acts to stop it o Tycho’s supernova and comet observations showed that the heavens could change. Galileo saw through the telescope that there were imperfections on the moon and Sun o Galilio saw through the telescope that the Milky Way resolved into countless individual stars therefore the stars are more distant than Tycho thought  He also discovered that there were four moons orbiting Jupiter, not Earth.  Venus also goes through phases in a way that make sense only if it orbits the Sun and not Earth The scientific method 1. Make observations 2. Ask a question 3. Suggest a hypothesis 4. Make a prediction 5. Test, experiment, additional observation If supports hypothesis, make additional predictions and test them If does not support hypothesis, repeat from 3. Hallmarks of science - Modern science seeks explanations for observed phenomena that rely solely on natural causes - Science progresses through the creation and testing of models of nature that explain the observations as simply as possible - A scientific model must make testable predictions about natural phenomena that would force us to revise/abandon the model if the predictions didn’t agree with observations Astrology – search for hidden influences on human lives based on apparent positions of planets and stars in the sky, no scientific validity. Chapter 4; Making sense of the Universe Speed – how far an object will go over a certain period of time Velocity – speed and direction Acceleration – velocity, speed or both changing Acceleration of gravity (g) = 9.8 m/s on Earth Momentum = mass x velocity Any object that’s either spinning or moving along a curved path has angular momentum . Angular momentum can change only when a special type of force is applied to it. The type of force that can change an object’s angular momentum is called a torque (twisting force). Mass – amount of matter in the body Weight – the force that a scale measures. Weight depends on mass and forces (e.g. gravity) that is acting on the mass. Free-fall causes weightlessness and occurs when there’s nothing preventing falling. The Space Station is orbiting the Earth as it is “falling around” the Earth. This constant state of free fall makes the spacecraft weightless. Newton’s Laws of Motion 1. An object moves at constant velocity if there is no net force acting upon it - Objects at rest tend to remain at rest and objects in motion tend to remain in motion with no change in either their speed or direction 2. Force = mass x acceleration - This explains why larger planets have greater effect on asteroids and comets than a small planet. o Because Jupiter is more massive, it exerts a stronger gravitational force on passing asteroids and comets, scattering them with greater acceleration - When travelling around curves, objects are accelerating even though they are at constant speed. A force pulls the object inward to keep it from flying off. 3. For any force, there is always an equal and opposite force - Objects always attract eachother through gravity - Smaller objects accelerate faster as the force is being divided by a smaller mass Conservation laws in astronomy Conservation of momentum ; the total momentum of interacting objects can’t change as long as no external force is acting on them i.e. total momentum is conserved. An individual object can gain/lose momentum only if some other object’s momentum changes by a precisely opposite amount. Conservation of angular momentum ; as long as there is no external torque, the total angular momentum of a set of interacting objects can’t change. - An individual object can change its angular momentum only by transferring some angular momentum to or from another object. Orbital angular momentum; Angular momentum = mvr Where m is Earth’s mass, v is its velocity around the orbit and r is the radius of the orbit (distance from Sun). Because there are no objects to give/take angular momentum from Earth as it orbits Sun, its orbital angular momentum must stay constant. This is why Kepler’s second law is true. Rotational angular momentum; The same idea explains why Earth keeps rotating. As long as Earth isn’t transferring any of the angular momentum of its rotation to another object, it keeps rotating at the same rate. Conservation of energy ; energy cannot appear out of nowhere or disappear into nothingness. Objects can gain/lose energy only by exchanging energy with other objects. Types of energy – - Kinetic; motion o Thermal - Radiative; carried by light - Potential; stored o Gravitational o Chemical Thermal energy measures the total kinetic energy of all randomly moving particles, while temperature measure the average kinetic energy of the particles. The density and number of particles also matter i.e. boiling water would burn faster than an oven. Potential energy - Gravitational potential energy depends on mass and how far the object can fall as a result of gravity i.e. more GPE when its higher up. o Gravitational potential energy = mgh  Where m is the mass, g is the acceleration of gravity and h is the height. Before a star forms, its matter is spread out in a large, cold gas cloud. Most of the particles are far from the center and therefore have a lot of GPE. The particles lose GPE as the cloud contracts under its own gravity and this “lost” GPE gets converted into thermal energy, making the center hot. - Mass-energy is the energy contained in mass itself. Mass is a form of potential energy, mass can be converted to other forms; o E = mc 2 - E is amount of potential energy, m is the mass of the object and c is the speed of light. o This suggests that a small amount of mass contains a huge amount of energy. o This also suggests that energy can be transformed into mass. This idea is important when thinking about when some of the energy of the Big Bang turned into the mass from which we’re made. Conservation of energy; energy cannot be lost or created; only transferred from one form to the other. Universal Law of Gravitation - Every mass attracts every other mas through gravity - The strength of the gravitational force attracting any 2 objects is directly proportional to the product of the masses. i.e. doubling the mass of one object doubles the gravity between the 2 objects - The strength of gravity between 2 objects decreases with the square of the distance between their centers. o Gravitational force therefore follows the inverse square law Ultimately; Where F ig the force of gravitational attraction, M 1nd M 2re the masses of the 2 objects, and d is the distance between their centers. G is the gravitational constant, 6.67 x 10 -11m /(kg x s )2 How Newton’s law of gravity extended Kepler’s laws; - He showed that any object going around another object will obey Kepler’s first 2 laws - He showed that bound orbits as ellipses (or circles) aren’t the only orbital shape; orbits can also be unbound and in the form of parabolas or hyperbolas - He showed that two objects actually orbit their common center of mass - Newton’s version of Kepler’s third law allows us to calculate the masses of orbiting objects from their orbital periods and distances Bound orbits = orbits in which an object goes around another object over and over again i.e. gravity creates a bond that holds the objects together Bound orbits are ellipses Unbound orbits = paths that bring an object close to another object just once e.g. some comets that enter the inner solar system follow this, they come in from afar once, loop around the Sun and never return. Unbound orbits are parabolas or hyperbolas. These orbital shapes are known as conic sections because they can be made by slicing through a cone at different angles. Objects on unbound orbits still obey the basic principle of Kepler’s second law: They move faster when closer to the object they’re orbiting and slower when they’re further away. Newton showed that 2 objects attracted by gravity both orbit around their common center of mass (the point at which the two objects would balance if they were connected. When one object is more massive than the other, the center of mass lies closer to the more massive object. The Sun is so much more massive than the planets that it is difficult to notice the Sun’s motion about this center. Newton’s version of Kepler’s third law This equation allows the measurement of orbital period and distance in any units. It shows that the relationship between the orbital period and average distance depends on the masses of the orbiting objects. When an object is much less massive than the object it orbits, we can calculate the mass of the central object from the orbital period and average distance of the orbiting object. Orbits, tides, and the acceleration of gravity Orbits cannot change spontaneously according to the law of conservation of energy i.e. total orbital energy = gravitational potential energy + kinetic energy. However, they can change through exchanges of energy. Ways; - Gravitational encounter, in which they pass near enough so that each can feel the effects of another’s gravity. o E.g. in rare cases in which a comet happens to pass near a planet, the comet’s orbit can change dramatically - Atmospheric drag; friction can cause objects to lose orbital energy e.g. Earth’s thin upper atmosphere can gradually cause a satellite to lose orbital energy until it falls. Orbital energy is converted to thermal energy so the satellite usually burns up - Escape velocity; an object that gains orbital energy moves into an orbit with a higher average altitude. o If a spacecraft has enough orbital energy, it may end up in an unbound orbit that allows it to escape Earth.  The minimum escape velocity from Earth is 40 000 km/hr  Escape velocity does not depend on the mass of the object, however does depend on whether the object starts from the surface or from someplace above the surface. The Moon’s tidal force Because the strength of gravity declines with distance, the gravitational attraction of each part of Earth to Moon becomes weaker as we go from the side of Earth facing the Moon to the side facing away from the Moon. - This difference in attraction causes a “stretching force” aka tidal force that stretches the entire Earth to create 2 bulges, one facing towards and one facing away from the Moon o This is tides rise and fall twice a day in most places - Tides affect both land and ocean but water flows much more readily than land o Earth’s rotation carries any location through each of the 2 bulges each day, creating 2 high tides. o Low tides occur when the location is at the points halfway between the 2 tidal bulges. - The height and timing of tides can depend on factors e.g. latitude, orientation of coastline (e.g. north facing or west-facing), and depth and shape of any channel through which the rising tide must flow The Sun’s tidal force - Overall weaker than the Moon’s as it is much further away - When tidal forces of Sun and Moon work together i.e. at both new moon and full moon, we get spring tides. When the tidal forces of the Sun and the Moon counteract eachother i.e. at first and third quarter Moon, we get neap tides. Because tidal forces stretch Earth itself, its rotation creates tidal friction. The Moon’s gravity tries to keep the tidal bulges on the Earth-Moon line, while Earth’s rotation tries to pull the bulges around with it. - The resulting “compromise” keeps the bulges just ahead of the Earth-Moon line - This causes Earth’s gravitation to slow very gradually, it also pulls the Moon slightly ahead in its orbit, adding to the Moon’s orbital energy and causing the Moon to move gradually farther from Earth. o The effects are barely noticeable but over billions of years, Earth’s day may have been a few hours long and the Moon may have been much closer to Earth. The Moon’s synchronous rotation is a natural consequence of tidal friction. The Earth’s tidal force on the Moon gives it 2 tidal bulges along the Earth-Moon line. If the Moon rotated through its tidal bulges in the same way as Earth, the resulting friction would cause the Moon’s rotation to slow down. - The Moon probably once rotated much faster than it does now, it rotated through its tidal bulges and the friction caused it to gradually slow down. At the point where the Moon and its bulges rotated at the same time (synchronously), there was no further source for tidal friction Chapter 5; Light and Matter Energy that light carries = radiative energy Rate of energy flow is power and is measured in watts. 1 watt = 1 joule/s A power of 1 watt means an energy flow of 1 joule per second Primary colors of vision (red, blue, green) are the colors directly detected by cells in the eyes. Spectrums (white light splitting) can be produced with a prism or diffraction grating How light interacts with matter: - Emission; - Absorption - Transmission (allows light to pass through) - Reflection/scattering Materials that transmit light are transparent and those that don’t are opaque Properties of Light Wavelength – distance from one peak/trough to the next Frequency – number of peaks passing by any point each second, measured in cycles per second or hertz Speed of the wave is how fast their peaks travel Wavelength x frequency = speed The forces that charged particles exert on one another in terms of electric fields and magnetic fields. Light waves are vibrations of both fields caused by motions of charged particles. Therefore light is an electromagnetic wave. Light travels at 300 000 km/s Light behaves as both a wave and particle i.e. light comes in photons. Each photo carries a specific amount of radiative energy. The shorter the wavelength, the higher the energy of the photon. Visible light is a small portion of the electromagnetic spectrum. Visible light has wavelengths ranging from about 400 to 700 nanometers. Wavelengths longer than red is called infrared, those shorter than violet are ultraviolet. Certain types of matter tend to interact more strongly with certain types of light, so each type of light carries different information about distant objects in the universe. Properties of Matter All ordinary matter is composed of atoms which come in different types, each type corresponds to a different chemical element. Each chemical element consists of a different type of atom. Atoms contain the particles proton, neutron, and electrons. The properties depend mainly on electrical charge (fundamental physical property that describes how strongly an object will interact with electromagnetic fields) in the nucleus. Isotopes have the same number of protons but different numbers of neutrons. The appearance of matter depends on its phrase: - Solid - Liquid - Gas At high temperatures, molecular dissociation breaks up molecules and ionization strips electrons from atoms. An ionized gas is called plasma. Electrons can exist in particular energy levels within an atom. Energy level transitions, in which an electron moves from one energy level to another can occur only when the electron gains or loses just the right amount of energy. Types of spectra; - Continuous = looks like a rainbow of light - Absorption line = specific colors are missing from the rainbow - Emission line = we see light only with specific colors against a black background  Emission or absorption lines occur only at specific wavelengths that correspond to particular energy level transitions in atoms or molecules  Every kind of atom, ion, and molecule produces a unique set of spectral lines, so we can determine composition by identifying these lines. Objects such as planets and stars produce thermal radiation spectra, the most common type of continuous spectra. We can determine the temperature from these spectra because hotter objects emit more total radiation per unit area and emit protons with a higher average energy.  The spectrum of a real object generally shows a combination of features of emission line, absorption line, and thermal radiation spectra, as well as features produced by reflection.  By carefully studying the spectral features, we can learn a lot about the object that produced them. The Doppler effect tells us how fast an object is moving toward or away from us. Spectral lines are shifted to shorter wavelengths (blueshift) in objects moving toward us and to longer wavelengths (redshift) in objects moving away from us.  The Doppler effect broadens spectral lines of rotating objects. The faster the rotation, the wider the spectral line. Chapter 8; Formation of the Solar System The nebular theory best explains the features of our solar system. It holds that the solar system formed from the gravitational collapse of a great cloud of gas and dust, successfully explains all the major features of our solar system. The cloud that gave birth to our solar system was the product of recycling of gas through many generations of stars within the galaxy. This material consisted of 98% hydrogen and helium and 2% of all other elements combined  A collapsing gas cloud tends to heat up, spin faster, and flatten out as it shrinks. Thus, our solar system began as a spinning disk of gas and dust. The orderly motions we observe today all came from the orderly motion of this spinning disk. Within the frost line, temperatures were so high that only metal and rock could condense; beyond the frost line, cooler temperatures also allowed more abundant hydrogen compounds to condense into ice. Terrestrial planets formed inside the frost line, where accretion allowed tiny, solid grains of metal and rock to grow into planetesimals that ultimately merged to make the planets we see today. - Accretion built ice-rich planetesimals in the outer solar system, and some of these icy planetesimals grew large enough for their gravity to draw in hydrogen and helium gas, building the Jovian planets What ended the era of planet formation was that the young Sun had a strong solar wind, which ultimately swept away material not yet accreted onto the planets. Once the solar nebular was cleared away, planet formation ceased because there was little material left to accrete. Asteroids are the rocky leftover planetesimals of the inner solar system, and comets are the ice-rich leftover planetesimals of the outer solar system.  Most of the exceptions probably arose from collisions or close encounters with leftover planetesimals, especially during the heavy bombardment that occurred early in the solar system’s history. Our Moon is probably the result of a giant impact between a Mars-size planetesimals and the young Earth. The impact blasted material from Earth’s outer layers into orbit, where it reaccreted to form the Moon.  A solar system like ours was probably destined to form from the collapse of the solar nebula, but individual planets were probably affected by random event that could have happened differently or not at all - Radiometric dating is based on carefully measuring the proportions of radioactive isotopes and their decay products within rocks. The ratio of the isotopes changes with time and provides a reliable measure of the rock’s age - The planets began to accrete in the solar nebula about 4.5 billion years ago, a fact we determine from radiometric dating of the oldest meteorites. Chapter 9; Planetary Geology What are terrestrial planets like on the inside? - In order of decreasing density and depth, the interior structure consists of core, mantle, and crust. The crust and part of the mantle together make up the rigid lithosphere. o In general, a thinner lithosphere allows more geological activity What causes geological activity? - Interior heat drives geological activity by causing mantle convection, keeping the lithosphere thin, and kee
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