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AST1002 Exam #1 Review

by: Anna Cappelli

AST1002 Exam #1 Review AST1002

Marketplace > University of Florida > Astronomy > AST1002 > AST1002 Exam 1 Review
Anna Cappelli
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this is a study guide for the first exam in astronomy Ch.0-Ch.3
Discovering the Universe
Reyes,Francisco J.
Study Guide
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This 19 page Study Guide was uploaded by Anna Cappelli on Thursday February 4, 2016. The Study Guide belongs to AST1002 at University of Florida taught by Reyes,Francisco J. in Fall 2015. Since its upload, it has received 50 views. For similar materials see Discovering the Universe in Astronomy at University of Florida.


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Date Created: 02/04/16
Thursday, February 4, 2016 Astronomy Exam #1 Review Charting the Heavens Distance Units Im = 1yard 1 km = .62 miled = 1,000 m 1 AU (astronomical unit) = distance from earth to sun = 150x10^6 km 1 light year (ly) = distance traveled nu light in 1 year = 10^12 km speed of light c= 3x10^5 km/s velocity = space/time v = s/t or t=s/v because it takes light a long time to reach other objects in space, we are usually observing distant object as they were in the past Constellations although many have a tendency to connect stars into shapes, they really don’t represent anything special - this cluster of stars is simply called a constellation 88 in the sky these stars within the constellation are usually not very close together constellations move from east to west across the sky but their relative position stays the same this is because of the spin/rotation of Earth greek letters are sometimes used to identity stars in a constellation according to their brightness however, later astronomer found there were not enough letters Celestial Sphere viewed as a giant “sphere” extended around the Earth that rotates east to west celestial equator- projection of the terrestrial equator onto the celestial sphere 1 Thursday, February 4, 2016 celestial coordinates: Declination - degrees, north or south of the equator, similar to latitude (+) values in north hemisphere (-) values in south hemisphere Right Ascension - angular units (hr, min, sec), increases eastward, like longitude earth’s rotation axis intersects the celestial sphere at the north and south celestial poles Polaris us at the north celestial pole ecliptic: path of the SUN in the celestial sphere Earth’s Orbital Motion the earth rotates on its axis once every day the earth orbits the sun once every year Solar day - our 24 hour day- 1 rotation relative to the sun diurnal motion - progression of the sun & stars across the sky sidereal day - 1 rotation of earth relative to the stars- different from solar day because the earth is simultaneously rotating on the central axis and revolving around the sun ~ 3.9 minutes less than a solar day 20 minutes longer than a tropical year because of precession - Earth’s axis changed its direction caused by the gravitational pull of the moon and sun why do seasons exist then? since the earth revolves around the sun, the dark side faces new stars/objects each night (this rotation is only 1 degree every night but after 6 months, that’s a huge difference) the zodiac is simply a special set of 12 constellations that happen to lie in the same plane as the earth’s orbital plane around the sun. the sun crosses the celestial equator twice a year; at the vernal equinox around March 21st and the autumnal equinox around September 21st the interval from one vernal equinox to the next is a tropical year (OUR CALENDAR) 2 Thursday, February 4, 2016 the point where the sun is at the northern most point above the celestial equator is the summer solstice (~June 21st) and when the sun is at the southern most point below the celestial equator lies the winter solstice (~Dec 21) Zenith- point in the sky straight overhead meridian- the circle that passes through the Zenith and the two celestial poles seasons are opposite in north and south hemisphere why is it SO HOT in summer? since the earth has a tilt (23.5 degrees) on its rotation axis which is relative to the ecliptic (hence seasons), the sun happens to be higher in the summer allowing for rays of sunlight striking the earth to become more concentrated in a small area resulting in hotter days. The Moon revolves around Earth and takes a month to complete its cycle (29 days) the moon actually doesn’t emit any light - it reflects off the sun which is not blocked by the earth because the moon’s orbit is inclined 5.2 degrees synchronous rotation - the moon keeps the same face to the earth Sidereal month- the time for the moon to complete one revolution respect to a reference star. the duration of this month is 27.3 days Synodic month- the time for the moon to complete a dull cycle of phases . the reference is the sun. duration is 29.5 days. 3 Thursday, February 4, 2016 Lunar Eclipse - when sun and moon are on opposite sides of the earth - the earth blocks the sun’s light from the moon - moon must be full - can be seen from anywhere on earth where moon is visible partial eclipses happen because alignment of all 3 is imperfect total eclipse- red color and lasts up to 100 minutes Solar Eclipse - when sun and moon are on the same side - the moon blocks the sun’s light from earth - must be new moon - only seen from specific place on earth total eclipse - they appear to have same angular size (sun is obviously bigger but since it is farther away, it looks the same) this shows the sun’s outer glow- corona annular eclipse - umbra never reaches earth and thin ring of sunlight can be seen surrounding the moon also a partial eclipse because the moons orbit is inclined, we do not see an eclipse every month parallax- apparent displacement of the foreground object respect to the background as the observer’s location changes stellar parallax- a nearby object (planet or star) will change position respect to the background of the stars if it is observes from two sites separated by a terrestrial diameter. if we measure the angle of displacement of the object and we know the length of the baseline (earth diameter) we can calculate the distance to the object. the amount of parallax is inversely proportional to an object’s distance 4 Thursday, February 4, 2016 Copernican Revolution Planets planets move irregularly in their motion throughout the celestial sphere Direction Motion - eastward movement across the sky Retrograde Motion- backwards westward movement, causing the planet to appear to make “loops” around the period of the retrograde motion, the planet gets brighter like the moon, they do not produce any visible light of their own they appear brighter the closer they are to earth astrologers - use data to make The Geocentric Model prediction about people’s destiny 1st model of solar system created by Aristotle geocentric model - viewed earth as center of the universe did not account for planets differing in brightness so new theories were made: yeah planet moved uniformly around a small circle - epicycle - whose center mover uniformly around the earth an another large circle -deferent Ptolemaeus created a new model that displayed the paths of the 5 planets known at the time - survived 13 centuries until Copernican Aristarchus proposed that the sun was the center of the universe and all else revolved around it - which is essentially true but no one believed him Copernicus rediscovered Aristarchus’ heliocentric model & he also found that: the earth spins on an axis & orbits the sun Copernicus idea was not widely his model explains daily & seasonal changes accepted mostly because it violated the doctrine of the roman Catholic Church his model accounts for planetary retrograde and brightness there was no observational evidence to support his model ex) if the earth revolved around the sun, why don’t we see stellar parallax 5 Thursday, February 4, 2016 Gailieo & Kepler would later provide the observational evidence needed to support the heliocentric model Gailieo was considered the father of experimental science and was the first to point the telescope at the sky- he discovered; the moon has valleys, mountains, and craters sun has dark spots (sunspots) - which ultimately led to the discovery that the sun rotates jupiter has 4 moons venus has a cycle of phases similar to that of the moon he was forced to retract his claim that the earth orbited the sun - this inquisition put him on house arrest for the rest of his life he used the scientific method when studying the sky Laws of Planetary Motion Johannes Kepler - wanted to find a simple description of the solar system that agreed with the copernican model and Tycho’s observation - he abandoned copernicus’ notion of circular planetary orbits Kepler’s Laws: 1) the orbital paths of the planets are elliptical with the sun at one focus ellipse - flattened circle perihelion - shortest distance from sun aphelion- largest distance from sun eccentricity = major axis - minor axis major axis in general, all orbiting bodies follow elliptical orbits. this applies to the moon, planets, binaries stars and all orbiting bodies semi-major axis and eccentricity are the only thing needed to describe size and shape of planet’s orbital path 6 Thursday, February 4, 2016 2) an imaginary line connecting the sun to any planet sweeps out = areas of the ellipse in = intervals of time there is a greater distance to travel in arc C which means the planet has to speed up as a result from applying the 2nd law, the planets move faster at perihelion and slower at aphelion 3)the square of a planet’s orbital period is proportional to the cube of it semi- major axis P^2 = a^3 P^2 = 1 a^3 P (period in years) = times fro one orbit a (semi-major axis in AU) = average distance (a corresponds to the radius if the orbit is circular) all objects that orbit the sun obey Kepler’s laws EXAMPLE) orbital period (p) of Earth is 1 year and distance (a) to the sun is 1 AU what is the orbital period (or the year) of a planet located at a distance of 10 AU from the sun? a=10 AU P^2 = 10^3 = 1000 P= square root 1000 P= 31.5 years Dimensions of the Solar System modern method for deriving the absolute scale of the solar system uses radar ranging — RADAR stands for radio detection and ranging radio waves are transmitted toward an object and their returning echo indicates the object’s direction, range or distance doesn’t work with sun because radio signals are absorbed at solar surface 7 Thursday, February 4, 2016 EXAMPLE) send a pulse to Venus - takes ~ 300 seconds to receive echo. one way travel time = 150 seconds. venus is .3 AU from earth at closest point D= s * t D= 300,000 x 150 = 45,000,000 km The AU is 45,000,000/.3 = 150,000,000 km Newton’s Laws Issac Newton developed an understanding of the way all objects move and interact with each other - Newtonian mechanics 1) an object at rest remains at rest and a moving object continues to move forever in a line with constant speed unless some external force changed the state of motion inertial - tendency of an object to keep moving at same speed and direction unless acted upon by force can be measures in mass - total amount of matter object contains greater mass = greater inertia = more force needed to change motion 2)the acceleration of an object is directly proportional to the net applied force and inversely proportional to object’s mass (a= F/m) ——— F = m *a acceleration - rate of change of velocity of an object if 2 objects are pulled with same force, the more massive accelerates less if 2 objects with same mass are pulled with different forces, the one experiencing greater force accelerates more 3) to every action there is an equal opposite reaction if object A exerts a force on object B, then B exerts a force on A that is equal in magnitude but oppositely directed Gravity Newton found that any object with mass exerts an attractive gravitational fore on all other objects - more massive = greater gravitational pull 8 Thursday, February 4, 2016 the magnitude of the gravitational force depends on masses of attracting bodies moon - less massive than earth- has less gravitational pull inverse square law- a specifies physical quantity or intensity is inversely proportional to the square of the distance from the source of the physical quantity gravitational force continually pulls planets towards the sun - because sun is the biggest, it dominates the interaction because the sun and planet have an opposite gravitational force, the sun also move, so the planet isn’t orbiting the sun’s center, both the planet and the sun orbit their common center of mass - “average” position of the matter making both bodies m1d1 = m2d2 —— center of mass P^2 (in earth years) = a^3 (in AU) Mtotal (in solar units) —— combined mass of 2 objects Light & Matter Light & Radiation our nearest large galaxy - constellation Andromeda- is 2.5 light years away we obtain info from such far away objets through electromagnetic radiation which refers to waves in which the energy is carried in the form of oscillating electric and magnetic field visible light is a particular type of electromagnetic radiation visible to the human eye radio, infrared, UV, x-rays and gmma rays are electromagnets radiation or light but invisible to the human eye the difference between all these types of electromagnetic radiation is the wavelength - or frequency Wave a wave is a way in which energy is transferred from place to place without physical movement material from one location to another 9 Thursday, February 4, 2016 wave period - # of seconds needed for the wave to repeat itself at some point in same place wavelength - # of meters needed for wave to repeat itself at a given moment in time amplitude - max departure of the wave from the undisturbed state frequency- # of wave crests passing any given point per unit time - expressed in units of inverse time hertz (Hz) wavelength x frequency = velocity Frequency = 1 Period diffraction - light waves tend to “bend around corners” interference- crests and troughs of waves coming from different sourced can reinforce or patly cancel one another radiation waves are different from all other kinds because they do not need a medium Magnetism electrons (-) and protons (+) exert an electrical force - like charges repel and opposites attract moving electric charges also produces magnetic fields a change in one of these fields necessarily creates one in the other together they make up electromagnetism which carries energy and info from one part of the universe to another electromagnetic waves move at the speed of light (3.00 x 10^5 km/s) frequency determines the color of light opacity - extent radiation is blocked by the material through which it is passing - because of this, only a fraction of radiation from space arrives to earth accelerate charges (electron/protons) produce: ripples in the ElectroMagnetic (E&M) field which ultimately = light 10 Thursday, February 4, 2016 Electromagnetic Spectrum radio-communication infrared- heat UV - sunburn X ray - penetrate tissue gamma ray - most energetic wavelength increases left frequency increases right Wavelength = color — visible light ranges in wavelength from ~400 to ~700 nm ROYGBV temperature of an object is a direct measure of the amount of microscopic motion with in it — increase temp = faster = more energy radiated intensity- specifies amount of strength of radiation at any point Blackbody Radiation Peak of object that absorbs all radiation falling upon it intensity blackbody curve describes the distribution of that reemitted radiation peak of frequency is directly proportional to the temp the kinetic energy is E = 1/2 m v^2 the higher the temp, the faster the particles move (larger) and the larger the kinetic energy when the charged particles change their state of motion electromagnetic radiation is emitted 11 Thursday, February 4, 2016 Thermal Radiation blackbodies, like stars, incandescent light bulbs, and irons, emit this characteristic spectrum of light - a body at a temp higher than 0 K will emit as a blackbody the intensity peaks at a given frequency and fall of to lesser values above and below that frequency Hotter blackbodies are “brighter” and “bluer” Blackbodies with different temperatures look like this Wien’s Law tells us that the hotter objects have bluer radiation cooler bodies radiate more at longer wavelengths (they’re redder) there is a wavelength at which the intensity of the radiation reached a maximum lambda max = 0.29 cm T (K) using this equation we can measure a star’s temperature from its spectrum Stefan’s Law hotter blackbodies are brighter overall (at every wavelength) F = oT^4 — Stefan - Boltzman equation F= total radiative flux (total energy radiated per second) o = constant energy emitted by a body rises a lot as body’s temp decreases a blackbody is a perfect emitter and absorber, whose temperature defines how much light it emits at each wavelength the total radiated flux or total energy radiated per second is proportional to the area under the black body cure 12 Thursday, February 4, 2016 Spectroscopy light can be separated into different wavelengths (separated in colors) to produce a spectrum the instrument used to produce and analyze a spectrum is known as a spectroscope it consists of a opaque barrier with a slit to produce a narrow beam of light, a prism or a diffraction grating and a detector - it can be the eye- or a screen to project the spectrum Kirchhoff’s Laws continuous spectrum - produced by a luminous 1) solid or liquid or a sufficiently dense gas which emits light of all wavelengths 2)emission lines - created by low density hot gas emitting light - these lines are characteristic of chemical composition of the gas 3)absorption lines - created from a low density cool gas absorbing certain wavelengths from a continuous spectrum - characteristic of composition of gas, they occur at same wavelengths as emission lines produced by the gas at higher temperatures Niels Bohr produced the 1st model that explained spectral lines - Bohr model electron orbits the proton (i.e. nucleus) kept in place by the Coulomb Force (Fc) Fc ~ 1/ R^2c electrons can only be in particular orbits (energy states) energy is “quantized” - quantum mechanics electron needs to gain energy to move from R1 to R3 (excited) electron needs to lose energy to move from R3 to R1 (de-excited) 13 Thursday, February 4, 2016 How electrons get energy to become excited: 1. collisions between atoms can excite electron to higher energy levels. passing an electric current - applying a high voltage to a low density gas- will make atoms collide 2. absorption of energy from light can excite electrons light can behave as a particle - light energy is carried in packets called photons Quantum Mechanics atoms can only absorb or emit photons with energies exactly equal to the energy difference between electron orbits the energy of a photon is related to the wavelength Eph ~ 1/lambda ~ f Eph = h f = h c/lambda (f= c/lambda) h= planck’s constant larger orbital jumps — shorter wavelength photons a radio photon has long wavelength and low energy a gamma ray photon has short wavelength and high energy the energy of the photon must be equal to deltaE Atoms of different elements have unique energy level structures — every electron transition corresponds to a unique wavelength ionization = rejection of electron electrons are not only particles but also waves, without exact locations The Doppler Effect moving sources change the pitch of the sound as they go by the pitch is higher - higher frequency- when they are approaching a lower - lower frequency- when they are moving away motion along the line of sight - radial motion- produces a Doppler effect no Doppler effect id the motion is perpendicular to the line of sight 14 Thursday, February 4, 2016 v/c = ∆lambda/ lambda = (lambda shift - lambda rest) / lambda rest v = radial velocity of an object c= speed of light ∆lambda = change in wavelength lambda shift = shifted or observed wavelength lambda rest = wavelength at rest * if the body emitting the Balmer series is receding - moving away form observer- the lines are shifted to the red part of the spectrum- the spectrum is said to be red shifted - the body doesn’t really look red if the body is approaching the observer, the lines are shifted to the blue part of * spectrum. the spectrum is said to be blue shifted- body doesn’t really look blue * assume object is only rotating - if the object is rotating , the side approaching the observer will be blue shifted and side moving away red shifted the line emitted from the center will have no shift as a consequence, the line will be wider than it would if the object has no rotation the rotation rate of the object can be determined by measuring width of spectral lines Zeeman Effect a single emission lines can split into 2 or more under the presence of magnetic field - presence of magnetic field splits energy levels of an atom Telescopes Refraction the bending of light when it passes from one substance into another - substance with different refraction index ex) air to glass the ray must hit the surface at an angle less than 90 degrees from the direction of the surface your eyes uses refraction to focus light 15 Thursday, February 4, 2016 refraction can cause parallel light rays to converge to a focus and form an image the focal plane is where light from different direction comes into focus Digital cameras detect and record images with an electronic device called Charge Coupled Device (CCD) a camera focuses light like an eye and captures the image with a deter the CCD detectors in cameras are similar to those used in modern telescopes Designs reflecting telescope - focuses light with mirrors. the curved (concave) mirror reflects light and forms an image refracting telescope- focuses light with lenses. the lens “bend” light by refractions and forms an image Reflecting Telescope has a primary mirror and secondary mirror - secondary can be flat or curves primary is curved concave and can be supported from the back in several places so it can maintain the curvature can have much greater diameters modern telescopes are reflectors Refracting Telescope uses lens instead of a mirror Disadvantages: lens separates light into different colors - focuses light at different distances along the optical axis which is called chromatic aberration need to be very long with heavy lenses heavy lenses can be supported from the outer part only. the weight distort the shape of the lens causing aberrations in the images light passing through a lens can get absorbed - absorption can be severe at UV and IR to manufacture a lens, you have to machine and polish two surfaces - expensive largest one = 40 inch diameter - Alvan Clark telescope at Yerkes observatory 16 Thursday, February 4, 2016 UF has 8’’ one manufactured about 80 years ago - lens built by Alvan Clark. Important properties of telescope light collecting area - telescopes with larger mirrors or lenses - larger diameter- have a large collecting area. a large collecting area can gather a greater amount of light in a shorter time and observe fainter objects angular resolution - telescopes that have larger mirrors or lenses are capable of taking image with greater detail both are increased with larger lens/mirror Light collecting area A= pie (D/2)^2 A= area D= Diameter diameter of telescope lens/mirror is aperture the light gathering power is proportional to the diameter square largest telescopes currently in use have aperture of 8-10 meters How does the collecting area of a 10 meter telescope compare with that of 2 meter one? - it’s 25 times greater Angular size and angular separation angular size depends on 2 parameters physical size of object distance to object measure in units of angle (degrees, arcmin and arcsec) angular size= physical size Distance angular size = physical size x 360 degrees/ (2 pie x distance) resolving power is the min angular separation that the telescope can distinguish 17 Thursday, February 4, 2016 Angular Resolution ultimate limit to resolution comes from interference of light waves within a telescope larger telescoped are capable of greater resolution its proportional to the wavelength lambda and inversely proportional to the D of the lens/mirror angular resolution = .25 (lambda/D) lambda is micrometer and D is meters high resolution means telescope can distinguish details separated by small angular distance the central bright spot- Airy- disc increases in size when the diameter of a telescope decreases larger diameter telescopes produce a small jury disc and have better resolving power there is a limit in the angular resolution that a telescope can achieve. it depends on its diameter - this limit in the resolution is known as the diffraction limit angular resolution = 0.25 (lambda/D) ƒ is the focal length ƒ is the distance from the lens to the focal point, where the image forms The magnification of a telescope how many times bigger and object looks through a telescope compared to naked eye focal length of a telescope (Ft) is = to distance from the lens/mirror to the plane where the image forms the focal length of an eyepiece is the distance between the lens of the eyepiece and the point where the image forms magnification ratio —- M= Ft/Fe magnifications around 250-350 are practical 18 Thursday, February 4, 2016 what do astronomers do with telescopes? imaging - taking images of object or large area of the sky spectroscopy - breaking right into spectra and analyze the spectral lines photometry - measure the intensity of light and variation in the intensity or brightness of the light from an object. obtaining the light curve of an object/ the brightness of an object can be expressed in an school called magnitude Charge Coupled Device (CCD) electronic camera with small pixels sensitive to light - when light strikes a pile it will develop an electric charge proportional to the intensity of light the charge in each pixel is read by the electronics controlled by a computer and stored as an array of numbers to display image, the numbers are sent to a computer monitor the value of each number is converted into intensity and displayed the intensity is proportional to the value of its number 19


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