Midterm Study Guide PDF

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MIDTERM STUDY GUIDE 1. Scales and the appearance of the sky a) The Distance Scale Astronomical  Unit (au) - Earth’s average distance from the sun, used to describe distances within solar system ➢ 150 million km / 93 million miles ○ Light year (ly) - distance light can travel in one year ➢ 10 trillion km / 6 trillion miles ➢ Unit of distance not time → The farther we look in distance, the further we look back in time → Distance of 14 billion light years marks boundary/horizon of observable universe. ( 1022 ) B) Daily Motion of Sky: The Celestial Sphere ○ Rotation - daily cycle, spin on axis ○ Orbit - revolution around sun, 1 year ➥ Earth’s orbital path defines ecliptic plane ➥ Axis tilted by 23 ½ ° perpendicular to ecliptic plane points almost directly ➥ Distance alters perception of time → Celestial sphere - imaginary sphere on which objects in the sky appear to reside when observed from Earth, with earth appearing to be in the center ○ North celestial pole - the point directly over Earth’s North Pole ○ South Celestial Pole - the point directly over south pole ○ Celestial equator - projection of Earth’s equator into space → Celestial positions ➥ Declination = latitude ➥ Right ascension = longitude C) Appearance of the Sky: Seasons on Earth, Stars and Planets, Winter and Summer constellations, southern and northern hemispheres → Seasons: cyclical changes in weather and length in days caused by the tilt of Earth’s axis causes sunlight to fall differently on Earth at different times of year. → Orientation of axis relative to the sun changed over course of each orbit ● Two hemispheres experience opposite seasons at the same time as the orientation the axis changes angle of sunlight ➥ Northern Summer/Southern Winter: Northern Hemisphere is tipped toward the sun in June as the Southern hemisphere is tipped away from the Sun in June ➥ Northern Winter/Southern Summer: The Southern Hemisphere is tipped toward the sun in December as the northern hemisphere is tipped away from the sun in December ➥ Summer: (in Northern Hemisphere in June) axis tilt cause sunlight at hit at a steeper angle ⟶ concentrated sunlight causes warmer climate, more hours of sunlight ➥ Winter: shallower sunlight angle makes it winter as sunlight is less concentrated, less hours of sunlight ● Sunlight gradually changed as Earth orbits sun ➥ Spring/Fall: in between summer/winter extremes, both hemispheres are equally illuminated in March and September ● Seasons on Earth caused only by axis tilt and not b y change in Earth’s distance from the sun ○

➥ Earth’s orbital distance varies over course of year; Earth is only about 3% farther away from sun at its furthest point (July) than to its closest (January); difference in strength of sunlight carried by distance is diminished by effects of axis tilt ➢ Axis tilt = reason for seasons ○ Extremes differ at poles and equatorial religions ○ Northern hemisphere seasons slightly more extreme than southern hemisphere → Constellations - region of sky with well-defined borders located through familiar patterns of stars (the celestial sphere) ● Milky Way - band of light circling celestial sphere, passing through more than a dozen constellations ● Local sky - sky as seen where you happen to be standing, appears to take shape of hemisphere ○ Angular size - angle an object as it appears in field of view ➥ Sun and moon are about ½ ° , does not mean true size (we see size on distance) Angular distance - angle that appears to separate pair of object in sky Earth, not celestial sphere, rotates ⟶ stars following paths through local sky ➥ Stars near northern celestial pole are circumpolar; perpetually remaining above horizon, circling (counter clockwise) around north celestial pole all day ➥ Stars near south celestial pole never rise above horizon ➥ All stars have daily cycles that are partly above & below horizon ⟶ appears to rise in east/set in west ○ Variation with Latitude & Longitude: ➥ Latitude measures north/south position on earth, Longitude measures east/west position ➥ Longitude at 0° and 90° at poles ○ Variation with time of Year ● Due to Earth’s changing position in orbit around sun ➥ Sun appears to move steadily east along ecliptic, stars of different constellations in background at different times of year ● Constellations along ecliptic makeup zodiac ➥ Sun’s apparent location along ecliptic determines which constellations are visible at night ➢ Example: Sun appears to be Leo in Late Aug. & we cannot see it as it is in daytime sky, but can see Aquarius all night because it is opposite Leo on celestial sphere ⟶ 6 months later in Feb, Leo at night but not Aquarius → Planets ○ Visible planets to the naked eye: Mercury, Venus, Mars, Jupiter, Saturn ○ Planetary motion: ● Complex movements and constellations ● Planets vary substantially in speed and brightness ● Usually move eastward but occasionally reverse course ➥ Apparent retrograde motion - backwards/westward movements last periods of few weeks to few months - backwards/ westward movements last periods of few weeks to few months, depending on planet D) Phases of the Moon, Eclipse ○ Lunar phases - 29 ½ day time period marking cycling in which Moon’s appearance in sky changes position relatives to the suns changes ○ ○

Half the moon always faces the sun while other is dark, amount of illuminated half depends on moon’s position in orbit ● Determines the times of day at which we see moon in sky ➥ Full moon must rise around sunset, reaches highest point at midnight, sets around sunrise; occurs when opposite sun in sky ➥ First quarter moon rise around noon, reaches highest point at sunset, sets at midnight; occurs when moon is 90° east of sun ● Phases new⟶full = waxing (increasing), full ⟶new = waning (decreasing) ➥ No “half moon” phase; half at first quarter & third quarter phase mark when moon ¼ or ¾ monthly cycle ➥ Just before and after new moon = crescent ➥ Just before and after full moon = gibbous ○ Synchronous rotation - moon rotates its axis in same amount of time it takes to orbit Earth ● Why we see nearly the same face of the moon constantly ● Consequence of Earth's gravity → Eclipses - shadows created when sun, earth, and moon fall into straight line ● Lunar eclipses - occurs when earth lies directly between sun and moon, so Earth’s Shadow falls on the moon ● Solar eclipse - occurs when the moon lies directly between the sun and earth, so the moon’s shadow falls on the Earth ○ Thought they occur equally often, you see the lunar eclipses more often ○ Conditions for eclipses ● Because of inclusion of moon’s orbit, it spends most of time either above or below ecliptic, cross through line only twice in orbit; coming out & and going back in (points are called nodes) ● Nodes are aligned approximately the same way throughout year ⟶align with sun in straight line with sun and earth twice each year ➥ Can only occur: ● Phase of moon is full (for a lunar eclipse) or new (for a solar eclipse) ● New or or full moon occurs at time when moon is close to a node ○ Umbra - region of shadow where sunlight is completely blocked ○ Penumbra - region of shadow where sunlight is only partially blocked ○ “Precession of the nodes” (18.6 years) → eclipse season slightly less than 6 months apart (173 days) ○ We can predict eclipses because we know the precise details of the orbit and earth and moon ●

2. Brief history of solar system explorations A) Eratosthenes measurement of the Earth’s radius → Eratosthenes ● First to measure Earth’s circumference ● Used zenith (point in sky/celestial sphere directly above observer) ➥ Compared the noon altitude of the sun on the same day in 2 locations, concluded; ● 7/360 x circumference = 42,000 km* *actual value = 40,000 km B) Geocentric versus heliocentric model of the solar system: How did they account for the retrograde motion of the planets? → Geocentric model - Greek, placed spherical Earth at center of universe ➥ Pythagoras and Aristotle used geometry as ‘evidence’ for sphere earth ➥ Plato asserted all celestial bodies to move at constant speeds in perfect circles

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However, retrograde motion shows this is not true; ● Ptolemaic model, geocentric centric models; placed earth in center, BUT held idea that each planet moved around earth on a small circle that turned upon a larger circle ➝ trace loop as seen from Earth, w/ backward portion of loop mimicking apparent retrograde motions Copernicus: ● Recognized heliocentric model, found geometric relationships that allowed him to calculate each planet’s orbital period around the sun and its relative distance from the sun in terms of Earth-sun difference ● Held on to perfect circles /heavenly motion idea Tycho: supernova and comet observations ● Convinced that planets orbit sun but was stationary; sun orbits earth, but planets orbit sun Kepler: ● Believed planetary orbits must be perfect circles but wanted to match Tycho’s data ● Came up with discovery of elliptical orbits ● Kepler’s laws of planetary motion

➢ All planets have elliptical orbits w the sun at one focus ➢ All planets sweeps out equal areas in equal times ➢ The ratio of a planet's average distance from the sun cubed to its orbital period squared is a constant for all the planets ○ Galileo ● Concluded that everything orbits the earth ● Answered all objections to idea that earth is not moving, challenged heavenly motions/perfect circles notion, but not had detected stellar parallax C) Observational tests: Parallax and how did Galileo show Venus goes around the sun? ○ Parallax/Stellar Parallax - shifting of object against background due to viewing it from different positions /apparent shift in the position of a nearby star (relative to distant objects) that occurs as we view the star from different positions in Earth’s orbit of the Sun each years → Galileo ● Stars were more distant than Tycho thought, Galileo used telescopes to show that the Milky Way had so many stars ⟶ helped Galileo argue that stars were numerous and distant ● Observed that Jupiter had moons orbiting it ● Observed that Venus goes through phases in a way that makes sense only if it orbits sun D) Kepler’s Three Laws of Planetary Motion → First Law: the orbit of each planet about the sun is an ellipse with the out one focus ● Law tells us planet’s distance from the sun varies during orbit ➥ Closest point = perihelion/farthest point = aphelion ➥ Average of distances is length of semi major axis = average distance from the sun

→ Second Law: A planet moves faster in the part of its orbit near the sun and slower when farther from the sun, sweeping out equal areas in equal times ● Planet moves greater distance & faster when near perihelion than in same amount of time near aphelion → Third Law: More distant planets orbit the Sun or slower average speeds, obeying the precise mathematical relationship ➢ p2 = a 3 , p: planet’s orbital period in years, a: average distance from the sun in AU ● Suggests that planetary motion might be the result of a force from the sun 3. Energy and motion A) Kinetic and Potential energy, link between mass and energy → Energy - what makes matter move ○ Kinetic energy - energy of motion ➢ Ex: falling rocks, orbiting planets, molecules in air ➢ 1/2mv 2 : m=mass, v=speed ○ Potential energy - stored energy later converted ● Chemical potential energy ● gravitational potential energy - depends on mass how far it can fall as a result of gravity (more when higher, less when lower) ➥ For an object near Earth’s surface: mgh (m=mass, g=acceleration, h = height above ground) ➢ Ex: Rock perched on ledge has gravitational potential, gasoline has chemical potential energy ○ Radiative energy - energy carried by light, radiative energy ● Light carried energy, light can cause charge in matter ● Why light alters molecules (sight, warmth) ○ Thermal energy → Mass-energy = amount of potential energy contained in mass; E = mc squared (e= amount of potential, m = mass, c = speed of light) B) Galileo concept of momentum ○ Theory of inertia ○ External force friction stops momentum C) Newton’s 3 Laws of Motion & Concept of force → 1st Law: an object moves at a constant velocity if there is no net force acting upon it ● Object at rest: velocity = 0 ● Objects in motion remain in motion with no change in speed/direction ● Reason astronomical objects don’t need fuel to travel through the universe → 2nd Law: force = mass x acceleration (F = ma), force = rate of change in momentum ● Reason why planets with more mass exert stronger gravitational force on passing asteroids/comets → greater acceleration ● Acceleration around curves ➥ The tighter the curve/faster object is moving, the greater the force needed to keep object moving

➢ Ex: ball swinging on a line, inward acceleration moving around circle → 3rd Law: for any force there is always an equal and opposite reaction force ● Tells us that objects always attract each other through gravity ● Greater acceleration for objects with smaller mass D) Law of universal gravitation E) Acceleration along a curved orbit and angular momentum F) Einstein’s principles of relativity and equivalence

4. Light and telescopes A) Dual Nature of Light B) Inverse square law: surface brightness decreases as inverse square of the distance C) Photons of different Wavelength: different type of photons ○ Photons have a precise wavelength, frequency, and energy ○ Higher the frequency/lower wavelength, the more radiative energy is released D) Refractor and Reflector Telescopes: how is light gathered in these telescopes ○ Reflecting telescope- a telescope that uses mirrors to focus light ○ Refracting telescope - a telescope that uses lenses to focus light E) Windows of Earth atmosphere: ability of different types of photons from outer probes: sharper images, avoid absorption, probe magnetic field and gravity variations

 5. Starlight and atomic structure A) Temperature and heat ○ Light bulbs, planets, and stars produced a particular kind of continuous spectrum that determine temperature ➢ Temperature represents the average of kinetic energy of the atoms or molecules in an object ○ Electromagnetic spectrum - (in order of decreasing wavelength/increasing frequency and energy) radio waves, microwaves, infrared, visible light, ultraviolet, X rays, gamma rays ➢ Wavelength X frequency = speed (of light) B) Intensity and color of Black Body Radiation ○ Thermal radiation - (also known as blackbody radiation) the spectrum produced by an opaque object that depends only on the object’s temperature ○ Two Laws of Thermal Radiation ● (stefan boltzmann law) each square meter of a hotter object’s surface emits morequal≈ light at all wavelengths ➢ Example: each square meter on the surface of the 15,000 K star emits a lot more light at every wavelength than each square meter of the 3000 K star ➥ Emitted power (per square meter of surface) = σ T 4 ● σ (s igma) constant with measure value of = 5.7 x 10−8 watt /( m2 x K 4 ), T o n kelvin scale (K) ● (Wein’s law) hotter objects emit photons with a higher average energy (shorter average wavelength) ➥ Why peaks of shorter wavelength spectra for hotter objects ➢ Example: peak for 5800 K sun is in visible light, and peak for 3000 K star is infrared ➥ λ max ≈ (2,900,000/T) nm ●

Lambda max is the wavelength in nanometers of maximum intensity, peak of a thermal radiation spectrum

➢ Example: find emitted power per square meter and the wavelength of peak intensity for a 10,000 K object emits thermal radiation ⟶plug in temperature into Law 1 ⟶ find wavelength of maximum intensity with Law 2 ⟶ λ max ≈ (2,900,000/10,000) nm = 290 nm C) Elements: atoms, protons, neutrons, electrons D) Absorption and Emission lines: atomic transitions ○ Continuous spectrum - shows a smooth continuous rainbow of light, broad range of wavelengths ➥ Spectrum of traditional or incandescent light bulb ○ Emission Line Spectrum - spectrum composed of bright emission lines against a black background ➥ Thin or low density cloud of gas emits light only at specific wavelengths ● Emission lines - a bright line of single color superimposed on a fainter or completely absent rainbow of light ○ Absorption Line Spectrum - dark absorption lines over background rainbow spectrum ➥ Occurs when cloud of gas cooler in temperature lies between light source being observed and viewer ● Absorption lines - a dark line on a rainbow of light ○ Transmission - when light passes through object ○ Reflection/scattering - light bounces off of the object;, reflection when light bounces in same direction, scattering when light bounces off in a more random manner ○ Hydrogen emits and absorbs light at specific wavelengths ○ Every kind of atom, ion, and molecule produces a unique set of spectral lines E) Stellar Spectra

F) Doppler effect ○ Can learn about motion of distant objects (relative from us) from changes in spectra caused by doppler shift ○ When moving object is closer, bunched up wavelengths result in shorter wavelength and higher frequency ⟶ causes blushift as shorter wavelength of visible light is blue ○ When object is moving away from us, redshift wavelengths of visible light are longer and redder ○ Calculate an object’s radial (toward/away from us) from its Doppler shift ○ V rad /C = λshif t − λrest / λrest

6. Overview of solar system A). Two Classes of Planets ○ Terrestrial - small and dense, rocky surfaces, abundance of metals in cores ● Few moons, and no rings ➢ Mercury, Venus, Earth, Mars ○ Jovian - large planets, lower in density, lack solid surfaces and are made of hydrogen, helium, hydrogen compounds (gas giants) ● Rings and many moons ➢ Jupiter, Saturn, Uranus, Neptune B) Dynamical and chemical properties of planets

C) Minor Planets: asteroids, Kuiper Belt objects, and comets → Asteroids and Comets ○ Asteroids - rocky bodies that orbit sun but are very small ○ Comets - small objects that orbit the sun, largely made of ice mixed with rock D) a brief tour of Individual planets and their distinguishing properties → Mercury ● 0.39 Au from sun ● Radius: 2440 km, Mass: 0.055 M( subscript)earth ● rocks , metals ● Average surface temperature: 700k at day/100K at night ● No moons ○ 56.8 day rotation period means it rotates exactly three times for every two of its 87.9 day orbits of sun ; days and nights last about 3 Earth months each → Venus ● 0.72 AU ● Radius: 6051 km, Mass: 0.82 M( subscript)earth ● Rocks, metals ● Average surface temperature: 740 K ● No moons ○ Rotates slowly and opposite direction of Earth, long days/nights, sun rises in west/sets in easst → Earth ● 1 Au from Sun ● Radius: 6378 km, mass 1.00 M( subscript)earth ● Rocks, metals, ● Average surface temperature: 290 K ● 1 Moon → Mars ● 1.52 AU ● Radius: 3397 km, Mass: 011M( subscript)earth ● Rocks metals ● Average surface temperature: 220K ● 2 small moons → Jupiter ● 5.20 Au from sun ● Radius: 71,492 km, Mass 318M ( subscript)earth ● Hydrogen and helium ● Cloud top temp: 125 K ● At least 67 Moons → Saturn ● 9.54 AU ● Radius: 60,268 km, Mass: 95.2M( subscript)earth ● Hydrogen and helium ● Cloud top temperature: 95 K

● At least 62 Moons ○ Rings of rock and ice particles orbiting → Uranus ● 19.2 AU ● Radius: 25,559 km, Mass: 14.5M( subscript)earth ● Hydrogen, helium, hydrogen compounds ● Cloud top temperature: 60K ● At least 27 moons → Neptune ● 30.1 AU ● Radius: 24,864 km, Mass: 17.1M( subscript)earth ● Cloud top temp: 60 K ● At least 14 moons E) space exploration and robotic missions → Four Categories of robotic spacecraft missions ○ Flyby - A spacecraft on a flyby goes past a world once and continues on its way ○ Orbiter - spacecraft that orbits world it is visiting, long term study ○ Lander or Probe - spacecraft designed to land on planet’s surface or probe a planet’s atmosphere by flying through it ○ Sample Return Mission - makes round trip to return sample of the world it has studied to Earth → Carry own propulsion, power, communication systems, can operate under pre-programmed control or with updated instructions from ground controllers

7. The formation of the solar system A)The Nebula Hypothesis ○ Nebula Hypothesis: theory that our solar system formed from the gravitational col...