Astronomy Exam 1 Notes PDF

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Day 1: January 23rd, 2020 Ch 1: Stars, Galaxies and the Universe ● Astronomy is the study of the universe (particularly beyond Earth) ○ Contains matter arranged into structures over a vast range of size scales ○ Structure of the universe has changed profoundly over an immense span of time ○ Considered an observational science ■ Large distances and sizes make it impossible for us to alter the universe ● Lots of what we understand about the galaxy comes from the properties of light ● Star = a large glowing ball of gas that generates heat and light through nuclear fusion ● Galaxy = a great island of stars in space, all held together by gravity and orbiting a common center ● Universe = the sum total of all matter and energy, that is, everything within and between galaxies ○ Cosmology = the study of the universe ● Learning goals: ○ How big is the Earth compared to our solar system? ■ The distances between planets are huge compared to their sizes – on a scale of 1 to 10 billion, Earth is the size of a Ballpoint pen and the sun is 15 meters away ○ How far away are the stars? ■ On the same scale, they are thousands of kilometers away ○ How big is the Milky Way Galaxy? ■ It would take more than 3000 years to count the stars in the Milky Way Galaxy at a rate of one per second, and they are spread across 100,000 light-years ○ How big is the universe? ■ Observable universe is 14 billion light-years in radius and contains over 100 billion galaxies with a total number of stars comparable to the number of grains of sand on all of earth’s beaches ○ How do galaxies move within the universe? ■ Through the expansion of the universe using Hubble Telescope ● The more distant the galaxy, the faster it is racing away ● We live in an expanding universe Day 2: January 27th, 2020 ● How do our lifetimes compare to the age of the universe? ○ The cosmic calendar: a scale on which we compress the history of the universe into 1 year. ○ The history of the universe in 1 year: ■ January 1 - The Big Bang ■ February - Milky way forms ■ September 3rd - Earth Forms ■ September 22nd - Early Life on Earth ■ December 17th - Cambrian Explosion ■ December 26th - Rise of the dinosaurs ■ December 30th - Extinction of the dinosaurs ■ December 31st, 9:00 pm - Early hominids evolve ● 11:58pm - Modern humans evolve ● 25 seconds ago - agriculture arises ● 11 seconds ago - pyramids built ● 1 second ago - Kepler and galileo show that earth orbits the sun ○ Human civilization is just a few seconds old, and a human lifetime is a fraction of a second ● What does the universe look like from earth? ○ We can see more than 2000 stars as well as the milky way ○ The night sky appears as a bowl over our heads ■ The Horizon is the circular intersection of this bowl with the ground

■ The Zenith is the point directly over our heads ■ The Meridian is the line running from the north point on the horizon through the zenith to the south point of the horizon ■ The Altitude of an object in the sky's the angle from the horizon (altitude = 0) to the

object ○ Angle measurements: ■ 360 degrees in a circle ■ 60 arcminutes in a degree ■ 60 arcseconds in an arcminute

● ■ Angle between the lines is the angular separation (or angular diameter)

● ○ Angular Separation (or Diameter)

■ 1 arc minute is about the smallest angle the naked eye can perceive ■ 1 arc second is about the smallest angle that can be perceived with an earth-based telescope because of blurring by the atomosphere ● The Sky in Motion ○ Sky moves from east from west over a few hours ○ Nearly all objects in the sky return to their original position in the sky in 24 hours ■ Known as diurnal motion ● Cycles in the Sky ○ The cyclic nature of celestial phenomena were first recognized by 2600 BC ○ Greek Civilization (600-150 BC) was first to describe this phenomena with a scientific model ■ Scientific model - a conceptual, often mechanistic viewpoint of how things work ● Both explains the observations and has predictive power ● Should simplify large collections of data ● Celestial Sphere ○ Greek model of the sky, saying earth is a sphere that sits at the center of the celestial sphere ■ Fictitious sphere with the stars on it ■ Much larger than the Earth ■ On the surface of the earth, we see half of it any one time ○ Pythagorean school proposed spherical shapes for the Earth, Sun and Moon.

○ ○ Diurnal motion of the sky is due to the turning of the Earth on its axis ■ Imagine someone standing on a stationary earth with the celestial sphere turning in the opposite direction to the earth around an axis going through the celestial poles

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● ● What have we learned? ○ What does the universe look like from earth? ■ The sky appears to be a bowl above us that intersects the ground at the horizon. The point directly overhead is the zenith ■ Another model of the sky is the celestial sphere that surrounds the earth. ○ Why do stars rise and set? ■ Because of earth’s rotation (rise in the east and set in the west) ○ At mid-northern latitudes ■ Stars appear to circle the north celestial pole (NCP) ■ Stars closer to the pole are above the horizon longer ● The Earth’s Rotation Axis ○ The north and south Day 3: January 30th, 2020

● Does the sun move with respect to the stars? ○ We can't see the stars when the sun is in the sky, but can look at the stars in the west shortly after sunset ○ We can also look at the stars high in the sky at midnight, when we are looking opposite the sun in the sky ○ At midnight, the sun is at our feet (lowest point) ○ Tonight a star sets at 8pm. In a month from now that star will set ■ Earlier in the evening ● Annual motion of the sun: ○ The ecliptic is a great circle of the sky (has the same center as the center of the celestial sphere ■ This indicates the earth moves around the sun (or vice versa) ■ Tilted by about 23.5 degrees to the celestial equator ● This is because of earth's rotation axis being tilted by that angle to the plane of the earth’s orbit around the sun

● ● The reason for seasons ○ Length of the daylight has some effects ■ Longer days and shorter nights in summer ■ Shorter days / longer nights in winter ■ Sun’s altitude change with seasons ● Higher altitude = more direct sunlight ● Lower altitude = less direct

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○ Earth’s axis points in the same direction (to Polaris) all year round, so its orientation relative the sun changes as earth orbits the sun ○ Summer occurs in your hemisphere when the sunlight hits it more directly ○ The sun is also above the horizon longer in the summer which causes more heating ■ AXIS TILT is the key to the seasons, without it, we would not have seasons on earth ○ Why doesn’t distance matter? ■ Variation of earth- sun distance is small - about 3% of this small variation is overwhelmed by the effects of axis tilt ○ Why are the tropics of earth near the equator warmer than the poles? ■ The Noontime sun is higher in the sky in the tropics than at the poles ○ How do we mark the progression of the seasons? ■ 1. Summer (June) Solstice ● Highest path, rises and sets at its furthest distance north of due east/west ■ 2. Winter (December) Solstice ● Lowest path, shortest path ■ 3. Spring (March) Equinox ● Rises due east and sets due west ■ 4. Fall (September) Equinox ● Rises due east and sets due west

○ Day 4, February 3rd 2020 ● Annual motion of the sun ○ Does the sun move with respect to the stars? ■ We can't see the stars when the sun is in the sky, but can look at the stars in the West shortly after sunset ■ Can see the stars at the night, when the sun is the opposite in the sky ○ Sun moves EASTWARD with respect to the stars ■ Moves about 1 degree a day around the sky (this is where we get the cycle of the seasons) ■ Ecliptic → the path of the Sun on the sky ■ The north/south component of the sun’s motion causes the seasons ● Motion of the Moon ○ Rises and sets once a day → diurnal motion ○ However, at the same time on successive nights, the Moon is at different points in the sky. ○ Motion is west to east (eastward), opposite of the diurnal motion (like the sun) ○ Moves 13 degrees a day with respect to the stars (who only move 0.5 degrees per hour)

■ Moves in a circle around the sky and returns to the same location with respect to stars in 27.32 days = sidereal month

○ ● Changing Appearance of the Moon ○ Over a month see: ■ Angular size changes ■ Same side always ■ Libration (rocking) ■ Phase change ● Phases of the moon ○ Half of the moon is always luminated ○ Observe during n phase of the moon determines how much the illuminated and dark halves are visible ○ Connected to when the Moon rises and Sets

○ ○ Synodic Month → the cycle of the phases is the 29.5 day synodic month

■ This is not equal to the sidereal month (27.3 days)

■ ○ What have we learned? ■ Sun and Moon move from the west to the east with respect to the stars ● Opposite diurnal motion ● The sun circles the sky in one year ● The Moon circles the sky in about one month ■ Moon will always keep the same side facing the earth ● Libration → rocking motion ■ Why do we see phases of the moon? ● Half of the Moon is lit by the Sun and half is in shadow ● What Causes Eclipses? ○ Earth and moon cast shadows ○ When either passes through the other’s shadow, we see an eclipse

○ ○ Why is the total eclipsed moon red? ■ Only the light rays bent by passage through the Earth’s atmosphere are reaching the moon ■ Red color is caused by scattering and absorption of blue light in the Earth’s atmosphere (the stratosphere) ○ When can eclipses occur? ■ Solar eclipses can only occur at new moon

● Can be partial, total, or annular Day 5, February 6th, 2020 ● Why don’t we have an eclipse at every new and full moon? ○ Moon’s orbit is tilted 5 degrees to ecliptic plane ○ 2 eclipse seasons each year, with a solar eclipse at new moon and lunar eclipse at full moon

● ● Two Conditions must be met to have an eclipse: ○ It MUST be a FULL MOON for a lunar eclipse ○ It must be a new moon for a solar eclipse ○ The moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes) ● What have we learned? ○ What causes eclipses? ■ Lunar eclipse - Earth’s shadow on the moon ■ Solar Eclipse - Moon’s shadow on the earth ■ Tilt of the moon’s orbit means eclipses occur 2 periods each year ● The Ancient Mystery of the Planets ○ Planetary motion shows complex motion ■ Always found close to the path of the sun in the sky – the ecliptic ■ Inferior planets: (Mercury and Venus) are always seen close to the Sun in the sky, known as conjunction ■ Superior planets: (Mars, Jupiter and saturn) are sometimes opposite the Sun in the sky, known as opposition ■ Motion is usually west-to-east (eastward) with respect to the stars, like the sun and the moon ● However, sometimes motion is slowed and reverses to become westward for a few weeks ○ Apparent retrograde motion ○ Assumes prograde motion eventually ○ Apparent retrograde motion - going westward (backwards) for a couple weeks in relation to the stars ■ Superior planets show retrograde motion near opposition (when opposite the sun in the sky) ● Brightest near opposition ■ Inferior planets also show retrograde and prograde motion too

○ Synodic period of a planet is the time to return to the same orientation with respect to the sun (opposition) ● Greek Astronomy ○ Believed in “Perfect” uniform circular motion ○ Also Earth was in the center (geocentric) ○ However, some greeks argued for a heliocentric model ○ Heliocentric Model - sun centered ■ Naturally explains the inferior / superior difference, retrograde motion Day 5: February 11th, 2020 ● Renaissance Astronomy: ○ Tycho Brahe (1546 - 1601) ■ Exceptionally skilled and methodical observers ■ Greatest pre-telescopic observer ■ Discovered a “new” star ● Showing no diurnal parallax ● Meaning the nova was beyond the orbit of the moon

○ ○ Kepler (1571-1630) ■ Publicly supported the Copernican model ■ Originally believed the orbit of planets were circular, but an 8-arcminute discrepancy led him to believe ellipses were the case. ● Kepler’s First Law (1609): The orbit of each planet around the sun is an ellipse (elongated circle) with the Sun at one focus

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● Kepler’s Second Law (1609): As a planet moves around its orbit, it sweeps out equal areas in equal times

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○ ● Kepler’s Third Law (1619): More distant planets orbit the Sun at a slower average speed, obeying the relationship p^2 = a^3 ○ Basically, planets farther from the sun move slower ○ P = orbital period in years ○ A = avg. distance from sun in AU ■ Kepler’s Heliocentric Model ● Planets move in elliptical orbits at non uniform speeds, suggesting motion is due to some force from the Sun that decreases with distance Aristotle: ■ Hypotheses: ● Heavy objects fall faster than light objects ● All objects naturally come to rest (in their natural place) Galileo ■ Hypotheses: ● All objects fall at the same rate. Both real experiments and “thought experiments” ● State of motion is as natural as the state of rest ○ Inclined planes balls rolling ○ Dropped objects of different size and found they reach the ground at the same time. ■ Object in motion will stay in motion unless a force acts on it ■ Argued that planets naturally continued their circular motion Descartes: ■ Realized circular motion requires a force to constantly change motion ● Directed towards circle Newton: ■ Discovered laws of motion and gravity ● Speed = rate at which object moves (distance / time) ● Velocity = speed and direction ● Accleration = change in velocity m/s^2 ■ First Law of Motion - Object stays in motion unless a net force acts to change its speed or direction ■ Second Law of Motion - Force = mass x acceleration ● Inertial mass = measure of how hard it is to change the motion of the body ● Acceleration is in the same direction as the force ■ Third Law of Motion - Equal and Opposite reaction force Universal Law of Gravitation: ■ Galileo’s studies of gravity showed: ● Gravity accelerates objects toward earth

● Same for all objects Day 6: February 13th, 2020 ● Why are astronauts weightless in space? ○ Moving in a circular direction around earth, knowing gravity exists in the earth’s orbit allows us to remain weightless due to a constant state of free fall. ● Determining the strength of gravity ○ Universal Law of Gravitation

■ ● Newton’s Law of Gravity extends kepler’s laws ○ Newton could derived Kepler’s first two laws from his laws of motion and gravity, stating these two laws apply to ALL ORBITING OBJECTS, not just planets ■ Ellipses are not the only orbital paths, can be bound (ellipses) or unbound (parabola and hyperbolas) ○ Can use Newton’s Laws of Motion and Gravity to derive Kepler’s 3rd law:

■ ● p^2 is not exactly == a^3 but the answer is negligible ● Einsteins theory of Gravity ○ Newton’s theory of gravity was made to produce all objects on Earth to fall at the same acceleration ■ Requires that the “gravitational” mass in the law of gravity is equal to the “inertial” mass in newton’s second law F=ma ○ Einstein’s solution: Gravity is not a property of the masses, but a property of space (which is curved by the presence of mass) ■ Predicts different accelerations than Newton’s theory only when the accelerations are very large ● Small differences near the Sun ● Big differences close to neutron stars and black holes ● Light ○ Light has both wavelike and particle like properties ■ Properties of Waves ● Wavelength = Distance between two wave peaks ● Frequency = # of times / sec that a wave vibrates up and down at a fixed location

● Wave speed = wavelength * frequency Day 7: February 17th 2020 (lecture 8) ● MISSED. Day 8: February 20th (lecture 9) ● MISSED.’ ● 3 Basic Types of Energy ○ Potential energy = stored energy ■ Gravitational Potential Energy ● PE = mgh ■ Electromagnetic Potential Energy ● Atom has positively charged nucleus and attracts negatively charged electrons ● Potential energy of an atom INCREASES when an electron changes from an orbit close to the nucleus to one farther away. ■ Nuclear potential energy ○ Mass-Energy ■ E = mc^2 ● Fun facts about the sun: ○ Is the sun on fire? No! ○ Is it contracting? No! ○ However, it can be powered by nuclear energy (e=mc^2_ ● Nuclear Fission in the Sun: ○ Fission → Big nucleus splits into smaller pieces ○ Fusion → Small nuclei stick together to make a bigger one. ■ Sun releases energy by fusing 4 hydrogen nuclei into one helium nucleus + energy ● How does energy from fusion get out of the sun? ○ Radiation Zone: Energy Transported upward by photons ○ Convection Zone: Energy transported upward by rising hot gas. ● 3 Basic Types of Spectra? ○ 1. Continuous Spectrum ■ Spectrum of common light bulbs spans all visible wavelengths, without interruption. ○ 2. Emission Line Spectrum ■ Thin or low-density cloud of gas emits light only at a specific wavelength that depends on its composition and temperature ○ 3. Absorption Line Spectrum ■ Cloud of gas between us and a lightbulb can absorb light of specific wavelengths, leaving dark “absorption lines” in the spectrum.

○ ● How is energy stored in atoms? ○ Electrons in atoms are restricted to particular energy levels (those of the hydrogen atom are shown in the diagram) ○ The only allowed changes are those corresponding to a transition between energy levels

■ ● Electromagnetic Potential Energy

○ ○ What is the composition of the sun? ■ 98% by mass hydrogen and helium ■ Nearly all stars in the vicinity of the Sun have a similar composition. Day 9: February 24th, 2020 ● Energy Level Transitions ○ Ground state (lvl 1) can only travel up and down to level 2 / 3 / 4… cannot travel in the middle or a little bit over it ■ Emission means going down, absorption means going up ● Chemical fingerprints ○ Each type of atom has a unique fingerprint due to its atomic structure

○ ● Composition of the sun ○ 71% hydrogen and 24% helium. ● Properties of Stars ○ Data and physical laws were not present until the 20th century ■ Telescopic observations: ● Positions on the sky (yielding distances) ● Brightnesses (yielding luminosities) ● Spectra (yielding composition and surface temp) ● Telescopes!!! ○ Telescope forms an image: light from one point in a scene ends up at one point in the image ○ Simplest camera is a pinhole camera

○ Telescopes replace the pinhole by devices that allow wayyyy more light to pass ■ This still yields a sharp image ■ Device must bend light using refraction or reflection ○ Refracting Telescope: ■ Focuses light with lenses (diverging) ○ Reflecting Telescope: ■ Focuses light with mirrors ■ It is easier and cheaper to build large mirrors, so large telescopes are reflectors ○ What are the two most important properties of a telescope? ■ 1. Light-collecting area: telescopes with a larger collecting area = greater amount of light in a shorter amount of time ■ 2. Angular resolution: telescopes that are larger are capable of taking images with greater detail ○ Light collecting Area: ■ Determined by the area of the main lens of the telescope (pi r^2) ○ Angular Resolution = minimum angular separation that the telescope can distinguish ■ Better angular resolution means distinguishing smaller angles ■ Diffraction of the light waves is unavoidable and creates faint rings around the source of light ■ Angle resolved is proportional to wavelength / (diameter of aperture) ● Large diameter = better angular resolution ● Shorter wavelengths = better angular resolution ○ Earth’s atmosphere (constant movement) also blurs our view of the stars ■ Can be solved by putting telescope in space, or through adaptive optics ● Properties of Stars ○ Modern stellar classification - Williamina Fleming and Annie Jump Cannon ■ Spectral type reveals surface temperature in a star’s spectrum ● (hottest 50,000K) O B A F G K M (coolest 3,000K) ○ Oh, Be A Fine Girl, Kiss Me

● ● Oh, Be A Fine Girl/Guy, Kiss Me ● Stellar Luminosities ○ Quantitative measurements were founded to discover the apparent...