Astronomy Exam 1 Study Guide PDF

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Lecture 1: A Modern View of the Universe ● ● ● ● ● ● ● ● ●

Star: A large, glowing ball of gas that generates heat and light through nuclear fusion Planet: A moderately large object that orbits a star; it shines by reflected light. ○ May be rocky, icy, or gaseous in composition Moon (or satellite): An object that orbits a planet ○ Ganymede orbits Jupiter Asteroid: A relatively small and rocky object that orbits a star Comet: A relatively small and icy object that orbits a star Solar (Star) System: A star and all the material that orbits it, including its planets and moons. Nebula: An interstellar cloud of gas and/or dust 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 all galaxies

Light travels at a finite speed (300,000 km/s ; 3 x 10^5) ● Moon: 1 second light travel time ● Sun: 8 minutes light travel time ● Sirius: 8 years travel time ● Andromeda Galaxy: 2.5 million years Thus, we see objects as they were in the past ● The farther away we look in the distance, the further back we look in time Light-Year: The distance light can travel in 1 year ● At great distances, we see objects as they were when the universe was much younger. Calculating the Distance of a Light Year ● Speed = distance/time so distance = speed x time ● Distance = (300000)(51556952) = 9.46*10^12 = 9 trillion km = 6 trillion miles Solar System: Au Galaxy: LY or Parsec Cosmology: Parsec, Mega Parsec or Mega LY ● On a 1-to-10-billion scale: The Sun is the size of a large grapefruit (14 cm) and the Earth is the size of a ball point, 15 meters away ● The stars are thousands of kilometers away The Milky Way Galaxy has about 100 billion stars ● Would take 3000 years to count all the stars in our galaxy and they are spread across 100,000 light years. ● Milky Way is one of about 100 billion galaxies ● 10^22 stars ● The observable universe is 14 billion light-years in radius ● There are as many stars as grains of dry sand on all of Earth’s beaches

Earth is part of the solar system, which is the Milky Way Galaxy, which is a member of the Local Group of galaxies in the Local Supercluster Lecture 2: The Starry Night, Seasons and Time ● With the naked eye, we can see more than 2000 stars as well as the Milky Way Constellations ● A constellation is a region of the sky ● Eight eight constellations fill the entire sky ● The brightest stars in a constellation may actually be quite far away from each other The Celestial Sphere ● Stars at different distances all appear to lie on the celestial sphere ● The 88 official constellations cover the celestial sphere

● The Eplictic is the Sun’s apparent annual path through the celestial sphere ● North celestial pole is directly above Earth’s North Pole ● South celestial pole is directly above Earth’s South Pole ● Celestial equator is a projection of Earth’s equator onto the sky/space The Local Sky ● An object’s altitude (above horizon) and azimuth (direction along horizon) specify its location in your local sky ● Meridian: line passing through the zenith and connecting N and S points on horizon ● Horizon: all points 90 degrees away from the zenith ● Zenith: the point directly overhead Celestial Coordinates ● We use latitude and longitude to pinpoint locations on Earth and we use declination and right ascension to pinpoint locations on the celestial sphere ○ Right ascension: like longitude on celestial sphere (measured in hours with respect to spring equinox)

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Declination: like latitude on celestial sphere (measured in degrees above celestial equator) ○ The Sun’s RA and dec change along the ecliptic during the course of a year ○ Sun’s declination is negative in fall and winter (south of equator) and positive in spring and summer (north of equator) ● Earth rotates from west to east, so stars appear to circle from east to west ● Stars near the north celestial pole are circumpolar and never set ● We cannot see stars near the south celestial pole (a star below your horizon never rises) ● All other stars (and Sun, Moon, planets) rise in east and set in west As the Earth orbits the Sun, the Sun appears to move eastward along the ecliptic ● At midnight, the stars on our meridian are opposite the Sun in the sky Stars rise and set because of Earth’s rotation The time of year determines the location of the Sun on the celestial sphere FALSE: Earth is closer to the Sun in the summer and farther from the Sun in the winter Seasons ● Seasons depend on how Earth’s axis affects the directness of sunlight ● Earth’s axis points in the same direction (to Polaris) all year round, so its orientation relative to the Sun changes as Earth orbits the Sun. ● Summer occurs in your hemisphere when sunlight hits it more directly; winter occurs when the sunlight is less direct ● AXIS TILT is the key to the seasons; without it, we would not have seasons on Earth. ● The spring and fall equinoxes are when both hemispheres get equally direct sunlight. Distance doesn’t matter ● Variation of Earth-Sun distance is small- about 3%; this small variation is overwhelmed by the effects of axis tilt ○ Variation in any season of each hemisphere-Sun distance is even smaller There are four special points in the progression of the seasons ● Summer (June) solstice ● Winter (December) solstice ● Spring (March) equinox ● Fall (September) equinox Even though Earth’s axis seems fixed on human time scales, it actually precesses over about 26,000 years ● Polaris won’t always be the North Star ● Positions of equinoxes shift around orbit: spring equinox was once in Aries and is now in Pisces Earth’s axis/tilt remains about 23.5 degrees but Earth has a 26,000 year precession cycle that slowly and subtly changes the orientation of Earth’s axis. Length of a Day ● Sidereal day: Earth rotates once on its axis in 23 hours, 56 minutes, and 4.07 seconds

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One full rotation represents a sidereal day and returns you to pointing in your original direction, but you need to rotate a little extra to return to pointing at the Sun. Solar day: The Sun makes one circuit around the sky in 24 hours ○ Earth rotates about 1 degree per day around its orbit, so a solar day requires about 361 degrees of rotation A solar day is longer than a sidereal day by about 1/360 because Earth moves about 1 degree in orbit each day

Length of a Month ● Sidereal month: Moon orbits Earth in 27.3 days. Earth and Moon travel 30 degrees around Sun during that time. (30/360 = 1/12) ● Synodic month: A cycle of lunar phases; takes about 29.5 days, 1/12 longer than a sidereal month. Length of a Year ● Sidereal year: Time for Earth to complete one orbit of Sun ● Tropical year: Time for Each to complete one cycle of seasons. Tropical year is about 20 minutes (1/26000) shorter than a sidereal year because of precession. Planetary Periods ● Planetary periods can be measured with respect to stars (sidereal) or to apparent position of Sun (synodic) ● Difference between a planet’s orbital (sidereal) and synodic period depends on how far planet moves in 1 Earth year ● Outer planets:

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Inner Planets:

Leap Years ● The length of a tropical year is about 365.25 days and in order to keep the calendar year synchronized with the seasons, we must add one day every 4 years (February 29) ● Years divisible by 100 are not leap years unless they are divisible by 400. Lecture 3: Lunar Phenomena ● Soviets had first contact with Moon ○ 1959: first spacecraft to fly past Moon, first spacecraft to crash/land on Moon, first pictures of far side of Moon ● US is so far the only country to send people to the Moon

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First person on Moon: July 1969 Last person on Moon: December 1972

Why do we see phases of the Moon? ● Lunar phases are a consequence of the Moon’s 27.3 day orbit around Earth. ● Half of Moon is illuminated by Sun and half is dark. We see a changing combination of the bright and dark faces as Moon orbits. ● Moon takes about 29.5 days to go through whole cycle of phases (synodic month) ○ Phases are due to different amounts of sunlit portion being visible from Earth ○ Time to make a full 360 degree rotation around Earth (sidereal month) is about 2 days shorter Phases of the Moon ● Waxing: Moon visible in afternoon/evening. Gets fuller and rises later each day ● Waning: Moon visible in late night/morning. Gets less full and sets later each day. Moon Synchronous Rotation ● The Moon is tidally locked to Earth--its rotation rate is the same as the time it takes to make one revolution, so the same side of the Moon always faces Earth. ○ Moon rotates exactly once with each orbit so that's why we only see one side from Earth. Lunar Eclipses: Earth’s shadow on the Moon ● The Earth and Moon cast shadows and when either passes through the other’s shadow, we have an eclipse ● Umbra: Full shadow ● Penumbra: Partial shadow ● Total Lunar Eclipse: Moon passes entirely through umbra ● Partial Lunar Eclipse: Part of the Moon passes through umbra ● Penumbral Lunar Eclipse: Moon passes through penumbra ● Lunar eclipses can occur only at full moon and they can be penumbral, partial or total Solar Eclipse: Moon’s shadow on Earth ● A total solar eclipse occurs in the small central region ● A partial solar eclipse occurs in the lighter areas surrounding the area of totality ● If the Moon’s umbral shadow does not reach Earth, an annular eclipse occurs in the small central region ● Solar eclipses can occur only at new moon and they can be partial, total or annular Why don’t eclipses occur every month? ● Eclipses occur when Earth, Moon, and Sun form a straight line ● Eclipses don’t occur every month because Earth’s and Moon’s orbits are not in the same plane

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So we have about two eclipse seasons each year, with a lunar eclipse at full moon and solar eclipse at new moon and they depend on the tilt of Moon’s orbit To have an eclipse: It must be a full moon (lunar eclipse) or new moon (solar eclipse) AND the Moon must be at or near one of the two points in its orbit where it crosses the ecliptic plane (its nodes) Eclipses recur with the 18 year, 11 ⅓ day saros cycle, but the type of eclipse and location may vary.

Surface Features of the Moon ● Moon has large dark flat areas due to lava flow, called maria (Early observers thought they were oceans) ● Moon also has many craters from meteorite impacts ● The far side of the Moon has some craters but no maria Lunar Cratering and Surface Composition ● Meteoroid strikes Moon, ejecting material; explosion ejects more material, leaving crater ○ Craters are typically about 10 times as wide as the meteoroid creating them, and twice as deep ○ Rock is pulverized to a much greater depth ○ Most lunar craters date to at least 3.9 billion years ago; there’s been much less bombardment since then ○ Craters come in all sizes, from the very large to the very small (5 mm) ● Regolith: Thick layer of dust left by meteorite impacts ○ Moon is still being bombarded, especially by very small micrometeoroids that softens features ● Meteorites also hit Earth ● More than 3 billion years ago the moon was volcanically active, forming rilles. Lecture 4: Harmony of the Spheres and Starry Messengers ● Tycho Brahe: His observations of the positions of stars and planets on the sky were the most accurate and complete set of naked eye measurements ever made Special Topic: Eratosthenes Measures Earth ● He measured it to be 42,000 km and modern value is approx 40,100 km How did Greeks explain planetary motion? ● Underpinnings of the Greek geocentric model ○ They developed models of nature and emphasized that the predictions of models should agree with observations ○ Earth at the center of the universe ○ Heavens must be “perfect”: Objects moving on perfect spheres or in perfect circles ○ BUT this made it difficult to explain apparent retrograde motion of planets

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Over a period of 10 weeks, Mars appears to stop, back up, then go forward again. The most sophisticated geocentric model was that of Ptolemy- the Ptolemaic model ○ Sufficiently accurate to remain in use for 1500 years ○ His work named the greatest compilation ○ The Ptolemaic model explains retrograde motion by saying that planets really do go backward in this model ■ The Ptolemaic model had each planet move on a small circle whose center moves around Earth on a larger circle

The Copernican Revolution ● Copernicus proposed a Sun-centered model (heliocentric model) (1543) ○ Used model to determine layout of solar system (planetary distances in AU) but the model was no more accurate than the Ptolemaic model in predicting planetary positions because it still used perfect circles. ○ Explained retrograde motion of planets naturally. Said Earth also moving around the Sun. ● Tycho Brahe ○ Compiled the most accurate (one arcminute) naked eye measurements ever made of planetary positions ○ Still could not detect stellar parallax, and thus still though Earth must be at center of solar system (but recognized that other planets go around Sun). ○ He hired Kepler who used Tycho’s observations to discover the truth about planetary motion. ● Johannes Kepler ○ Kepler first tried to match Tycho’s observations with circular orbits but an 8 arcminute discrepancy led him eventually to ellipses Ellipses: An ellipse looks like an elongated circle

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Eccentricity: e = c/a ; It described how much an ellipse deviates from a perfect circle

Kepler’s three laws of planetary motion

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Kepler’s First Law: The orbit of each planet around the Sun is an ellipse with the Sun at one fous

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Peri - greek for near Apo - greek for away, apart ○ PD = A(1-E) ○ AD = A(1+E) Kepler’s Second Law: As a planet moves around its orbit, it sweeps out equal areas in equal times.

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This means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun. All orbiting bodies in our solar system exhibit this behavior with the Sun at one foci Kepler’s Third Law: More distant planets orbit the Sun at slower average speeds, obeying the relationship p^2 = a^3 ○ P = orbital period in years ○ A = avg distance from Sun in AU (aka semi major axis) SO Copernicus created a sun centered model, Tycho provided the data needed to improve this model and Kepler found a model that fit Tycho’s data

Galileo’s role in solidifying the Copernican revolution ● His experiments and observations overcame the remaining objections to the Sun centered solar system model ● Three key objections rooted in Aristotelian view were:

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1. Earth could not be moving because objects in air would be left behind 2. Non circular orbits are not perfect as heavens should be 3. If Earth were really orbiting the Sun, we’d detect stellar parallax Overcoming the first objection ○ Galileos experiments showed that objects in air would stay with Earth as it moves ■ Aristotle thought that all objects naturally come to rest and Galileo showed that objects will stay in motion unless a force acts to slow them down (Newton’s first law of motion) Overcoming the second objection ○ Tychos observations of comet and supernova already challenged this idea ○ Using his telescope Galileo saw ■ Sunspots on Sun (imperfections) ■ Mountains and valleys on the Moon (proving it is not a perfect sphere) Overcoming the third objection (parallax) ○ Tycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth ○ Galileo showed stars must be much farther than Tycho thought - in part by using his telescope to see the Milky Way is countless individual stars ■ If stars were much further away, then lack of detectable parallax was no longer so troubling Galileo also saw four moons orbiting Jupiter, proving that not all objects orbit Earth Galileos observations of phases of Venus proved that it orbits the Sun and not Earth The Catholic Church ordered Galileo to recant his claim that Earth orbits the Sun in 1633 ○ His book on the subject was removed from the Church’s index of banned books in 1824 ○ He was formally vindicated by the Church in 1992

Lecture 5: On the Shoulders of Giants How do we describe motion? ● Speed: Rate at which an object moves ○ Speed = distance/time (units of m/s) ● Velocity: Speed and direction ○ 10 m/s, due east ● Acceleration: Any change in velocity (units of speed/time (m/s^2)) = Fg/ M The Acceleration of Gravity ● All falling objects accelerate at the same rate (not counting friction of air resistance) ● On Earth, g is approximately 10 m/s^2: speed increases 10 m/s with each second of falling ● Galileo showed that g is the same for all falling objects, regardless of their mass ○ Mass: the amount of matter in an object ○ Weight: the force that acts upon an object

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○ You are weightless in free fall!! There IS gravity in space ○ Weightlessness is due to a constant state free fall

How did Newton change our view of the universe? ● Realized the same physical laws that operate on Earth also operate in the heavens (one universe) ● Discovered the laws of motion and gravity ● Much more: experiments with light, first reflecting telescope, calculus Newton’s three laws of motion ● First Law of Motion: An object moves at constant velocity unless a net force acts to change its speed or direction ● Second Law of Motion: Force = mass x acceleration ● Third Law of Motion: For every force, there is always an equal and opposite reaction force. Objects continue at constant velocity because of conservation of momentum ● The total momentum of interacting objects cannot change unless an external force is acting on them ● Interacting objects exchange momentum through equal and opposite forces Conservation of Angular Momentum ● Angular momentum = mass x velocity x radius ● The angular momentum of an object cannot change unless an external twisting force (torque) is acting on it ● Earth experiences no twisting force as it orbits the Sun, so its rotation and orbit will continue indefinitely ● Angular momentum conservation also explains why objects rotate faster as they shrink in radius What determines the strength of gravity? ● The universal law of gravitation 1. Every mass attracts every other mass 2. Attraction is directly proportional to the product of their masses 3. Attraction is inversely proportional to the square of the distance between their centers

How do gravity and energy together allow us to understand orbits? ● Total orbital energy (gravitational + kinetic) stays constant if there is no external force ● Orbits cannot change spontaneously ● Total orbital energy stays constant ○ Friction or atmospheric drag or a gravitational encounter can make an object gain or lose orbital energy ○ Change in total energy is needed to change orbit. Add enough energy and object leaves. Gravity and tides ● Moon’s gravity pulls harder on near side of Earth than on far side ● Difference in Moon’s gravitational pull stretches Earth and its oceans ● Size of tide depends on phase of Moon Tidal Friction ● Tidal friction gradually slows Earth’s rotation (and makes the Moon get farther from Earth) ● The Moon once orbited faster (or slower); tidal friction caused it to “lock” in synchronous rotation. Objects fall at the same rate because mass of object in Newton’s second law exactly cancels mass in law of gravitation. Lecture 6: Light: The Messenger Dark lines in visible spectrum: caused by the absorption of light in the hot star’s cooler atmosphere. How do we experience light? ● The warmth of sunlight tells us that light is a form of energy ● We can measure the flow of energy in light in units of watts: 1 watt = 1 joule/s White light is made up of many different colors How do light and matter interact?

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Emission ○ Sun and lamp both emit light ● Absorption ○ Snow absorbs light but scatters most light so it looks bright ○ Sp...