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Economics for Management Studies
Victor Yu

Chapter 1 Solar system- the Sun, planets, asteroids, comets, moons - Moon moves 13 deg east from the night before Planet- nonluminous body in orbit around a star, large enough to have cleared it orbita - lunar eclipse up to 6 hr, solar eclipse up to 7.5 mins - can only see half of celestial sphere, half above horizon, can see entire Celestial sphere at l zone of other objects, shine by reflecting light equator Star- globe of gas held together by its own gravity and supported by internal pressure, - seasons caused by changed in solar energy Earth’s northern/southern hemi receive at diff generates energy by nuclear fusion times of year (result from tip of Earth’s equator and axis relative to orbit) AU- average distance from Earth to Sun (1.5x10 km) 8 Light year- unit of distance equal to the distance light travels in 1 year (10 km/63000 AU) - in summer solstice, sun shine direct at northern latitudes, steeper angle and spreads in Galaxy- large system of stars, star clusters, gas, dust, nebulae, orbiting a common centre southern - moon orbits eastward around Earth , same side facing Earth of mass - 1 cycle of lunar phase= 1 cycle of moon relative to Sun Milky way- cloudy band of stars/faint diffuse light around the celestial sphere - when Moon is eclipsed, does not disappear completely, no direct sunlight, the Moon in Milky way galaxy- the spiral galaxy containing our Sun and 100 billion stars, visible in umbra does receive some sunlight refracted through Earth’s atmosphere the night as Milky Way Spiral arms- long spiral pattern of bright stars, star clusters, gas and dust (where stars form) - in totality, not see Sun because hidden behind Earth but can see Earth’s atmosphere Supercluster- a cluster of galaxy clusters illuminated from behind by the Sun (red glow) - to see lunar eclipse, must be on dark side of Earth (b/w sunrise and sunset) when Moon Universe- all physical matter and energy, clusters of galaxies passes Earth’s shadow -sunset: west to east, sunrise: east to west -superclusters are linked to form long filaments and walls outlining voids (largest structure in universe) - larger star in photograph= brighter - big bang>Milky Way>Solar System forms>primitive life>complex living structures form> dinosaurs>end of dinosaurs -Sun is 5 billion years,last another 5 billion, become a white dwarf, cool down and become mostly carbon, stay this form until universe dies - light year can tell how far back viewing galaxy Chapter 2 Asterism- named grouping of stars that is not one of the recognized constellations Magnitude Scale- astronomical brightness scale (First magnitude star= brightest, Sixth=fainter) Apparent Visual Magnitude- brightness of a star seen by human eyes on Earth (does not take to account distance from Earth) Flux- measure of flow of energy (light) out of a surface Celestial sphere: an imaginary sphere of very large radius surrounding Earth to which the planets, stars, Sun and the Moon seem to be attached Chapter 3 Precession- change in orientation (wobbing) of the Earth’s axis of rotation First principle- seems obviously true and needs no further explanation North/South celestial poles- on celestial sphere directly above north/south pole, pivots which Uniform circular motion- idea that heavens were perfect (sphere) and moved by uniform sky rotates motion along circular orbits Angular distance- angle formed by lines extending from observer to 2 locations in the sky Geocentric universe- model universe with Earth at centre (Ptolemaic universe) Arc minute- 1/60 of a deg Parallax- apparent change in position of an object due to a change in location of observer Arc second- 1/60 of an arc minute Retrograde motion- planets move westward, then resume their eastward motion (backward Angular diameter- angle formed by lines extending from the observer to opposite edges of an object motion) Circumpolar constellation- constellations so close to celestial poles that they never set/rise Heliocentric universe- model of universe with Sun in centre, Earth rotated on its axis and Rotation- Earth’s rotation on axis produces day and night revolved around Sun (Copernican universe) Revolution- orbital motion about a point located outside the orbiting body, revolves around Sun Ellipse- closed curve around 2 points (foci), distance from 1 focus to the curve and back to produces yearly cycle the other focus remains constant Ecliptic- apparent path of Sun around sky Semimajor axis- half of the longest diameter of an ellipse Vernal equinox- Sun crosses the celestial equator moving northward Eccentricity (e)- half the distance between the foci divided by the semimajor axis (when e Summer solstice- Sun is at its farthest north equal 1, ellipse is elongated, equal 0, circular) Autumnal equinox- Sun crosses celestial equator going southward Empirical- description of a phenomenon based only on observations, without explaining why Winter solstice- Sun is at its farthest south it occurs (Kepler’s laws) Perihelion- orbital point closest to Sun (opposite: aphelion) Speed- rate at which an object moves (distance/time) Solar eclipse- New Moon, b/w Earth and Sun (Sun, Moon, Earth), blocking view of Sun (moon Velocity- speed and direction of travel of an object and sun have equal apparent diameters) Acceleration- rate of change of velocity with time Umbra- region of total shadow Mass- measure of amount of matter making up an object (same no matter what forces act on Penumbra- portion of a shadow that is partially shaded object) Annular eclipse- Moon’s apparent diameter smaller than Sun, too small to fully cover Sun Weight- force that gravity exerts on an object Lunar eclipse- Full Moon, (Sun, Earth, Moon) darkening of Moon moves through Earth’s shadow Inverse square relation- force (gravitational) decreases as the sq of the distance b/w objects (visible to all people on 1 side of Earth) increases Saros cycle- 18 yr, 11 1/3 day period after which the pattern of lunar and solar eclipses repeat Circular velocity- velocity of an object needed to stay in orbit around another object Declination- latitude, degrees, arc mins/secs north(+) or south(-) of the celestial equator Geosynchronous satellite- satellite that orbits eastward around Earth in 24 hrs and remains Right ascension- longitude, hours, minutes, seconds of time above same spot on Earth’s surface (42,250 km) Timekeeping by Day Centre of mass- balance point of a system of 2 bodies, rotates in the absence of external Solar day- average time between successive crossings of the Sun on the local meridian (24 hrs) forces Sidereal day- time between crossings of any star on the local meridian (23 hr, 56 mins) Closed orbit- orbit repeatedly return to starting point Timekeeping by Month Escape velocity- initial velocity an object needs to escape from the surface of a celestial body Synodic month- complete cycle of lunar phases (29.5 days) (into open orbit) Sidereal month- time for Moon to orbit Earth once relative to any star (27.3 days) Spring tides- at New and Full Moon, lunar and solar tides add together to produce extra high Timekeeping by Year and low tides st rd Sidereal year- complete one full orbit around Sun relative to any star Neap tides- 1 and 3 quarter Moons, solar tides cancel out part of lunar tides so high/low Tropical (solar) year- time between successive spring/autumnal equinoxes tides are not extreme Apparent solar time- time measured by the location of the Sun in the local sky - ancient astronomers thought Earth did not move because no parallax - former times, constellations were a loose grouping of bright stars, boundaries were approx, region - thought if Earth moves, could see sky from diff locations at diff times of year, and see s in southern sky that were not visible in parallax distorting shapes of constellations northern latitudes were not identified with any constellations - saw no parallax because parallax of stars is too small to see with the unaided eye - 48 of form constellations still in use, added 40 to fill gaps - Aristotle thought the Sun, moon, stars were carried around Earth on circular spheres - constellations/stars move in westward direction from one season to next - Ptolemy created a mathematical model, kept Earth-centred model, by adjusting size and rate - star with ancient arabic name probably relatively bright of rotation of epicycle and deferent, he could approx the retrograde motion of a planet - all stars are part of some constellation - Christians believed in Aristotle’s model that most perfect region is heavens, most imperfect - limitations to apparent visual magnitude system: is Earth’s centre (1) some stars are so bright, magnitude scale must extend to negative - Copernicus was Roman Catholic, fear of persecution, did not challenge Ptolemaic model (3) some stars emit infrared/ultraviolet light, invisible to human eye - Copernican model failed to predict positions of the planets any more accurately than (4) doesn’t tell anything about star’s true power output because star’s distance is not included Ptolemaic model could, used circular orbits - if Earth did not turn on axis, a day = a year - Copernican model: provided simple explanation of retrograde without using large epicycles, - Earth’s equator is 23.5 deg relative to its orbit all planets were treated the same, followed orbits that circled Sun - Earth’s large mass and rotation keep its axis of rotation pointed toward near Polaris - Tycho Brahe: detected star beyond the Moon, which contradicts Aristotle’s unchanging - Earth has a bulge around middles, the gravity of the Sun and moon pull on it, twisting Earth’s axis starry sphere (stars must be nearer than Moon) upright perpendicular to its orbit (cause rotational axis of Earth to precess) - Kepler’s Laws of Planetary Motion - these forces and Earth’s rotation cause Earth’s axis to precess in a slow circular sweep (26000 (1) orbits of planets are ellipses with the Sun at 1 focus, orbit faster when near Sun years, 1 cycle) (2) a line from a planet to the Sun sweeps over equal areas in equal intervals of time - precession moves celestial poles and equator since they are defined by Earth’s rotational axis (conservation of angular momentum) rd 2 3 - eclipses visible at a given location the same for every 3 saros cycle (3) P y a AU (orbital period squared= semimajor axis cubed) - eastward rotation of Earth causes sun, moon, stars to move westward in sky - Galileo adopted Copernican model, not publicly because fear of persecution - Galileo was first person to observe sky carefully with telescope about place of Earth - new theory of solar nebula: rotating gas and dust of solar nebula could have (1) mountains and valleys on Moon become unstable and formed outer planets by direct gravitational collapse, (2) 4 Moons of Jupiter (revolved around Jupiter, there are centres of motion other than Earth) without first accreting a dense core from planetesimals (explains how Jovian (3) phases of Venus go through phases like the Moon (so revolved around the Sun) planets formed present mass so quickly, because so far from Sun, accretion - Galileo condemned by Inquisition for defending Copernicus, later confined in his villa would have taken long time) - Newton’s 3 Laws of Motion - Sun and planets revolve/rotate in same direction: formed from same rotating (1) a body continues at rest/in motion in a straight line unless acted upon by some force cloud (2) a body’s change of motion (acceleration)f is proportional to the force acting on it & direction of the force - orbit of planets lie on same plane: rotating solar nebula collapsed into a (3) when 1 body exerts a force on second body, the second exerts an equal and opposite force back on first body disk, planets formed in that disk - Plato proposed all heavenly motion is circular and uniform - asteroids formed as rocky planetisimals b/w Mars and Jupiter, Jupiter - Newton thought some force must pull the Moon toward Earth’s centre: gravity prevented them from forming a planet (gravitationally disturbed) - all objects with mass attract all other masses in the universe - Solar nebula hypothesis: planetary systems should be common, planets form - gravitational force of attraction b/w 2 objects depends on product of masses of 2 objects from gases surrounding a star after it forms, disks of gas, dust, planets - an object orbiting Earth is falling (being accelerated due to gravitational force) toward Earth’s centre. An object in discovered orbiting other stars a stable orbit continuously misses Earth because of its horizontal velocity - 2 bodies of diff mass balance at centre of mass, located closer to more massive object - lowest velocity farthest from Earth and highest velocity closest to Earth Chapter 14 - Earth attracts Moon, Moon attracts Earth, Moon’s gravity explains ocean tides 14.1 - moon’s inertia keep Moon from smashing on Earth surface - jovian: hydrogen rich, low density (formed in outer nebula), rich in - centre of mass of Earth-Moon system is 80x closer to centre of Earth, inside Earth hydrogen and helium - centre of mass: point closer to more massive of two objects by how many more times massive it is than the less - Jupiter 11x Earth’s diameter, 71% of planetary matter in solar system - Jupiter and Saturn called gas giants, but filled with liquid massive object, massive object smaller orbit - Uranus and Neptune called ice giants, water in solid and liquid, blue - tidal force b/w Earth and Moon push Moon to higher orbit, decrease its orbital velocity (farther from Sun) - tide affect shape, orbit, rotation coloured from small amonts of methane in atmosphere - rotation of Earth drags tidal bulges slightly ahead of the Moon, and the gravitation of bulges of water pull Moon - Jovian planets core of rock and meter, no solid surface to walk forward in its orbit (grow largest by 4cm/yr) - atmospheres marked by cloud belts parallel to equators - have extensive moon system which affects planetary ring systems, some Chapter 12 active Solar nebula theory- theory of formation of solar system consistent with our current observations that supposes a 14.2 Jupiter rotating cloud of gas and dust gravitationally collapsed and flattened into a disk around the forming Sun at the centre, from which planets were formed Jupiter’s interior Terrestrial planet- small, dense, rocky, inner 4 planets -1.3x denser than water Jovian planet- large, low density, thick atmosphere, liquid/ice interior, outer 4 -orbits sun at 5.2 AU in 11.9 yrs 3 Types of Space Debris - sidereal rotation is 10 hrs, fastest spinning rate Asteroid- small rocky worlds, most orbit between Mars and Jupiter in asteroid belt - interiors composed mostly of liquid metallic hydrogen - stirred by convection currents and spun by planet’s rapid rotation, drives Comets- small icy bodies that orbit the Sun and produce tails of gas and dust when they approach Sun dynamo effect and generates magnetic field, 20x stronger than Earth’s Volatile- easily evaporated Kuiper belt- collection of icy planetesimals orbiting in a region from just beyond Neptune out to 50 AU or more - magnetic field traps charged particles from solar wind in radiation belt Oort cloud- hypothetical source of comets, a swarm of icy bodies understood to lie in a spherical shell extending to - rocky core of heavy elements 4x hotter than surface of sun 100,000 AU from the Sun Meteoroids- a meteor in space before it enters Earth’s atmosphere Atmosphere Meteors- small bit of matter (rock and metal) heated by friction to bright vapour as it falls into Earth’s atmosphere -magnetosphere responsible for auroras around magnetic poles - magnetic field and solar wind generate electric currents that flow around Meteorite- a meteor that survives its passage through the atmosphere and strikes the ground Carbonaceous chondrite- stony meteorite that contains small glassy spheres called chondrules and volatiles. These magnetic poles chondrites may be the least altered remains of the solar nebula still present in the solar system - rings discovered in 1979, Voyager I Meteor shower- display of meteors that appear to come from 1 point in the sky, understood to be cometary debris - belt zone circulation: atmospheric circulation where dark belts of bright Halflife- time required for half of the radioactive atoms in a sample to decay zones encircle the planet parallel to equator Uncompressed density- density of a planet would have if its gravity did not compress it - cloud layers are positioned at certain temperatures where ammonia, Ice line- boundary beyond which water vapour could freeze to form ice (low densities/ice in Jovian planets) ammonium hydrosulphide and water can condense Condensation sequence- sequence in which different materials condense from the solar nebula Planetesimal- small bodies that formed from the solar nebula and eventually grew into protoplanets Ring Protoplanet—massive object destined to be a planet, from the coalescence of planetesimals in the solar nebula -less than 1% as bright as saturn’s rings, reddish indicating ring is rocky Gravitational collapse- process which a forming body captures gas rapidly from surrounding nebula material not ice Differentiation- separation of planetary material inside a planet according to density - Forward scattering: optical property of finely divided particles to Outgassing- release of gases from a planet’s interior (Earth’s first atmosphere was outgassed) preferentially direct light in the original direction of the light’s travel -Roche limit: distance between a planet and satellite that can hold itself Heavy bombardment- intense cratering that occurred sometime during first 0.5 bill yrs in history of solar system together by gravity (when most craters formed) NEO(near earth object)- small solar system body (asteroid/comet)
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