2024F unit 3 lecture slides (Part 2 of 2) .pdf

Introductory Astronomy (PHYS1000-2) Unit 3: History of Astronomy (Part 2) Chapters 2.2–2.4, 3 (all) Ptolemy’s Improved Geocentric Model In the 300 yrs since Aristotle, mr precise positional data fr planets dvlpd – resulted in chngs needed to geocentric model… Ptolemy moved deferents off-centre frm E (but still circular) →Supported idea tht motion of planets ws uniform, but not uniform w.r.t. Earth Lots of epicycles needed to accuratly expln planet motions, esp. retrograde motions. (later models: no fewer than 80 circles used) -Fine-tuned, model worked remarkably well in predicting motion of planets/Moon/Sun given measuring techniques at time. To better understand this model, click: https://youtu.be/wGjlT3XHb9A Bc model supportd human’s central importnce in U & principles of harmony/perfection in nature’s design, RC Church supported this model well into the 1600s – Upheaval in European society: Wars/ Plagues/ Famine/ Social Structure hold back any advancmnt of new ideas. Ptolemaic Model Problems Slow improvmnts technology ovr following centuries did allw plotting mr precise planetary positions Data → Ptolemy’s model flawed – no way to adjust (Can’t predict planet motions really accurately) → mainly bc main ideas were completely wrong! -E not centre of U/ motn of objts not uniform/ nor circular Problem: Entire theory was built frm philosophical basis - Not based on scintfc observs/principles Copernicus and the Heliocentric Model Nicholas Copernicus (1473–1543) – polish mathematician, astronomer & RC cleric (wealthy family connected politically → schooling) → Ptolemy’s model too complex to be real - nature should be simple →Copernicus aware of & adopted Aristarchus’s sun-centered idea – added new details & supporting arguments – backed up w math → Proposed his own Sun-centered (HELIOCENTRIC) model but fearing Church, not published until aftr death.(1543 AD) Points of Model: - Moon goes arnd E - E spins on own axis & orbits Sun like othr plnts - Planets arranged: Merc, Venus, E, Mars, Jup, Sat, then strs in orbt arnd Sun - By themslvs, orbits/speed of plnts could account fr planetary motn (motn of inner plnts & retrograde) -But still used perfect circles (some offset) & used smll epicycles on ea. planets orbit → both wrong! *Critical argument that E not center of the U led to enorms chg in undrstng of U and shift towrds freer thinking/creativity/ experimntatn/ evidnc-based reasoning - helped open door to rapid development of science/philosophy/techn - Copernican Revolution Heliocentric (Sun-Centred) Model & Retrograde Motion One of best attributes of Copernicus’ S-centred model: hw accurately it reproduced retrograde motion of outer planets…eg. Mars Earth’s travels faster around its orbit than Mars (29.8 km/s vs. 24.1 km/s) – smaller orbit as well → E yr: 365d vs. M yr 688 d →Earth “passes” Mars every 18 months… As “passing” happens, alignment agnst bkgrnd stars shws Mars reversing course in sky. Once past Mars, curvature of E’s orbit & speed dffrnc betwn planets means Mars appears (from Earth) to move prograde again in the sky. Unfortunately, Copernicus’s ideas not widely accepted bc contradicted conventional wisdom & was believed to violate RC church doctrine at the time (publshd @ C’s death) Tycho Brahe - TB (1546-1601) Danish astronomer/ nobleman/ part-time mathematician Like Copernicus, family well-connected (related to Danish King) Used family money to build Uraniborg (castle & observatory) Rich aristocrat, flamboyant & eccentric lifestyle – threw many parties, drank/ate excessively – lost part of nose in duel Invented new astro instruments for measuring star/planet positions. Geocentrist but knew Ptolemaic model had real problems Obsessed w modifying Ptolemy’s model to explain retrograde motion & predict positions better. Collected most precise data on planetary motion up to his time – particularly Mars. Brahe Develops a Modified Geocentric Model: Still thought Earth must be at center of slr system w Sun orbiting E (but recgnzd tht other planets go arnd Sun) – still using perfect circles/spheres. Brahe’s math skills relatively good, but not great; Frustrated: couldn’t modify model to explain Mars’ retrograde motion well & ego wouldn’t allow his to accept his model fundamentally flawed. →Finally hired Johannes Kepler (young German mathematician) -diffrnt views, bt eventlly JK takes ovr work when Brahe dies (1601) Johannes Kepler (1571–1630) Deeply religious, sickly, from poor family; Worked up to academic positns & contracts thru brilliant mathematical & theoretical abilities in astronomy. While v. religious, mixed astro ideas: - followd ideas of Copernicus & ancient Greeks “God made U according to mathematical plan” Attemptd to relate sun-centred U structure to nested geo. solids to hold spherical shells (Greek philosphrs) Unable to complete modified model of U w/o lots precise data (data availbl not complete engh to test) until TB’s death (Brahe jealous). For yrs, Kepler tried to match TB's obsrvns w circular orbits/spheres…Hwvr, 8-arcminute discrepancy frm obsrvs →finally discards core ideas: Perfect Geometric structrs do not support plnt orbits Planets must orbit Sun in ellipses (not perfect circles)! → pointed to a complete reformation in astronomy → (comeback to Kepler’s revolutionary ideas later) Birth of Modern Astronomy: Galileo Galilei Italian astronomer, inventor, 1st scientific physicist; mathematician, writer, philosopher Considered Father of modern science - grew up in Pisa, Italy: sent to Jesuit school –wanted to be monk (1564-1642) (father: NO – a doctor!) – studied at U of Pisa Inventions: Thermometer, compass, Withdrew frm U @ 21 yrs old, became mathematics hydraulic pump, pendulum clock, prof/engineering consultant (wrote books as well). (improved (astronomical) telescope) Conducted mny sci expts.; Using inclined planes→ discvrd gravity accelerates objcts same amt no matter their mass. (Apollo 15 xprmnt) First to mathematically describe motion of objects in E’s gravity (projectile motion) – Self-assured; among 1st applications: military artillery/orbits/rocketry to publically question First to mathematically explain non-uniform ancient ideas/church motion in terms of forces (applied/friction/etc) teachings. Galileo’s Contributions: Birth of Modern Astronomy Sci Method: Devlpd a firm belief in the need to perform experiments to test ideas/ use observatns as evidnc - build theories frm bottom-up →radical approach went agnst acceptd ideas of Greeks (human mind superior – creation of G(g)od(s) so no need to actually physically test ideas in real world) Note: At this time church-instituted education system: maintain status quo - less divergent thinking keeps ppl frm questioning system -Mny of those in pwr used eductn sys (amg othr things) to maintn pwr/status/control 1609 – Galileo hears of new invention “TELESCOPE” built by lens maker frm Holland (H. Lippershey) & builds own w improved design. Realizes he cn mk money, wrks hard to improve lens quality, power & design – sell to Venice merchants. At night, aims telescope at sky & begins making incredible discoveries… Observations of Galileo with Telescope (Moon) Observes Moon over 2 months & makes sketches (some detailed) of terrain & changing lighting on surface (phases) – shadows shw elevation features -Concludes Moon has mountains, valleys & craters (terrain much like E’s). -Obsrvtns contrary popular view (frm Aristotle) - that all heavenly bodies are perfect & spherical… how can Mn’s sphere be imperfect – like E’s? - (E not a “heavenly body” to people of time ) Observatns raised othr questions too… -Can there be other imperfect heavenly bodies? or -Can E now be called a heavenly body? (not a special case)? Observations of Galileo with Telescope (Sun) Projects image of Sun through telescope & sees it hs drk blemishes “sunspots” tht ↑ & ↓ size & change w time. Sunspot motion frm day-to-day also show that Sun rotates on own axis (estimates 1x/month) -axis of rotation ~perpndclr to ecliptic plane (ie. Sun’s eqtr @ ecliptic, whereas E’s eqtr is tilted to ecliptic) For Galileo, these hv Implications: S another imperfect heavenly body & one that is not even constant in appearance… Is Sun somehow more closely connected to the ecliptic plane than E? → more connected to the other planets than E? Observations of Venus w Telescope (1610) Galileo observes Venus telescopically: sees changing phases & changing size of planet as it swings first Away frm Sun, thn back towards it. In fact, as predicted by Copernican model, Venus shows complete cycle of phases, much like our Moon bt w differncs (doesn’t orbit E) Ptolemy’s geocentric model predicts dffrnt phase pattern thn tht seen. (no full/ gibbous Moon) Only a heliocentric (Sun-centred) model accurately explains observed cycle. Observations of Jupiter w Telescope Observes four tiny points of light very close to planet Jupiter moving in cyclical pattern from one side of it to other. Realizes they are moons circling Jupiter just as our Moon circles E. Fact tht another planet hs moons orbiting it provided greatest support, in his mind, for the Copernican heliocentric model. E not at the center of all things! Spent a lot of time studying moons -discvrd they ea. diffr in brightness (sz) & some even chng slightly in individl brightness as well. (dynamic?) Called the “Galilean moons” of Jupiter Galileo Takes on the RC Church All these observatns ran directly counter to acceptd scientific beliefs of the day. (taught by Church) →Strongly supported view tht E not centre of all things, at least 1 plnt orbited S, not E & at least some heavnly objcts not “harmonious/ perfect” (Late 1610) Galileo published observtnl findings along w controversial conclsns supporting Copernican model, challenging both “scientific” orthodoxy & teachings of the Church. (books in Italian not Latin) Upset a lot of Church’s elite (bishops, not initially the Pope though) & warned to back off. Didn’t: Published satirical novelette mocking & ridiculing powerful people opposing his ideas, using faintly-veiled caricatures. 1616 Church judged ideas heretical; banned his & Copernicus’ works; Galileo continued to collect data/publish. 1633 Inquisition→Forced undr threat of torture to retract his claim (Heliocen-model) Copernican System & Scientific Method Win Out John Milton (poet) visits Galileo →Galileo spent rest of life (10 yr) under house arrest. But damage to orthodox view (geocentric U) alrdy done - everyone bcm aware of G’s dscvries & conclsns – Copernican model of U quickly bcm prevailing view. Galileo’s use of objective approach in his scientific methods demonstrated that personal biases, political pressures & other influencing factors cn eventually be overcome to discover the “truth” about how nature works. Galileo’s scientific method became foundation for all future scientific research. The Laws of Planetary Motion: Kepler Reprise Johannes Kepler contemporary of Galileo (corresponded) – Theorist, not really observer (poor eyesight) – depended on positional data of planets frm others -Work hindered by Brahe until his death (then rcvd decades of v. accurate positional data). -Kepler believed in basic Copernican model, but should be simpler – no epicycles Aftr yrs of reworking/testing diff orbit properties, conclusion: Circles don’t work to explain motions seen (particularly Mars) Found that planets follow elliptical orbits instead! Work led him to develop 3 Laws of (ellipses highly exaggerated) Planetary Motion: Kepler’s 1st Law of Planetary Motion… The orbital paths of the planets are elliptical with the Sun at one focus of the ellipse. Semi-major axis Ellipse is a flattened circle. 2 foci equidistant from centre and lay on major axis (longest axis) Farther foci apart, the mr stretched from a circle an ellipse becomes (↑℮) Eccentricity = (dist between foci) (℮) major axis length Semi-major axis: half length of major axis - it is the longest radius frm centre - together with (e), all we need to describe Value btwn 0 1 size & shape of planet’s orbital path (knowing the semi-mjr axis means u also knw length of (circle → 0) major axis) Kepler’s 1st Law (cont’d): Terminology Perihelion: point where object comes closest to Sun in its orbit AD Perihelion Distance (PD) –distance of planet frm Sun at closest approach Aphelion: point in orbit where PD planet is farthest from the Sun Aphelion Distance (AD) –distance away frm Sun at farthest in pt. of orbit Only Mercury has an orbit whose eccentricity is noticeable by the human eye (e= 0.21) …othr plnt orbits ~ look like circles. (“weak” ellipses) Earth (0.017); Venus (0.007); Mars (0.09) →Only fr this reason did Ptolemy & Copernicus’ models appear to work at all. Kepler’s 2nd Law of Planetary Motion… An imaginary line connecting the Sun to any planet sweeps out equal areas (A) of the ellipse in equal intervals of time (t). Kepler discovered tht the speed of a planet in its orbit increases as it travels towards the Sun (from aphelion to perihelion) and decreases as it moves away (from perihelion back out to aphelion) →Now we know that this is due to Sun’s gravity working with & against planet’s motion. So planets travel faster near the Sun (wide/short area) and slower when farther away (long/skinny areas). Applies to all objects held gravitationally in orbit around anything in U! Kepler’s 3rd Law of Planetary Motion… After studying planet orbits w his elliptical orbit model another 10 yrs, published 3rd law (1619): The square of a planet’s orbital period is proportional to the cube of its semi- major axis. P2 = a3 (Earth years) (in astronomical units) ∴ 𝜌 = √𝑎3 or 𝛼 = ∛𝜌2 Kepler’s insight boils down to…not only do planets speed up and slow down, but also orbit Sun w overall (avg) speed set by their distance from Sun. Closer a planet orbits Sun, faster its overall speed around the Sun (Shorter its Period - time planet takes to complete 1 sidereal orbit) Farther a planet orbits Sun, slower its overall speed, longer its period. →Relatnshp cn be descrbd mathematically (see above) What is an “Astronomical Unit” (AU)? To simplify measuring/ comparing distances in Mars Mercury 1.52 AU 0.38 AU space, AU was developed. 1 AU set to Earth’s average Earth distance from Sun = 1 AU 149,597,870 km. (150M km) Venus Compare to other planets… 0.7 AU Saturn 9.5 AU Jupiter 5.2 AU Radar ranging by reflecting radio waves off of distant 19.2 AU planets (not Sun) currently best method of direct 30 AU measurement of distance (timing of signal back and forth). Kepler’s 3rd Law (Cont’d) Below: basic data describing orbits of 8 classical planets in solar system. Remember: Semi-major axis ‘describes orbit size”, Eccentricity describes “stretch” Periods get longer with distance, (e) varies, but ratio of P2/a3 is a constant! Kepler only had data on six, yet relationship still seems to hold pretty well (predicts) →Uranus/Neptune constant deviations due to grav. attractions btwn them. Isaac Newton: Father of Gravitation & Dynamics (1642-1727) British physicist/mathematician/astrnmr. -One of most brilliant people ever/ influential scintst - He (& Gottfried Leibniz) invented calculus -many accmplshmnts: (eg. Presdnt Royal Society, published books, parlimentarian, Chair of Math at Cambridge Univ, knighted, Master of British Mint ,etc.) -obsrvrd that when prism breaks white light into continuous spectrum of light rays, each colour L ray bends (slows down) differently – diffrnt L rays behave diffrntly →Colour an intrinsic property of light rays themselves →that means, objects hv no colour; they appr to have colour bc of their interaction w colours of light) (eg. When reflecting/absorbing/scattering the light they receive) →invented new type telescope: reflector - used 2 mirrors 1st collects light/concentrate it; 2nd sends L sideways to mag. lens (Newtonian Telescope) Isaac Newton (cont’d) Shortly after receiving MA (Cambridge) forced home, U tmprly closed due to Great Plague (1665). V. Productive period – developed major ideas for theories on Calculus, Optics & Light, & Gravity. Gravitation: Newton had read the works of Ptolemy,Copernicus,Galileo & Kepler -they could describe motion (Galileo ‘freefall’) – but no clear ideas abt why happens (forces at work? - vague) Stdyng Galileo’s exprmnts, Newton developed idea diff. forces @ work: - Some act instantaneously, others continuously. Saw grvty as continuous force twrds E’s centre. Moon just like apple – accelerates twrds E’s centre due to G Motion any object in E’s grav. field can be imagined as combination of vert/hrzntl components Moon doesn’t hit ground bc has → only vert compnnt affected by gravity perpendclr motion (which is unaffected). Newton’s Universal Law of Gravitation Newton soon realized all objects in space have gravity & pull on each other. Strength of the gravitational (force) pull btwn them depends on: 1) How massive they each are (how much is being pulled/ how strong is gravity of each) 2) How far apart they are (grav. pull weakens exponentially as distance increases) Developed mathematical relationship known as the Universal Gravitation Equation: For two massive objects, the gravitational force is proportional to the product of their masses divided by the square of the distance between them. Newton’s Laws The gravitational pull of the Sun keeps the planets moving in their orbits. Because planet’s direction of Gravitational pull of Earth motion is changing, its velocity is changing→ so it is accelerating This acceler of E is caused by Sun’s gravit. force. Similarly E’s gravity pulls back on Sun, causing it to accelerate (v. small wobble orbit)→ but E’s relatively small mass (gravity) and Sun’s large mass cause Sun’s Different planets’ orbital motions affected acceleration to be incredibly small. by masses of individual planet and Sun and distance btwn their centres. Newton’s Laws Massive objects actually orbit around their common center of mass; if one object is much more massive than the other, the center of mass is not far from the center of the more massive object. For objects more equal in mass, the center of mass is between the two. Newton’s Laws of Motion 1679 - Newton considers Kepler’s laws of planetary motion & gravitation’s effect on the orbits of planets. Newton's reawakening interest in astronomical matters further stimulated by appearance of a comet in winter of 1680–1681. Gained confidence rules governing motion of objects in space also could be applied on E Eventually dvlpd 3 general laws of motion tht could be used to explain exactly hw objects interact w the world & with each other - published in book “Principia Mathematica” (V. important book in history of science) Newton’s Laws of Motion Newton’s first law: (Law of Inertia) -really restating something Galileo discovered, in a new way… An object at rest will remain at rest (a) Example: Think of a and an object moving in a straight line at magician pulling a table constant speed (uniform motion) will not cloth out from under a change its motion (b) unless an external set of plates… force acts on it (c). …or why seatbelts are necessary… Momentum: a measure of an object’s motion = (mass x velocity) speed, direction - object’s momentum conserved unless outside force changes it. Newton’s Laws Newton’s second law: When an overall outside force (Fnet) is exerted on an object, the object’s acceleration is directly proportional to the net force acting on the object and inversely proportional to the mass the object has: Lrgr Force → lrgr acceleration acceleration = Fnet vs. Smaller Force → smaller acceleration of object object mass Bigger mass, smaller acceler. vs Smaller mass, lrger acceler. a = Fnet When lifting force of wings m is balanced by force of gravity, jet remains in level flight. If thrust force of fuel exhaust is lrgr than drag force on jet, jet will accelerate forward. Newton’s Laws Newton’s third law: When object A exerts a force on object B, object B exerts an equal and opposite force on object A. (how rockets work) Rocket engine pushes fuel backward out exhaust cone as it explodes (acceler. it backward) Object A and B may react differently to the force acting on them because of their own mass and/or different other Expanding exhaust pushes back on forces at work on them. rocket’s exhaust cone (moving it forward). Types of Orbits Around the Sun 1) Circular – SS objects rarely hv perfect circular orbits althgh some planets’ orbits close to circles (Venus, Neptune, Earth) - orbits nudged mny times, ovr Bs yrs by othr planets (rounded out) 2) Elliptical – characteristics of orbit dependt. on how/where object originated, & history of grav. interaction w other SS bodies over Bs years Eccentricity: - Classcl planets: Mercury most elliptical orbit how much orbit deviates frm - Pluto even ↑eccentricity thn Mercury circle (how 3) Parabolic – Orbits of most comets: spend v. little stretched time nr Sun. Most time, out in farthest part of orbit. out orbit is) 4) Hyperbolic – open-ended orbits - these objects are coming into solar system frm outside. - Traveling v. fast so they can escape gravitational pull of Sun. eg. Rogue comets/asteroids (Oumuamua) /stars Comet vs. Asteroid vs. Trans-Neptunian Objects (TNOs) Comets generally hv orbits of lrgr sz & grtr eccentricity than asteroids. Typically, e≥ 0.8 or higher, highly inclined. Bennett Halley Asteroid orbits most conctrtd. in belt between Mars & Jupiter “main asteroid belt”; but mny exceptions. TNO orbits transition btwn planets/asteroids/comets. Avg distance: always farther than Neptune. (30 AU) Most inclined in 2D or 3D, some very inclined Orbits: Terminology For bodies directly orbiting the Sun (like E): Perihelion: the pt in the orbit where body is closest to Sun (also traveling fastest) Aphelion: the pt in the orbit where body is farthest frm Sun (also traveling slowest) Earth: Perihelion: Jan 3rd Distance: 147.1 Mkm Aphelion: July 6th Distance: 152.1 Mkm (eccentricity greatly exaggerated & not to scale) For bodies traveling around a planet (moons/satellites): Perigee: the pt in the orbit closest to the planet (traveling fastest) Apogee: the pt in the orbit farthest from the planet (traveling the slowest) Launching Satellites into Orbit Earth’s gravit. pull constant – Fire a bullet horizontally frm gun: Faster the initial velocity of bullet, farther it travels before hitting ground. (see diagram) If velocity is fast enough (vc), it will never reach the ground – gravity will continually bend its path (c) - Bullet acheives orbit – falls continuously - Needs lots of initial energy bc E has a lot of mass (rel. strong gravity nr surface) Needs to reach 8km/s (17,500 mph) for circular E orbit >50 new satellites launched into orbit by Russia, Canada, USA, China, Japan, India, Israel & by the European Space Agency (ESA) ea. yr. Used for military surveillance, weather Escape Velocity: Speed needed to leave forecasting, remote sensing, global the Earth’s grav. Field and travel out into positioning, communications & tv/radio. solar system – needed vel.= 11km/s Controlling Satellite Orbits Because sats travel slower near To get continuous coverage of one apogee, orbits sometimes adjusted to area, put 2 satellites in similar elliptical allow longer dwell time over certain orbits, but time them to be at opposite part of planet’s surface. ends of orbits… For continuous coverage over entire planet at all times, such as Department of Defense's Global Positioning System (GPS), then we must hv a constellation of satellites with orbits that are both different in location and time.

2024F unit 3 lecture slides (Part 2 of 2) .pdf

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