Nats 1585: Astronomy Exploring The Universe - Lecture Notes PDF

Nats 1585: Astronomy exploring the universe Lecture 1: How did the greeks explain planetary motion? - Greeks geocentric model - Earth at the center of the universe - Heavens are perfect, therefore objects moving on perfect spheres or perfect circles This made it difficult to explain...

Nats 1585: Astronomy exploring the universe Lecture 1: How did the greeks explain planetary motion? - Greeks geocentric model - Earth at the center of the universe - Heavens are perfect, therefore objects moving on perfect spheres or perfect circles This made it difficult to explain apparent retrograde motion of planets - Over 10 weeks, mars appears to stop, back up, then go forward again The most sophisticated geocentric model was that of Ptolemy, the Ptolemaic model: - Accurate for 1500 years Summarize the *universal law of gravitation* both in words and with an equation.univaround an invisible point in a perfect circle (retrograde loop) The Copernican Revolution - Proposed a sun-centered model - Used model to determine layout of solar system (planetary distances in AU) - Model was no more accurate than Ptolemaic model, because it still used perfect circles Tycho Brahe - Compiled most accurate (one arcminute) naked eye measurements ever made of planetary positions - Still could not detect stellar parallax, and thus still thought earth to be at center of solar system (but recognized other planets go around the sun) - Hired Kepler, who used Tycho's observations Johannes Kepler - First tried to match Tycho's observations with circular orbits - 8 minute discrepancy led him to ellipses as opposed to perfect circles Ellipse: elongated circle. Eccentricity: how much an ellipse deviates from a perfect circle Major axis: the longest direction of an ellipse Semimajor axis: half of the major axis Perihelion: the point closest to the sun Aphelion: the point furthest from the sun Eccentricity is calculated using: distance between two foci, divided by the length of the major axis Keplers three laws of planetary motion 1. The orbit of each planet around the sun is an ellipse with the sun at one focus (nothing lies at the other focus) 2. As a planet moves around its orbit, it sweeps out equal areas in equal times - This means that a planet travels faster when it is nearer to the sun and slower when it is further from the sun To sweep out equal areas in equal times, the object moves ra/rp times faster at perihelion than at aphelion\ ra + rp = 2a, (a =semi-major axis) to find out how much faster an object is moving at perihelion vs aphelion, you could rearrange formula into rp = 2a -- ra 3. More distant planets orbit the sun at slower average speeds, obeying the relationship p\^2 = a\^3 - Where p = orbital period in years, a = average distance from sun in AU Orbital period = how long an object takes to move around its orbit once. How did Galileo solidify the Copernican revolution? - Overcame major objections to the Copernican view. Three key objections rooted in Aristotelian view were given below: 1. Earth could not be moving because objects in air would be left behind 2. Noncircular orbits are not perfect as heavens should be 3. If earth were orbiting the sun, we'd detect stellar parallax GO THROUGH WORKSHEET NEWTON First objection (nature of motion) - Galileo's experiments showed that objects in air would stay with earth as it moves - Aristotle thought that all objects naturally come to rest - Galileo showed that objects will stay in motion unless a force acts to slow them down (Newton's first law of motion) Second objection (Heavenly perfection) - Tycho's 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 non-perfect sphere) 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 using his telescope to see milky way is countless individual stars - If stars were much farther away, then lack of detectable parallax was no longer troubling - Also saw four moons orbiting Jupiter, showing not all objects orbit earth - Observations of phases of Venus showed that it orbits the sun and not earth Lecture 2: How did newton change our view of the universe? - Realized the same physical laws that operate on earth also operate in the heavens, builds on the idea of one universe - Discovered laws of motion and gravity What determines the strength of gravity? The universal laws 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 does Newton's loss extend Kepler's laws - Keplers laws apply to all orbiting objects not just planets - Ellipses are not the only orbital paths, orbits can be: - Bound (ellipses) - Unbound: parabola, hyperbola Center of mass - Because of angular momentum conservation, orbiting objects orbit around their center of mass Distance d1 and d2 of stars 1 & 2 from their center of mass are related by d1/d2 = m2/m1 Force of gravitation = g (m1 X m2) / d\^2 Newton's version of Kepler's third law P\^2 = 4pi\^2/ G(m1 + m1)(a\^3) OR M1 + M2= 4pi\^2a\^3/Gp\^2 P= orbital period (time taken to complete a single full orbit) A= average orbital distance between objects (dmin + dmax)/2 (m1 + m2) = sum of object masses Newton's law of gravity and motion showed the relationship between the orbital period (p) and average orbital distance (a) of a system tells us the total mass of the system. Examples: - Earth's orbital period (1 year) and average distance (1 AU) tells us the suns mass Newton's three laws of motion 1. An object moves at a constant velocity unless a net force acts to change its speed or direction Newtons second law of motion - Force = mass x acceleration - Force = rate of change in momentum Newton's third law of motion - For every force, there is always an equal and opposite reaction force Lecture 4: Light and matter Colours of light: white light is made up of all the colours of the rainbow 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 1. Emission 2. Absorption 3. Transmission a. Transparent objects transmit light b. Opaque objects block (absorb) light 4. Reflection / scattering c. A mirror reflects light in a particular direction d. A movie screen scatters light in all directions Interactions of light with matter - Determine the appearance of everything around us What is light? - Light can either act like a wave or a particle - Particles of light are called photons Waves: - Pattern of motion that can carry energy without carrying matter along with it Properties of waves - Wavelength: distance between two wave peaks - Frequency: number of times per second that a wave vibrates up and down - Wave speed = wavelength x frequency Electromagnetic waves - A light wave is a vibration of electric and magnetic fields - Light interacts with charged particles through these electric and magnetic fields Wavelength x frequency = speed of light = constant Photons: Particles of light - Particles of light are photons - Each photon has a wavelength and a frequency - The energy of a photon depends on its frequency Lambda = wavelength, f = frequency, c = speed of light C = 3.00 X 10\^8 m/s = speed of light Planck's constant H = 6.626 X 10\^-34 Joule x s E = h x f = photon energy Atomic terminology Atomic number = \# of protons in nucleus Atomic mass number = \# of protons + neutrons Molecules = 2 or more atoms Isotope: same \# of protons but different \# of neutrons How is energy stored in atoms - Electrons in atoms are restricted to particular energy levels If a photon does not satisfy any energy level requirements the photon and electrons will not interact with each other. The energy requirement must be exactly the eV required (e.g ground state of 0 to 10.2 eV, energy of photon must be exactly 10.2eV) Electrons moving up energy levels results in an excited atom The only allowed changes in energy are those corresponding to a transition between energy levels Ground state 0ev At the highest excited state, if given an eV larger than that of the discrete state belonging to the highest excited state, the electron will be kicked out of the atom. Photon emanated eV will always correspond to the DIFFERENCE between energy levels For example: 0: 0eV 1:10.2eV 2:10.8eV From 1 to 2, you would get a photon of 0.6eV What are the three basic types of spectra? - Spectra: astrophysical objects that are usually combinations of three basic types 1. Continuous (e.g, filament lightbulb, sun) 2. Emission There is a probability that electrons will drop from excitement levels, this results in photons being emitted. On a wavelength intensity graph, this is depicted as energy spikes. 3. Absorption - Happens when there Is a continuous spectra that goes Chemical fingerprints Each type of atom has a unique set of energy levels Each transition corresponds to a unique photon energy, frequency, and wavelength Downward transitions produce a unique pattern of emission lines Because those atoms can absorb photons with those same energies, upward transitions produce a pattern of absorption lines at the same wavelengths Each type of atom has a unique spectral fingerprint How does light tell us the temperatures of planets and stars? The two laws of thermal radiation - Nearly all large or dense objects emit thermal radiation - An object's thermal radiation spectrum depends only on one property, its temperature 1. Hotter objects emit more light at all frequencies per unit area 2. Hotter objects emit photons with a higher average energy How does light tell us the speed of a distant object? The doppler effect - Measured in shifts in the wavelengths of spectral lines The amount of blueshift or redshift tells us an object's speed toward or away from us Blueshift = object moving towards us, wavelength decreases, frequency increases Redshift = object moving away from us, wavelength increases frequency decreases Formula: lambdaobs -- lambdaem / lambdaem = v/c Doppler shift tells us only about the part of an object's motion toward or away from us: you can only get one velocity direction Lecture 5: the sun Is it on fire? Chemical energy content/luminosity \~ 10,000 years The sun is not on fire, not enough energy to explain how long the sun has been active Is it contracting? - Each layer of the sun has its own mass Gravitational potential / luminosity \~ 25 million years Sun is not contracting It can be powered by nuclear energy (E=mc\^2\_ Nuclear potential energy (core) / luminosity \~ 10 billion years The stable sun - Sun is in gravitational equilibrium (also called hydrostatic equilibrium) - Weight of upper layers compresses lower layers Gravitational equilibrium: - Energy supplied by fusion maintains the pressure that balances the inward crush of gravity (this is why the sun is neither contracting or expanding) Energy balance: - The rate at which energy radiates from the surface of the sun must be the same rate at which it is released by fusion in the core Gravitational contraction: - Provided the energy that heated the core as sun was forming - Contraction stopped when fusion began Basic properties of the sun Radius: 6.9 X 10\^8m (109 times earth) Mass: 2 X 10\^30kg (300,000 Earths) Luminosity: 3.8 X 10\^26 watts Rotation: 25 days at the equator to 30 days at the poles Structure of the sun Solar wind: a flow of charged particles from the surface of the sun Corona: very thin material, outermost layer of solar atmosphere \~ 1 million K Chromosphere: middle layer of solar atmosphere \~ 10,000 -- 100,000 K Photosphere: where the plasma becomes transparent, visible surface of sun \~ 6000k Convection zone: energy transported upward by rising hot gas Radiation zone: energy transported upward by photons Core: energy generated by nuclear fusion at \~ 15 million K How does nuclear fusion occur in the sun? - At low speeds, EM repulsion prevents the collision of nuclei - At high speeds, nuclei come close enough for the strong force to bind them together Fission: - Big nucleus splits into smaller pieces (nuclear power plants e.g) Fusion: - Small nuclei stick together to make a bigger one (e.g, the sun, stars) The sun releases energy by fusing four hydrogen nuclei into one helium nucleus The proton-proton chain is how hydrogen fuses into helium in the sun In: 4 protons Out: - 4He nucleus - 2 gamma rays - 2 positrons - 2 neutrinos Total mass is 0.7% lower. This difference in mass is converted to energy by E=mc\^2 HAVE TO FINISH THIS LECTURE Lecture 6: Surveying the stars 15.1 properties of stars (will be on midterm) How do we measure stellar luminosities? Luminosity: total amount of power (energy per second) the star radiates into space Apparent brightness is the amount of starlight reaching earth (energy per second per square meter) The brightness of a star depends on both distance and luminosity Apparent brightness versus luminosity Luminosity: amount of power a star radiates (energy per second = watts) Apparent brightness: amount of starlight that reaches earth (energy per second per square meter) The amount of luminosity passing through each sphere is the same - Area of sphere 4pi X (radius)\^2 - Divide luminosity by area to get brightness The relationship between apparent brightness and luminosity depends on distance: Apparent brightness = luminosity / 4pi (distance)\^2 We can determine a stars luminosity if we can measure its distance and apparent brightness: Luminosity = 4pi(distance)\^2 X (brightness) Stellar parallax - Parallax is the apparent shift in position of a nearby object against a background of more distance objects - Apparent positions of nearest stars shift by about an arcsecond as earth orbits the sun - Parallax angle depends on distance - Parallax is measured by comparing snapshots taken at different times and measuring the shift in angle to star How do we measure stellar temperatures Spectral type and temperature Cecilia Payne-Gaposchkin showed in her phd that the level of ionization also reveals a stars temperature - This tied spectral types to stellar temperatures Every object emits thermal radiation with a spectrum that depends on its temperature 1. Hotter objects emit more light per unit area at all frequencies Lambdapeak = b/T Where b is a constant with value = 2.898X10^-3^ m K Lambda peak is inversely proportionate with temperatures High temp = lowlambda peak Low temp = highlambda peak How we measure stellar masses? Measuring stellar masses and radii - The orbit of a binary star system depends on strength of gravity Types of binary star systems - Visual binary: we can directly observe orbital motions of these stars - Spectroscopic binary: we determine orbit by measuring doppler shifts - Eclipsing binary: measuring periodic eclipses We measure mass using gravity - Direct mass measurements are possibly only for stars in binary star systems P^2^ = 4pi^2^/G(M1+M2) (a)^3^ P = period A = average separation Need 2 of 3 observables 1. Orbital period (p) 2. Orbital separation (a or r = radius) 3. Orbital velocity (v) V = 2pi(r) / p Lecture 7: stellar nurseries Star-forming clouds - Stars form in dark clouds of dusty gas in interstellar space - The gas between the stars is called the interstellar medium Composition of clouds - Determined using absorption lines in star spectra - 70% H, 28% He, 2% heavier elements in our region of milky way Molecular clouds - Most of the matter in star forming clouds are molecules - Molecular clouds have a temp of 10-30 K and a density of 300 molecules per cubic centimeter Interstellar reddening - Stars viewed through the edges of the cloud look redder because dust blocks blue light (short wavelength) more effectively than red light (long wavelength) Long wave-length infraredlight passes through a cloud more easily than visible light. Observations of infrared light reveal stars on the other side of the cloud Observing newborn stars - Visible light from newborn stars are often trapped within dark dust gasclouds where they formed - Observing the infrared light from a cloud can reveal the newborn star embedded inside it Glowing dust grains - Dust grains that absorb visible light heat up and emit infrared light of even longer wavelength - Long wave infrared is the brightese from regions where many stars are forming Why do stars form? Gravity vs pressure - Gravity can create stars only if it can overcome the force of thermal pressure in a cloud - Emission lines from molecules in cloud can prevent a pressure buildup by converting thermal energy into infrared and radio photons Mass of a star-forming cloud - A typical molecular cloud must contain at least a few hundred solar masses for gravity to overcome pressure - Emission lines from molecules in a cloud can prevent a pressure buildup by converting thermal energy into infrared and radio photons that escape the cloud Fragmentation of a cloud - Gravity within a contracting gas cloud become stronger as the gas becomes denser - Gravity can therefore overcome pressure in a smaller pieces of the cloud, causing it to break apart into multiple fragments, each of which may go on to form a star Each lump of the cloud in which gravity can overcome pressure can go on to become a star Isolated star formation - Gravity can overcome pressure in a relatively small cloud if the cloud is unusually dense - Such a cloud may make only a single star Stages of star birth What slows the contraction of a star-forming cloud? Trapping of thermal energy - As contraction packs molecules and dust particles of a cloud fragment closer together, it becomes harder for infrared and radio photons to escape - Thermal energy begins to build up inside, increasing internal pressure - Contractions slow down, and the center of the cloud fragment becomes a protostar Growth of a protostar - Matter from the cloud continues to fall onto the protostar until either the protostar or a neighbouring star blows the surrounding gas away. Called the T-Tauri phase of stars.