Astronomy, week 3 notes
Astronomy, week 3 notes ASTR 1504 - 300
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This 8 page Class Notes was uploaded by Emily Notetaker on Saturday February 6, 2016. The Class Notes belongs to ASTR 1504 - 300 at University of Oklahoma taught by Xinyu, Dai in Spring 2016. Since its upload, it has received 113 views. For similar materials see Astronomy: Exploring the Universe in Astronomy at University of Oklahoma.
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Date Created: 02/06/16
Astronomy Week 3 Chapter 3 Early astronomy was used as a way to tell time and keep track of the seasons People observed objects in the sky and recorded their movement but didn t know what caused this movement Over time three main models for explaining the motion in the sky where proposed Aristotelian Model Geocentric or Earthcentered Sun Moon stars and planets orbit Earth in perfect circles Celestial objects are perfect spheres Couldn t explain retrograde motion the occasional apparent reversal of direction of the planets orbits Ptolemaic Model Geocentric Sun Moon stars and planets orbit Earth in perfect circles Each planet also orbits a point on its larger orbit of Earth creating epicycles Retrograde motion caused by epicycles Luau o I Pl l quot l39m w 0 Copernican Model Heliocentric or Sun centered Planets including Earth orbit the Sun in perfect circles Retrograde motion caused by Earth catching up to and passing other planets in orbit Couldn t accurately predict where a planet would be in its orbit at a given time The geocentric models seemed incredibly obvious to most people After all looking at the sky from Earth everything appears to be moving around us and we can t feel the motion of the Earth The Catholic Church also supported the geocentric model because it positioned Earth and therefore humanity in a privileged place in the universe For these reasons it would take the discoveries of two other scientists Galileo and Kepler for Copernicus heliocentric model to gain acceptance Galileo Galileo was the first person to use a telescope to observe space He was then able to observe craters on the Moon and spots on the Sun which proved they were not perfect spheres as Aristotle had believed He also discovered the four largest moods of Iupiter called the Galilean Moons proving that not all objects in space orbited the Earth He observed that Venus had phases like those of the Moon that corresponded to the apparent size of Venus as seen through his telescope which can only be explained by the heliocentric model Galileo published his findings in a book that indirectly insulted the Pope and was forced to recant his statements on Earth s motion and placed under house arrest by the church Galileo also conducted experiments with falling and rolling objects of different masses and found that they fell at the same speed He concluded that Earth s gravity accelerates all objects at the same rate regardless of mass Kepler Kepler used the extensive data on the motion and position of planets gathered by his fellow scientist Tycho prior to his death to form three laws that explained the motions of planets Kepler s First Law Planets orbit in ellipses Kepler explained discrepancies between predictions made about the orbits of the planets using the Copernican Model and actual observations of the positions of the planets by adjusting planetary orbits from circles to ellipses An ellipse has two foci and the Sun is one focus of the planetary orbit There is nothing at the other focus The distance between foci or eccentricity of a planet s orbit is nearly 0 meaning the planets orbit nearly in a circle Kepler s Second Law or Law of Equal AreasIf you imagine a line connecting the Sun and a planet the area swept by this line during a set time interval will be equal at any point in the planet s orbit Kepler s Second Law Planet on elliptical orbit Sun t5 These three areas A B and C will be equal t4 IKE1 if wu This is due to the fact that planets move faster during the time when their orbits are close to the sun and slower when they are farther away The different speeds at different points in a planet s orbit are caused by the gravitational pull of the Sun on the planet As the planet moves way from the Sun it is moving against the pull of gravity and slows down until it eventually changes direction and begins to move towards the Sun It then gains speed and at its fastest point swings around the sun and begins to move away again You can observe a similar effect by throwing an object into the air The object will slow down as it moves upward against Earth s gravity until at the top of its arc it changes direction and picks up speed as it falls back towards the ground Kepler s Third Law Period squareddistance cubed Planets farther from the Sun move more slowly than planets near the Sun For example even though Iupiter s orbit is only 52 times larger than that of Earth but it takes Iupiter nearly12 years to complete one orbit Kepler discovered the mathematical relationship between a planets distance from the Sun and its period or the time it takes to orbit one time Newton s Laws of Motion Newton s First Law An object at rest will stay at rest and an object in motion will stay in constant motion until acted upon by an outside force This law describes the tendency of objects to resist a change in motion also known as inertia Newton s Second Law If a net force acts on an object then the object s motion changes Fmaj The change of motion can be a change of speed or direction Velocity is an objects speed and it s direction Acceleration is the rate at which velocity changes You can find the net force that acts upon an object by multiplying the objects mass and the resulting acceleration so Fma You can calculate the acceleration that will result from a force on an object by dividing the force by the mass aFm Newton s Third Law Every action has an equal opposite reaction Forces act in pairs that are exactly as strong as each other and push in exact opposite directions When you drive a car the tires backwards against the Earth while the Earth pushes forward on the tires causing the car to move forward The Earth doesn t move because it has a much larger mass and therefore more inertia than the car so it would take much more force to cause a change in its motion Newton s Law of Gravity FGxm1xm2dquot2 Newton applied his laws of motion to gravity and reasoned that if the Earth exerts a force an object to keep it on Earth s surface that object must exert an equal force on the Earth He also reasoned that if the Earth exerts twice as much force on an object with twice as much mass then doubling the mass of the Earth would also double the force Therefore the force of gravity between two objects is directly proportional to the product of their masses If gravity acted between the Earth and objects on it then it stood to reason that it would act between any two mass objects in the universe including the Sun and the planets Kepler had observed that whatever force acted between the Sun and the planets decreased as the square of the distance between them increased causing more distant planets to orbit more slowly This is an example of an inverse square law Newton added this to his observations on the effect of mass on gravity and devised the equation FGxm1xm2dquot2 G stands for the universal gravitational constant which was later measured as G6673x10quot11 mquot3kg squot2 Circular Velocity If an abject is propelled forward fast enough the surface of the Earth will curve out from underneath it as it falls Instead of being pulled back to the ground it will continuously fall around or orbit the Earth This is how the Moon and manmade satellites interact with Earth s gravity and also the reason the planets orbit the Sun If a satellite were to slow down or speed up it would no longer be moving at circular velocity and would either fall to Earth or y off into space Bound Orbit planets orbit the Sun in bound orbits because they are gravitationally bound to the Sun and never achieve enough velocity to break from their orbit Unbound Orbit Some comets travel by the Sun in an unbound orbit They are pulled towards the sun by gravity once but then achieve escape velocity and continue on into space never returning Chapter 4 Light is the primary way of observing astronomical objects It is the fastest thing in the universe and its speed in a vacuum is a fundamental constant c30x10quot8ms Light behaves as both a wave and a particle Light as a wave Changing magnetic and electric fields create an electromagnetic wave This wave will move forward at the speed of light The motion of an electromagnetic wave is similar to the ripples caused by a drop of water falling into a pond Waves are characterized by four quantities amplitude speed frequency and wavelength Amplitudeathe height of a wave Wavelength the distance between crests of a wave Frequencyf the number of crests that pass a certain point each second measured in Hertz Hz Speed fo gomagnetic waves is equal to the speed of light am itue r leinunL 39 39 Wavelength is equal to velocity divided by frequency Acf so wavelength and frequency are inversely proportional Light as a particle Particles called photons carry energy at the speed of light Photons carrying more energy result in an electromagnetic wave with a higher frequency and those carrying less energy result in a lower frequency so energy and frequency are directly proportional You can calculate the energy of a photon using the equation Ehf h represents Planck s constant h663x10quot34 rm A spectrum is light sorted by frequency The visible spectrum or rainbow is a very small section of the electromagnetic spectrum with wavelengths between 350nmviolet and 750nmred Gamma rays have the shortest wavelength and highest frequency in the electromagnetic spectrum and radio waves have the longest wavelength and lowest frequency A Increasing energy WWW Increasing wavelength 0000l nm 001 nm 10 nm 1000 nm 001 cm 1 cm i m 100 m l I 1 1 1 l Gamma rays X rays Ullra Infrared Radio waves violet Radar TV FM AM Visible light 400 nm 500 nm 600 nm 700 nm Telescopes Aperture diameter of the largest mirror or lens Refracting Telescopes 0 Use lenses to bend or refract light 0 Limits aperture size because large lenses are heavy o Chromatic aberration different colors of light pass through the lens at different angles and cause fuzzy images in the telescope Reelecting Telescopes 0 Use concave mirrors to direct light 0 Mirrors can be made thinner the lenses so the aperture can be larger without becoming too heavy 0 Mirrors don t refract light so there is no chromatic aberration 0 Most modern telescopes are re ecting Integration Time Time interval for collecting photons Quantum Efficiency Number of responses for each photon received Angular Resolution how close together two points of light can be before becoming indistinguishable TheEye Photons detected by the retina and interpreted by the brain 0 Integration timelOOmilliseconds 0 Quantum Efficiency10 ten events1 response 0 Angular resolution16O of a degree Photographic Plates Photosensitive substances react to exposure to light and create images 0 Integration time can be adjusted by leaving the shutter open 0 Quantum Efficiency 13 ChargeCoupled Devices CCDI Photons strike pixels on an array and cause a slight charge that is digitally recorded 0 Quantum Efficiency approaches 90
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