Lecture notes from Astronomy Week 5
Lecture notes from Astronomy Week 5 AST2002-16Fall 0001
University of Central Florida
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This 18 page Class Notes was uploaded by Becca Petersen on Saturday October 1, 2016. The Class Notes belongs to AST2002-16Fall 0001 at University of Central Florida taught by Dr. James Cooney in Fall 2016. Since its upload, it has received 7 views. For similar materials see Astronomy in Science at University of Central Florida.
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Date Created: 10/01/16
Astronomy Week 5 Some basic physics – Kepler’s laws seem kind of arbitrary – there are basic laws of nature and physics that underlie Kepler’s laws Motion Position Requires a coordinate system (ex: it lies 3 meters above.) Displacement – change in the position of things Velocity Rate of change of position – describes how quickly that displacement takes place A vector Not only the speed but the direction** (ex: 60 miles per hour, north) Acceleration Rate of change of velocity (ex – if you go from one meter per second to to meters per second then your acceleration was 2 meters per second-‐ per second) Also a vector – has a direction Understand that…. You can accelerate without changing your speed – going around in a circle where your speed is the same but your direction changes Moving in a straight line in uniform speed – you have a velocity but no acceleration You can have acceleration not equal to zero but velocity equal to zero – if you toss something up in the air – its direction of its velocity is going up but the acceleration is going down – it slows down as it travels higher in the air – and that statement is the case at its very peak Isaac Newton Between 1665-‐1667 (he was 22 in 65) Known for… *He sort of co-‐invented calculus *Newton’s laws *Basis of all physics until Einstein *Law of universal gravitation He wanted to understand the nature of the universe and why Kepler's laws worked the way they did. So he basically found the fundamental laws of nature Came up with the universal law of gravitation Newton’s Laws of Motion 1. A body remains at rest or moves with constant velocity unless acted upon by an outside force – I.e. whatever state of motion they are in, they are going to keep that exact velocity until you do something to it. There are things in our every day lives (friction, gravity, air resistance) that will act on objects to change their velocity or stop them. Being at rest is essentially the same thing as being in perfect constant motion (think about being on an airplane-‐ do you know you’re moving? – the only way you know you’re moving is by gaging it on other things. So motion is very relative. 2. The change in a body’s velocity due to an applied force is in the same direction as the force and proportional to it. But is inversely proportional to the body’s mass. F=ma Force = mass times acceleration Mass is a measure of how much something does not want its motion changed. High mass thing will have a very low acceleration and vise versa. So pushing a brick will move more slowly than pushing a stack of sticky notes. Think of the example from class – if you out a lead brick over your hand (lets say its 30 pounds) it has a higher mass and doesn’t want to move so you can hit it really hard with a hammer and feel no pain. And vice versa with a block of wood. It has less mass and is much easier to move because of the less resistance so you will experience much more pain 3. For every applied force, a force of equal size but opposite direction arises. Object A acts on object B and object B acts on object A So the earth is pulling you down by 160lbs and you are pulling the earth up by 160lbs. Discussion on the interaction of things – where the force came from – so it’s a discussion of pairs of a thing where if I do something to you, you do something to me Example – someone trying to lift themselves up by their ankles – they exert an upward force of their body weight on their ankles but their ankles are exerting that same force of their body mass downwards – therefor they can’t lift themselves. Fundamental trouble with space travel is that you have to bring along everything with you – the more mass you have – the harder it is to accelerate. The rocket exerts a force on the heated gas and the heated gas exerts a force back on the rocket – but the fuel is accelerating much more than you are because its mass is so much less Momentum p=mv Momentum= mass times velocity Saying essentially the same thing as F=ma Newton’s laws can be expressed in terms of momentum Weight Weight -‐> gravity One example of a force Usually, W=mg G= acceleration due to gravity at earth’s surface= 9.8 m/s/s The difference between weight and mass is important to understand Mass – how much an object is resisting change Weight – how hard the earth is pulling on you 60 kg on earth and you go to the moon where your weight is 1/6 of that on the moon. Your mass will still be 60 kg on the moon. B ut you will weigh 20 kg on the moon. Four fundamental forces in nature (magnetic, strong, weak, and gravity) but in astronomy, gravity is by far the most important Gravity: Universal Law of Gravitation – “Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.” Newton’s third law is implicit in this F g =G M 1 M 2 d^2 D= distance Is you doubled the mass of object two (m2) the force of the equation is doubled If you doubled the distance between them you have decreased f by a factor of 4 You feel weightless in space because you are falling – falling into orbit It’s kind of like jumping out of an airplane where you feel weightless within the first few seconds In both instances you are falling with some horizontal velocity When you drop something it heads towards the center of the earth Tides: Gravitational force decreases with distance The moon’s pull on earth is stronger on earth on the side facing the moon and weakest on the opposite side The earth gets stretched along the earth – moon line Tides are an application to the universal law of gravitation Both the earth and the moon are sort of falling towards each other – which means they both want to stretch along the line that connects them – the oceans are what “stretch” If the earth and moon were stagnant, all the water would collect on one side 2 high tides every day and 2 low tides every day Every day on earth passes through high tide twice per day as the earth rotates High tides occur every 12 hours 25 minutes The sun produces tides on the earth as well -‐ it is much less important to tides than the moon is. The sun is so far away that the difference across the earth is kind of irrelevant “Even though the sun pulls harder than the moon the difference n how hard it pulls on different parts of earth is small because it is so distant” Geography also plays into tides’ complications Spring and Neap Tides When the Sun and the moon pull in the same directions (new and full phases) High tide is higher than usual (spring) – because the tides seem to spring way up from being very low to very high When the sun and moon pull at right angles, (first and last quarter phases) high tide is lower than usual – called a neap tide) Tidal Friction – Remember that earth’s bulges want to face towards (and away from) the moon. But the earth is spinning and obviously the oceans are attached to the earth so they have to spin with them. So there is this fight between where the moon wants to bulges to do and the earth, which wants to drag the bulges with them. This causes friction This fight between moon’s pull and earth’s rotation causes friction ^ Earth’s rotation slows down 1 second every 50,000 years – this is because the moon moves further away from earth Synchronous rotation ** need finished Is what the rotation period of a moon, planet, or star equals its orbital period about another object Tidal friction the moon caused by earth has slowed its rotation down to a period of one month Conservation Laws Momentum = mv `Has a direction because it is a vector Angular momentum = r x mv Is a rotational version of momentum – basically the momentum of things going in a circle R = radius Energy Very fine law Energy comes in many forms Even when newton’s laws fail, conservation of energy holds Acceleration is not a form of energy* Various types of energy in the universe Kinetic – kinetic means motion so the faster you’re moving the more energy you have Potential energy – most of the kinds of energy we see Called potential because it has the potential to turn into kinetic energy if you do the right thing Gravitational potential energy In space, an object or gas cloud has more gravitational energy when it is spread out then when it contracts A contracting cloud converts gravitational potential energy in the form of thermal energy Chemical – energy stored within the bonds of molecules – like how we consume food for energy. Same thing with gasoline. Energy is produced by breaking those bonds Nuclear – energy stored in the nuclei of atoms. Difficult process but if you do it properly you can release large amounts of energy Radiative-‐ Light – light itself is energy Total orbital energy (gravitational plus kinetic) stays constant if there is no external force Orbits cannot change spontaneously Changing an orbit: For example, the space station is orbiting around the earth – it takes about an hour and a half to do that There is still a tiny bit of thin atmosphere a couple hundred miles up where it orbits. The atmospheric molecules hitting the thing are slowing it down. So occasionally they have to use a little bit of internal energy to stay in the orbit that they are in. What makes an object gain or lose orbital energy: Friction and atmospheric drag A gravitational encounter An aside on temperature It is a measure of the average kinetic energy of the particles in a thing Temperature scales: Fahrenheit (bad) Based on the boiling and freezing point of water – 32 degrees and 212 degrees Celsius (better) It also uses the freezing and boiling points of water as its benchmark Kelvin (best) Puts zero where zero should be The reason why Celsius and Fahrenheit are bad because molecules actually can reach a point where they stop moving – called absolute zero-‐ so there is an absolute minimum – which is not the case with Celsius and Fahrenheit Light Light is a vibration in an electromagnetic field through which energy is transported Dual Natures Light acts as a wave A wave is very different than a particle – it is spread out is space, it doesn’t have one point it has crests and troughs If you want a water wave – a wave in the ocean, you fundamentally need water. A water wave is a disruption of a medium, in this case water. The same is said with a slinky – there is a disruption in the slinky. A sound wave is vibration of air molecules – density/ pressure wave in the air. Light is the exception. It is not a thing that is vibrating, because it is a wave that travels without a medium. Light acts as a wave – its speed is: v = f • λ But the speed of light is a constant, c For light, f • λ = c The higher f is the smaller λ is and vice versa Our eyes recognize f as color Color isn’t a real thing – it’s just your brain interpreting different frequencies Light can also behave as a particle Light can also be treated as photons – packets of energy The energy carried by each photon depends on its frequency (color) E=hf = hc / λ Light acts as a particle: E=hf Questions frequently missed from the previous exam – How far serius moves along the celestial sphere every 6 months – remember that stars are painted on the celestial sphere, they don’t move. The sun, however, does. Where can you live to maximize the amount of light each day? Anywhere – North Pole – 6 months of light, 6 months of dark Equator – 12 hours of light, 12 hours of dark… so 6 months of light and 6 months of dark You are moving faster than the empire state building if you are in Orlando because you both have to go around in a circle every day but your circle i s bigger because you are closer to the equator Galaxy with the youngest appearance – You are seeing light that has already passed when you look at galaxies. The youngest appearance would be the one that is furthest away – because that means it has taken more time for light to travel so the light we see would be considered younger – say 4 billion years old rather than 2 million years old. The Electromagnetic Spectrum: Oselating electromagnetic fields; It is all light and all travels at exactly the same speed the only difference is frequencies of wavelengths Blue and violet on the high frequency end and red on the low frequency end In the lower frequency end of things – lower meaning that each photon has less energy and the wavelength is longer … lots of things give off infrared. (goggles allow us to see it) We see people and things because light is reflecting off of them. If we went into a dark room, we couldn’t see anything or anyone, but people are still giving off light. Any object with a temp above zero gives off radiation. – But our eyes don’t pick that up. Night vision goggles – just amplify small amount of visible light that is there and then infrared goggles work because warm things give off of light. Longer wavelength and lower frequency are microwaves and radio waves. Billions and billions of radio wave photons passing through you – but it is so low energy that it cant do anything to you. We can use these for communication On the opposite end of the spectrum – Ultraviolet is higher frequency than you can see. Sunburns are caused by UV light. It has higher frequency, which means that it can do more damage. X-‐rays and gamma rays have extremely high frequency within the photons X-‐rays break bonds and can cause issues Gamma rays – even higher frequency-‐ energy of photons is very, very high. No natural processes on earth produce gamma rays other than nuclear explosions. But there are gamma rays in space. How light and matter interact – Matter The nature of matter Matter is what most of the universe is made up of. Matter is made up of atoms. They used to be thought of as the fundamental unit of everything. Pieces of the atom are the nucleus, which is made of protons (positively charged) and neutrons (neutral) and they are surrounded by electrons, which are negatively charged. The electrons do not orbit the nucleus The nucleus is nearly 100,000 times smaller than the atom but contains nearly all of its mass Electrons are smeared out in a cloud around the nucleus Periodic Table All of the ways to make elements – Atomic number = # of protons in the nucleus of that atom Atomic mass number = # of protons + # of neutrons Hydrogen – the simplest thing and almost everything in the universe is hydrogen (like 70%) Atomic number 1 and atomic mass of 1 (1 proton) Helium – atomic number 2 and atomic mass number 4 So two protons, two neutrons in the nucleus, and two electrons Isotope – a version of the element with a different number of neutrons For example, a hydrogen atom with a neutron If two or more atoms combine to form a particle it becomes a molecule The atoms form bonds-‐ think of water – h20 – consists of two hydrogen’s and one oxygen Phases of Matter – Solid, liquid, gas, plasma Depends on how tightly bound the atoms and/or the molecules are As temp increases these bonds are loosened Solid phase-‐ Atoms or molecules are held tightly in place – the bonds are very strong (Lets pretend its ice) If you heat it up you are giving it more energy and breaking those bonds because things are moving faster When you break those bonds it becomes a liquid with groups of bonds and things can move around If you heat it up even more you eventually break every one of those bonds and it becomes a gas -‐ steam If you heat it up even more it becomes a gas of just oxygen and hydrogen If you heat it up even more you have broken all of the bonds and have started stripping electrons away – the difference is that its charged things – ions and electrons flying around rather than just neutral things. This is plasma. Ex: Plasma TV – flames and lightning – you don’t see it all the time because the temp needs to be really high and you need a lot of energy to strip electrons off of stuff. Electron Orbits Electrons gain or lose energy while they orbit the nucleus Some rules for the amount of energy that the electron can have 1. There is a minimum amount of energy that the electron can have – and it likes to be in that state – that minimum amount is called the ground state. It can’t wander very far away from the proton because it is not moving very fast. 2. Electrons may only gain or lose certain, specific amounts of energy 3. Each element (atom and ion) has its own distinctive set or pattern of energy levels 4. The diagram in the notes depicts energy levels of hydrogen 5. You can give it 10.2 units of energy so it can get from its ground state of zero to 10.2 but it can ONLY go to 10.2 and nothing in between. Not 5 not 7.8, only 10.2 When electrons have the lowest energy possible we say the atom is in the ground state When electrons have more energy than this, we say the atom is in an excited state It is moving a little farther away from the nucleus When electrons gain enough energy to escape the nucleus, we say the atoms are ionized. Too much energy – the electron can just completely break off from the atom and this is the plasma state. Light conveys information: By studying an object’s light spectrum, we can gather its composition, temperature, and velocity Interaction of light with matter Electrons can Absorb light and gain energy or Emit light when they lose energy. Only photons whose energies (colors) match the “jump” in electron energy levels can be emitted or absorbed Emission Spectrum The atoms of each element have their own distinctive set of electron energy levels. Each element emits its own pattern of colors, like fingerprints. If it is a hot gas, we see only these colors, called an emission line spectrum. Absorption spectrum If light shines through a gas, each element will absorb photons whose colors match their electron energy levels The resulting absorption line spectrum has all colors minus those that were absorbed. We can determine which elements are present in an object by identifying emission & absorption lines. Continuous spectrum – hot, dense objects give off wavelengths Something called, “thermal radiation” Spectrum is continuous but not equal in intensity at all wavelengths The hotter something is the more light it gives off Rules for emission by opaque objects If you analyze the spectrum of light coming from a thing that means you can also gage its temperature 1. Hotter objects emit more total radiation per unit surface area . Ø Stephan-‐Boltzmann Law Hotter objects emit bluer photons (with a higher average energy.) Ø Wien’s Law If you look at the sun you are going to see a very complicated absorption spectrum Even more complicated when looking at an asteroid 3 things we can measure with the spectrum of light The Doppler Effect – Light emitted from an object moving towards you will have its wavelength shortened Blue Shift- Light emitted from an object moving away from you will have its wavelength lengthened We see a blue shift with the Andromeda galaxy – which means eventually we will crash into it Red shift – light emitted from an object moving perpendicular to your line of sight will not be shifted You cant determine if its moving perpendicular to your line of sight The further away a thing is the slower it appears to move in relation to you For sound frequency corresponds to pitch For light frequency corresponds to color Motion and velocity are relative Bending light 2 fundamental ways to bend light 1. Reflection – mirrors – many telescopes use mirrors to bend light 2. Refraction – lenses – you can use shaped glass to make the light go where you want it. Focus – to bend all light waves coming from the same direction to a single point -‐ light rays, which come from different directions coverage at different points to form an image Yerkes 40 inch telescope – the largest refractor in the world Telescope troubles One problem you might have is you may build the shape wrong. The outer part of the lens has to be a parabola If it is shaped wrong it wont focus – called spherical aberration Refractors only – Chromatic aberration Sagging – glass is supported around the edges so it can sag in the middle Inhomogeneties – fancy word for impurities We use telescopes to see smaller details and 1. Resolution – smallest angle which can be seen a. Resolving finer and finer detail on something – so you can see individual craters and mountains 2. Light collecting area – think of the telescope as a photon bucket