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AS 101 FINAL NOTES.- Wilfrid Laurier

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Patrick Mc Graw

Post Midterm Notes Lecture 11 Meteoroid → A small rocky object (smaller than 10m across) in the solar system. Meteor → The visible phenomenon of a meteoroid or a small asteroid entering the Earth's atmosphere, glowing as it heats up. Meteorite → A rock that has fallen to the ground from outer space. Newton's Law of Universal Gravitation  Any two objects attract each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres.  ,  This means that, for example, the moon exerts a greater force on a piece of the Earth close to the moon than on the centre, or the opposite side. Tides  Tides are mostly noticeable in the oceans, but the Earth's crust itself also bulges slightly in response to tidal forces.  Over time, tidal bulges can affect an objects rotation.  The synchronous rotation of the moon is probably a result of "tidal locking" What is Light?  The warmth of sunlight reminds us that light is a form of energy.  Energy can take many forms and can be converted from one form to another.  Some other forms of energy: kinetic energy, heat, sound, chemical energy.  When light from the Sun warms the ground or your skin, light energy is being converted into heat.  Solar power plants convert light into electrical energy.  Green plants convert light into chemical energy through photosynthesis. Light is a Form of Energy  Units of energy : joules.  1 joule of energy is enough to : → Start a 2-kg object moving at 1m/s → Heat up one gram of water by approx 0.25 degrees C.  Watts are a unit of power. → Energy per unit time. → 1 watt = 1 joule/sec.  A 100w light bulb is using 100 joules per second. → Only part of that energy is actually emitted as light, the rest of it becomes mostly heat. Quantifying Light Intensity  Intensity of light can be measures in W/m . 2  If the intensity of light from a source is measured to be 1W/m , then that means the amount of energy falling every second on every square meter of surface is 1 joule. → If that surface is perpendicular to the direction the light is coming from.  The intensity of light is related to its brightness.  Light involves a flow of energy.  Intensity tells you how much energy is passing through each unit of perpendicular area each second.  But if a surface is at an angle, then the same energy is spread over a larger area. Inverse Square Law  As you get farther from the source, the same energy gets spread over a larger area.  That means the intensity decreases as you get farther away from the source.  Stars that are farther away look dimmer than they would close up.  Mathematically speaking, light acts like gravity: → If you double the distance, the intensity becomes 1/4 as much. → Triple the distance, intensity becomes 1/9 as much.  This is because if you double the distance, the same amount of light energy gets spread over four times as much area.  That's the same type of mathematical behaviour as in Newton's law of gravity. → Gravity gets weaker as distance increases but never really goes away. Is Light a Wave or Particle?  Light travels through space as a wave.  But some of its interactions with matter are best understood in terms of particles. What is a Wave?  A wave is a periodic motion that can carry energy without carrying matter along with it. → Water waves. → Sound waves.  Wavelength → Distance between two wave crests.  Frequency → Number of times per second that a wave vibrates up or down.  Wave speed = wavelength x frequency.  Wave speed depends on the type of wave and what its moving through.  The frequency depends on the source it's coming from. Light as a Wave  James Clerk Maxwell understood light as an electromagnet wave → A vibration of electric and magnetic fields together.  Light interacts with matter through these electric and magnetic fields.  Visible light and radio waves are two forms of the same thing. → Both are electromagnetic waves.  Electromagnetic waves in a vacuum travel at the speed of light. Wavelength, Frequency and Colour  Wavelengths and frequencies are related to colours.  Longer wavelengths mean lower frequencies and that is represented with redder light.  Short wavelengths mean higher frequencies and are represented with bluer light.  Newton showed that white light consists of many different colours (wavelengths) mixed together. The Electromagnetic Spectrum  Human eye cannot see most forms of electromagnetic radiation.  Electromagnetic spectrum is the full range of possible frequencies. → There is really no upper or lower limit.  Visible light is only a small part of the electromagnetic spectrum.  It consists of electromagnetic waves with a certain range of frequencies. Light: Our Messenger from the Universe  Light is our window on the Universe. → Almost everything we know about any object outside Earth comes from observing either visible light or other forms of light.  Some objects emit light processes that convert other forms of energy into light. → Example: Stars including the Sun.  Others, such as planets, do not emit their own light but are visible through reflected light.  By understanding how light interacts with matter, we can get a lot of information from light about the temperature and chemical composition of distant objects, and about their motion.  Not all forms of light can get through Earth's atmosphere. → This is one of the reasons for building observatories in space. → On Earth, we can only see astronomical objects through visible light and radio waves. How Telescopes Help  Light intensity describes the amount of energy falling on a surface per unit area.  Some objects are hard to see because they are too dim.  Not enough energy from them is reaching our eyes.  But you can increase the amount of energy collected by increasing the surface area.  Pupils of eyes have a small area, so telescopes concentrate light from a larger area.  The ability for a telescope to collect more light is called "light-gathering power". Brightness and Magnitude of Stars  Stars are classified by apparent visual magnitude. → A number representing their brightness.  Originally, there were just six numbered classes. → First magnitude = Brightest stars. → Sixth magnitude = Faintest visible with the unaided eye.  Ptolemy used this magnitude system in his writing, others may have used it earlier.  More recently it became possible to measure flux of light more precisely, allowing a more precise numerical measurement of brightness. → Energy per square meter per second.  Smaller numbers mean brighter, larger numbers mean fainter.  With the new scale, some of the brightest objects have negative numbers.  Visual magnitude only counts visible light. Photons: Particles of Light  When light energy interacts with matter it is emitted or absorbed in discrete chunks or packets: photons.  The size of a photon depends on its frequency.  Photons of higher frequency light have more energy than for lower frequency light.  Medical consequences of this : → Higher-energy photons can do more damage to living cells when absorbed. → So visible light is pretty harmless but ultraviolet light can cause sunburn and skin cancer.  X-ray and gamma ray photons have even higher energies, so too much exposure to them can be more dangerous. Diffraction  Limitation of human eyes : Diffraction.  Diffraction is the bending of the edges of waves as they pass through an opening.  Diffraction blurs images, so if two stars are too close together in angular distance, their images blur into one.  This puts a limit on the smallest angular sizes we can observe with a telescope. Other Factors Affecting Angular Resolution  Telescopes are based on either reflection or refraction of light.  Both reflection and refraction are basic wave behaviours that also happen with sound, water waves, as well as light.  Refraction is the bending of waves when they cross a boundary between two different media where they travel at different speeds.  Ray Tracing is often helpful to describe refraction and other wave phenomena by drawing rays which represent the direction a wave is moving.  A wave moving from a faster to slower medium bends so that its direction is closer to perpendicular to the surface. → From slower to faster is the opposite.  Refracting telescopes use two lenses: → Objective lens creates a very small real image at its focus. → Eyepiece lens then magnifies the real image, forming a larger virtual image that you can see. Powers of a Telescope  Light-gathering power is the ability to collect and concentrate light. The wider the objective lens, the greater the light-gathering power.  Resolving power is the ability to see fine detail clearly. This is partly limited by diffraction and partly by the quality of the lend, and partly by the atmosphere.  Magnifying power is the increase of apparent angular size. This is easily changed by changing the eyepiece, and in some ways is the least important, since magnifying a faint or blurry image doesn't help. Limitations of Lenses  Spherical aberration or other imperfection prevent a sharp focus.  Different colours focus at different points, because different wavelengths of light refract at different angles this is known as Chromatic aberration.  This is actually what is used to separate colours in a prism, but it's a problem for telescopes or cameras.  Coatings on lenses or sets of multiple lenses can reduce chromatic aberration.  Large, high quality lenses are difficult and expensive to make.  Large lenses are also very heavy, so they tend to sag under their own weight when supported only at the edges.  Chromatic aberration is never completely eliminated.  To get around these problems, Newton built the first reflecting telescope. Reflecting Telescopes  Use a curved mirror instead of a lens to focus light.  Light reflects off a reflective coating and does not have to pass through glass. → That means no chromatic aberration.  Only the surface needs to be polished, while a lens needs to be free of defects all the way through to work well.  Mirrors can easily be supported from behind. Another Challenge for Astronomers  Distortion cause by Earth's atmosphere is called "seeing".  Uneven temperature and moisture cause refraction as light travels through the air, blurring and distorting images.  As atmospheric conditions change, image is unsteady and stars appear to twinkle.  Why don't planets twinkle? They have bigger angular sizes, so light from different parts of the planet's image is affected differently. What to do About Seeing  Adaptive optics technology uses a computer and small motors to compensate for atmospheric distortion by continuously changing the shape of the secondary mirror.  Requires a bright source in a known location for the computer to focus on and calculate the correction.  Or create an artificial guide star by bouncing a laser beam off the upper layers of the atmosphere. Observing Non-Visible Light  Earth's atmosphere is transparent to visible light and radio waves.  With adaptive optics, we may soon be able to get visible-light images from the ground that are as clear as we get from the Hubble Space telescope.  But to observe other types of light that don't get through the atmosphere, we still need telescopes in space. Why Look at Other Types of Light  Infrared and radio waves can pass through clouds of gas and dust that are opaque to visible light.  This allows us to see more of our own galaxy.  Different types of sources emit different ranges of wavelengths.  Objects that care cooker than stars emit mostly infrared.  Cosmic microwave background shows us the last remaining heat from the Big Bang and gives us clues to the early history of the Universe.  Some radio sources include active galactic nuclei.  Many stars emit at least some X-rays. → Including the Sun.  Matter falling into black holes emits a lot of X-rays.  Short gamma-ray bursts from distant galaxies may come from the explosions of very large dying stars. Radio Telescopes  Radio telescopes are reflecting telescopes for radio waves.  Since radio waves have large wavelengths, diffraction is a problem. We need large mirrors to get a good angular resolution.  The good news: an optical mirror needs to be smooth compared to wavelengths of visible light, but a radio mirror just needs to be smooth compared to radio waves. Interferometry  Another way to improve angular resolution is to combine signals from several telescopes.  Interferometry is easiest with radio waves, but it can now also be done with visible light.  As far as angular resolution is concerned, it's like having a much bigger telescope. Infrared Astronomy  In most ways, infrared optics are not that different from visible light.  The problem is that Earth's atmosphere blocks a lot of infrared radiation.  IR telescopes also need to be insulated from heat. Shorter Wavelengths: X-ray and Gamma-ray Astronomy  X-ray and gamma-ray telescopes need to be above the atmosphere.  X-ray and gamma rays are very difficult to focus: an ordinary lens or mirror won't work.  To focus X-rays, we use grazing-incidence mirrors. Spectroscopy: Getting more information from light  We can learn more from light if we understand more about how light interacts with matter: how it is emitted and absorbed.  Spectroscopy is the breaking of light from an object into its different wavelengths, and comparing the amounts of light emitted at different wavelengths. Continuous Spectrum (Thermal Radiation)  A hot, dense object emits light at all wavelengths at once in a continuous spectrum.  Examples: A standard incandescent light bulb, the sun, a glowing heating coil on the stove, a human body.  This emission is also called blackbody radiation.  The spectrum depends on the temperature.  Stefan-Boltzman Law: Hotter objects emit more radiation than cooler ones.  Wien's Law: Hotter objects emit photons with a higher average energy. The wavelength of peak intensity shifts toward lower wavelengths as temperature increases.  This means that we can figure out the temperature of a star by looking at its thermal spectrum.  Betelgeuse is redder in colour than Rigel: it is a cooler star.  Objects at temperatures around room temperature or body temperature emit most infrared light. Line Spectra  Continuous spectra are produced by dense objects with many atoms packed together. To understand the other two types of spectra, it helps to understand a bit about atoms, and how individual atoms absorb or emit light.  A full understanding involves quantum mechanics, a branch of physics developed in the 11920s and '30s.  Electrons in an atoms can only orbit in specific orbits with particular energies. They can only absorb or emit energy by moving from one level to another.  Under normal conditions, an atom spends most of its time in the ground state (lowest energy state).  If a photon with the right energy comes along, the electron can absorb the energy and bounce up to an excited (high-energy) state.  The energy is emitted again as the atom falls back to the ground state.  Each type of atom has particular energies of photons that it is able to absorb or emit.  These photon energies correspond to particular transitions between energy levels of that atom.  The set of all these energies form a kind of chemical fingerprint for that atom.  Molecules often have more complicated spectral fingerprints than single atoms. Doppler Effect  When we observe spectral lines from an astronomical source, we can compare them with a reference spectrum from hydrogen gas in the lab.  If the source is moving toward us, the spectral lines will be shifted to higher frequencies compared to the reference spectrum.  If the source is moving away from us, the lines will be shifted to lower frequencies. Solar System Objects: Planets  Terrestrial planets → Mercury, Venus, Earth, Mars → Are small, rocky and closer to the Sun.  Jovian planets → Jupiter, Saturn, Uranus, Neptune. → Are large, and gassy, they contain a lot of hydrogen, helium and methane. → They are farther from the Sun.  Jovian planets also have more moons than the terrestrial planets.  Jovian planets all have rings, but Satur
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