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Transcript
Stefan’s Law • A point on the Blackbody curve tells us how much energy is radiated per frequency interval • Question: How much energy is radiated in total, i.e. how much energy does the body lose per unit time interval? • Stefan(-Boltzmann)’s law: total energy radiated by a body at temperature T per second: P = A σ T4 • σ = 5.67 x 10-8W/(m2 K4) Energy & Power Units • Energy has units Joule (J) • Rate of energy expended per unit time is called power, and has units Watt (W) • Example: a 100 W = 100 J/s light bulb emits 100 J of energy every second • Nutritional Value: energy your body gets out of food, measured in Calories = 1000 cal = 4200 J Group Activity: Estimate Power • Estimate how much energy you radiate per second • Estimate how many candy bars you would have to eat per day to be able to do that • Ponder the paradox Doppler Shift • From Wikipedia Doppler Shift • Can use the Doppler shift to determine radial velocity of distant objects relative to us • Transverse velocity can be measured from the motion of stars with respect to background over a period of years Homework: Doppler Shift of Hydrogen spectrum • The discrepancy between the wavelength of a line measured in the lab versus measured on an object is proportional to the velocity of the object • Apparent/ true wavelength = 1+ velocity/c • Example: – Observed(or apparent): 698 nm – Actual( or ture or lab) wavelength: 656.3nm – velocity = (698nm/656.3nm -1) c = 19100 km/s Atomic Energy Levels • For Hydrogen, the energies of the atomic levels are given by a simple formula that just depends on the (excitation) number n of the orbit: En = – Ry / n2 where Ry = 13.6 eV = 2.179 x 10-18J E1, E2=¼ E1, E3=1/9 E1,… • Electrons in higher levels will cascade down, producing many different spectral lines • Formula can be converted to frequency, wavelength Group Work • What is the wavelength of a photon emitted as an electron in a Hydrogen atom jumps from the second to the first level? • What is the frequency of the emitted photon? • How many different photons can be emitted as hydrogen goes from the fourth to the first level? Light hits Matter: Refraction • Light travels at different speeds in vacuum, air, and other substances • When light hits the material at an angle, part of it slows down while the rest continues at the original speed – results in a change of direction – Different colors bend different amounts – prism, rainbow Application for Refraction • Lenses use refraction to focus light to a single spot Light hits Matter (II): Reflection • Light that hits a mirror is reflected at the same angle it was incident from • Proper design of a mirror (the shape of a parabola) can focus all rays incident on the mirror to a single place Application for Reflection • Curved mirrors use reflection to focus light to a single spot Telescopes • From Galileo to Hubble • Light collectors • Two types: – Reflectors (Mirrors) – Refractors (Lenses) • Magnification: – ratio of focal lengths of objective and eyepiece – M = fobj/feye – Example: 2000mm telescope with 40mm eyepiece: 50x Telescopes Reflecting Telescopes Problems with Refractors • Different colors (wavelengths) bent by different amounts – chromatic aberration • Other forms of aberration • Deform under their own weight • Absorption of light • Have two surfaces that must be optically perfect Telescope Size • A larger telescope gathers more light (more collecting area) • Angular resolution is limited by diffraction of light waves; this also improves with larger telescope size Resolving Power of Telescopes Andromeda Galaxy Telescope 1 Telescope 2 of double size Resolving Power of Telescopes (II) Andromeda Galaxy Resolution: (a) 10’ (b) 1’ (c) 5” (d) 1” Magnification • The magnification of a telescope can easily be changed by plugging in a different eyepiece with a different focal length • M= focal length of main lense or mirror focal length of eyepiece Example: F= 2000mm, f = 40 mm M= 50 Atmospheric Limitations Atmospheric Limitations Optical Window Radio Window IR Window Largest Earth-Based Telescopes • Hobby-Eberly Telescope, Davis Mountains, TX – 11 m diameter – Cannot see all parts of the sky • Keck I and II, Mauna Kea, HI – 36 1.8 m hexagonal mirrors; equivalent to 10 m – Above most of atmosphere (almost 14,000 ft ASL) – Operating since 1993 Other Techniques • Put telescopes on satellites – Hubble Space Telescope: 2.4 m, since 1990 • Use computers to correct optics during light gathering: adaptive and active optics • Interferometry • Radio astronomy Other Wavelengths • Must be carried out on satellites (or rockets, balloons, etc.) due to strong absorption in the atmosphere • Infrared astronomy • High-energy (UV, X-ray, gamma-ray) astronomy Full-Spectrum Coverage • Radio • Infrared Each region of the • Visible electromagnetic spectrum gives us valuable information about the universe • X-Ray (only these frequency bands can be observed with groundbased telescopes) • Gamma -ray Activity - Telescopes • Pick up a telescope • Tasks: – – – – – – – What type of telescope do you have? How big is it, i.e. what is its biggest optical device? What is its focal length? What is the focal length of the eyepiece? What is its magnification? Try to focus on an object. Describe the image. Is it upside down? If the telescope is on a mount: • How many axes does the mount have? Does it have a motor? What for? • Do you know how the mount is called? You’ll probably have a lot of questions. Ask me! Famous Telescopes - Galileo • Galileo’s first telescope was 3x magnifying • his last one 32 x Famous Telescopes -Newton • First Reflector ever • Built around 1670 • After this: gargantuan Telescopes! Famous Telescopes - Hevelius Rooftop observatory of Johannes Hevelius (1670) Famous Telescopes - Hevelius 60 inch ^ 140 inch Famous Telescopes - Herschel Herschel detected Uranus (1781) Famous Telescopes – Lord Ross • 72 inch Reflector • built during potato famine in Ireland • Largest Telescope until Mt Wilson (1917) Famous Telescopes – Yerkes • Largest Refractor Telescope ever • 40 inch lens • Built 1897 Famous Telescopes – Mt Palomar • 5 Meter Telescope – Huge and heavy mirror • On Mt. Palomar in California Visiting Mount Palomar • November 2005 Model of the 200” Telescope Model of the Mirror • The telescope is located between Palm Springs and San Diego on top of 5000 ft high Mount Palomar Actual 5m Mirror • Took 3 years to cool down • 10 years to polish Transport of the Mirror ~ 1945 Famous Telescopes – Hubble Space Telescope • In orbit around earth • No limitations due to earth’s atmosphere • Brilliant pictures Famous Telescopes – Arecibo Radio Telescope • Located in Puerto Rico • 300m diameter • Receives Radio waves • Built 1963 • SETI Visiting Arecibo • Spring Break 2006 Famous People Hubble in prime focus of Mt Palomar. Einstein visits Mt Wilson Hubble detected the Expansion of the Universe Proof of Einstein’s General Relativity Theory Largest Earth-Based Telescopes • Keck I and II, Mauna Kea, Hawai’i – 36 1.8 m hexagonal mirrors; equivalent to 10 m – Above most of atmosphere (almost 14,000 ft ASL) – Operating since 1993 Visiting Mauna Kea – December 2004 Mauna Kea • Elevation: 14,000 ft. • Oxygen: 60% • Freezing on top, snorkeling at sea level • Road: strictly 4 wheels! Mauna Kea Maui • 325 observing days per year! • Darkest skies on the planet! The biggest Telescopes in the World Sunset on Mauna Kea