ASTRO 1102 1104 Discussion Section 4 Goals Radiometric Dating Energy Radiation Reflectivity Asteroids Mathematical Exercises 1 Lunar Rocks You are dating Moon rocks based on their proportions of uranium 238 half life of about 4 5 billion years and its ultimate decay product lead Find the age for each of the following using Using N t N0 0 5 t t1 2 where N t is percent remaining in decimal format N0 is the initial percent t1 2 is the halflife and t is the age a A rock for which you determine that 55 of the original uranium 238 remains while the other 45 has decayed into lead 1 2 Energy and Frequency The relationship wavelength meters f requency hertz speed m s holds for any wave For light which travels in a vacuum i e space at speed c 3 108m s this relationship becomes f c where lambda stands for wavelength and f stands for frequency The radiative energy E joules carried by a photon of light is given by E h f where h is Plank s constant h 6 626 10 34joules s a What is the wavelength of a radio photon from an AM radio station that broadcasts at 1120 kilohertz b What is the energy in joules of an ultraviolet photon with wavelength 120 nm 3 Thermal Radiation The Sun radiates a total power of about 4 1024 watts into space The Sun s radius is about 7 108 meters a Calculate the average power radiated per square meter of the Sun s surface Hint The formula for the surface area of a sphere is A 4 r2 b Using your answer from part a and the Stefan Boltzmann law to calculate the average surface temperature of the Sun in units of J m2s P is power A is area and T is temperature is the Stefan Boltzmann constant 5 6703 10 8W att m2K 4 Note The temperature calculated this way is called the Sun s effective temperature P A T 4 2 4 The Role of Reflectivity The no greenhouse temperature of a planet depends on It can be its distance from the Sun its overall reflectivity and the sun s brightness calculated with the equation cid 114 T no greenhouse 280K 4 1 reflectivity d2 where d is the distance between the sun and the planet in AU and reflectivity is as a fraction instead of percentage i e 0 2 instead of 20 a What reflectivity would be necessary to keep the average temperature exactly at the freezing point of water 273 Kelvin b How does your answer compare to Earth s actual reflectivity of 29 2 3 Group Discussion Questions 1 Suppose that today some parts of the world saw a partial solar eclipse Is it possible that you would also see a lunar eclipse tonight Discuss 2 Briefly define asteroid comet dwarf planet meteor and meteorite How did the discovery of Eris force astronomers to reconsider the definition of planet 4
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