Electromagnetic Theory - Questions with Answer | ECE 330, Exams of Electrical and Electronics Engineering

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1. (20 points) An important law of astrodynamics says that the Period # (seconds) that it takes for & planet to orbit a star is related to the distance of the planct from the star a (meters) by the following equation a GM Po dn where G is the universal constant of gravitation in m*/kg-s® and M is the mass of the star in kg. ‘Tho exponents @ and y are integers. Using dimensional analysis, determine x and y. In the theory of the evolution of planetary atmosphere, an important consi hood that a gas molecule of ma: A (meters). If the atmosphere escape is proportional to lexation is the likeli- m (kg) will escape from a planet of mass M (kg) and radius at a temperature T (K) the probability that a niolecule will GM = (- ETR ) where G again is the universal gravitation constant in m®/kg-s’, and & is Boltzmann's constant. This is called Jean's escape of an atmosphere to space. Using dimensional analysis, determine the dimensions of Boltzmann's constant &.