Fourier Analysis

# Fourier Analysis - Abstract The analysis examines the...

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Abstract: The analysis examines the radial velocity measurements of two different stars and uses time series analysis in order to search for extra-solar planets around these known stars. Through the computer program used to analyze the data, Star 1 does not have an extra-solar planet orbiting it whereas Star 2 does. The periods at which the maximum signals for the power spectra were seen at 5.39965 days and 3.0967 days for Star 1 and Star 2 respectively. The time series evaluation of the data set resulted in a power spectrum for each star, which later was used in order to phase the data and find the residuals. These residual plots allowed us to figure out whether or not there was an extra- solar planet orbiting each star or not. Introduction: Two Hundred and Eighty Seven extra-solar planets have been found to date through the use of multiple methods. One method is called the Doppler shift method. Essentially many measurements of stars are made from observations of the star’s velocity. In other words, we are able to see the star’s motion towards or away from earth. Direct observations of stars are made from their spectra, which depend on the composition of the star. Depending on what the star is made of, the observed spectra differ. Also, once we can determine the spectra of a star, we can determine how fast the star is moving according to Hubble’s Law. In brief words, Hubble’s Law determines how fast celestial bodies move depending on how far away they are from earth. Equipped with the velocity (that is, how fast the star is moving away from or towards us), we can use the variations

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in the speed of the star’s motion relative to the earth to determine whether there are any planets orbiting this star. To day, most of the planets found outside the solar system follow what are known as Keplerian orbits, essentially orbits which are elliptical with the star at one of the foci, and the planets are found to be massive gas giants in small orbits around their parent stars. A good way to picture it is to imagine giant Jupiter-sized planets much closer to their parent stars than the earth is to the Sun. These extra solar planets are found using radial velocity method which depends on the number of orbital cycles that have passed and the number of observations that we make per cycle. If the orbital period of the planet is much shorter than the observation time that we spend on the planet-star system, then we use Fourier techniques in order to detect velocity measurements. Hence, this method can be used in order to find planets that are at orbital periods that are very small (smaller than 2 AU). This suggests that many of these extra-solar planets must have formed in situ or have migrated inwards from where they were formed. The following experiment is designed to understand the use of Fourier analysis
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Fourier Analysis - Abstract The analysis examines the...

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