Radial Velocity Curve Fitting

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This Demonstration shows 10 radial velocity data points folded over a varying period. A sinusoidal fit is calculated using a nonlinear regression technique. This is supposed to show the difficulty of finding a single value for a period based on such a small number of data points. The data comes from real observations made by UCL Astronomy students in 2006 and 2010 using a 1.52 m telescope at OHP, France.

Contributed by: Jakub Bochinski (March 2011)
Open content licensed under CC BY-NC-SA


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Details

Nonlinear curve fitting is based on a mathematical concept of regression analysis, which tries to minimize differences between the fit and nearby data points (residuals). This can be done for any given type of function and a possibly unlimited number of variables. Mathematica can compute nonlinear regression to fit a model sinusoidal function

to a dataset, taking into account uncertainties associated with each data point separately. In the equation, is a radial velocity, is a Julian date (or phase), and , , , are adjustable parameters. It is clear that this function can be stretched and shifted along either axis, but not tilted sideways.



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