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My assignment is to identify how many planets are in this curve and what the orbital period is. I'm just confused on the way it looks, as most curves I've seen up to this date are more smooth and connected in appearance

Transit Method

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    $\begingroup$ Try to zoom in into one of the transit events, then you'll see more smooth data. Is this real data? Usually you either Fourier-Transform your data to see how many periods are in the data if the times are equidistantly spaced, or you need to perform a Lomb-Scargle analysis if it's non-equidistantly spaced. $\endgroup$ – AtmosphericPrisonEscape Mar 4 '19 at 16:24
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It would have been be great if you had shared the original data. As @AtmosphericPrisonEscape mentioned it could well be that you are seeing only some kind of aliazing effect in the plot, i.e. the underlying data actually looks the same for all four light curve dips.

First off, there is a related question: How to recognize exoplanet transit where lightcurve is used in Python.

If you are working in Python, you may also look e.g. at the PyTransit github project which seems rather well maintained. I am not affiliated with the author nor have I tested it, but it is worth a try.

In R, you may try to have a first look at your time series using the zoo library and follow e.g. the introductory tutorial.

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