Once you have acquired two, three or more minima for a target, you can work out its orbital period P (in days) and determine a zero epoch E0 (in HJD). A zero epoch is just one minimum, chosen hopefully because you had a clean light curve and it yielded a very good minimum calculation. Then the LEs are often expressed in ephemeris form, En = E0 + nP, to calculate future minima (n is the number of periods since E0):There are two basic methods of calculating periods. For each you really need three or more minima to make them provide a non-trivial result. It’s best to take primary minima - they are deeper hence better measurable, and particularly for EAs you can’t be sure that secondary minima occur exactly half a period after primaries - the orbit may be elliptical.It’s best if your three-plus minima were obtained in the same observing season, i.e. over small number of months. If you use minima separated by a year or more you may find it hard to get a period with small uncertainties, because period change is showing up. But, particularly with detached binaries, there may be no period change. Up to you to assess that.As described on the page for Times of Minimum, you should already have a Minima Analysis Form for your target binary. It will store your light elements when you derive them (indeed several sets so you can play around).
Linear Regression on minima times
This uses just the times of minima. Excel has a linear regression array function Linest, included with the project’s Minima Analysis Form and running automatically. This will effectively alter your chosen E0 a little, to minimize the residuals from the straight line it makes through your minima points. You should adopt the corrected E0. To make the regression work, avoiding period aliasing, you need to know the approximate period to begin with, which is usually available in the literature, e.g. through the AAVSO VSX. This is necessary since the regression needs to assign a correct period number n to each minimum after your E0.The Minima Analysis Form has instructions covering all this. Linest outputs P, E0, their uncertainties aka errors, and other statistical measures. You should always include the uncertainties in your LEs.
Finding the best fit to light curve data (period only)
This does not require minima times, just two or more light curves around primary minima, though again 3+ is desirable. PERANSO is widely used for this task. You import into it files of error> rows - standardly output by photometry applications - one for each night’s work, which it displays as light curves. (See the diagram in the Times of Minimum page). Then you command it to find the best period it can that fits the light curve data. For eclipsing binaries, the ANOVA routine seems to work best. Similarly to linear regression, you do need to provide a period range to begin with. In the diagram here, that was 0.2 to 0.35 days, knowing the period is about 0.3 days; and ANOVA found a best fit at 0.29252 days. A folded light curve (see the Phased Light Curve page) is also displayed. You may well find by eye a better fit than ANOVA by sliding its best fit marker to nearby period values - and watching the folded light curve adjust as you do so. Reporting your light elementsAs described on the page for Times of Minimum, you should already have entered the minima you’ve measured into the Dropbox Excel file ‘Minima & LEs ’. Simply enter your light elements (with uncertainties) in the same row as the last minimum measure you used to make those LEs. If you get more minima in future you can repeat this, putting your revised LEs against the last minimum entry.Forging aheadBy combining your minima with others in the literature, using your Minima Analysis Form, you can investigate period change.