Questions regarding an object 'falling around' another object, due to a combination of gravity and momentum.

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Singularity in Laplace Method for Orbit Determination

I have a question about Laplace angle-only method for orbit determination where the line of sight vectors are being interpolated. I read somewhere that the method fails (due to a matrix being ...
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In 2016, the summer solstice will coincide with a full moon. How often does this happen?

I found that the solstices work on a 400 year cycle based on this. I can't find anything similar for the lunar cycle. Is there a formula I can use to calculate the date of the full moon?