Introduction
In the "Laws of Sanctification of the Moon", Rambam gives algorithmic description of two calendars: fixed ("arithmetic") and observational ("astronomical"). Both calendars are described in a form ready to be implemented, but the reasons for the calculation steps  especially for the astronomical calendar  are not always given: what are the models  and the formulae resulting from them  that reproduce the numbers? Sometimes Rambam describes the models, so only the formulae need to be reconstructed; sometimes the models are not described, so both the models and the formulae need to be reconstructed.
Goals of this paper are:

reconstruct models that Rambam uses from the Rambam’s text

describe the models with diagrams and formulae

reconstruct parameters of the models from the numbers given by Rambam

identify misprints in the traditional editions

analyze correspondence with the fixed calendar

verify Rambam’s tables and rounding decisions against his models

analyze impact of various misprints on the sighting calculations

verify consistency of Rambam’s numbers

see how Rambam’s calculations of the moon visibility compare to the current models

translate relevant chapters of Rambam into English The translation does not have to be literal; literal translations are already available ([Yale], [Moznaim]). The goal of our translation is to make the text complete and accessible for collaboration by people not proficient enough in Hebrew.
Approximate timeline of the project:

In 1984, The Rebbe instructed Jews to learn Rambam every day. As a result, in 1991 I encountered calendar chapters of Rambam, decided to reconstruct the models behind the calculations described in them, and discovered mistakes in the text of one of the laws (15:6). The results were published in "Notices of Temimim and Anash", a weekly of the central Lubavicher Yeshiva 770. Some of the readers were appalled that someone dares to correct the text of Rambam! My point was that the text as published contains mistakes that need to be corrected. Indeed, Frenkel edition [Frenkel], that was already published at the time, corrects all of the mistakes I did. In fact, they were already corrected by Hazon Ish in his commentary on Rambam [HazonIsh]  but I did not know it then.

2008: I acquired a pile of books on the subject and started looking into it; I also experimented with various ways of publishing the work on the web.

2009: coded some of the algorithms to look into the rumors the dates of Birkhat HaHamah that were circulating then.

2013: code converted to Scala.

20172018: splitfile encoding of the family polymorphism and current representation of the dates and angles were implemented in the supporting code.

20182019: generation of reading and learning schedules was added to the code.