https://fantasy-calendar.com/calendar.php?action=view&id=74f318ecdb0f72e0e2fe0b68ed6d0489
^^ Now one way of pursuing that fascination which I recently fell into has been an effort to construct calendars based on the ones described in MORE THAN HONOR using the engine linked to above (a most useful device which I highly recommend to those working out or working up calendars for their own home-brew settings). ^^
While this may sound somewhat dry, the Fantasy Calendar Generator asks questions of those who use it which have made me think about issues to which I had never previously given thought - for example how long does the natural lunar cycle of Egg last? (as opposed to the calendar month of 36 days short and 37 days long); for the record my guess would be 35.35 days, assuming that a relation between Egg's natural cycle and a calendar month roughly equivalent to that of our own Lunar cycle & a Gregorian month.*
*This conclusion was arrived at by determining that the natural cycle of Luna (at least for the purposes of this calendar generator) was defined as 29.53 - or 95.26% of the longest calendar month; Applying the same ratio to Thorson, moon of Planet Manticore, suggested a natural cycle of 36.19 days.
Now while I was quite happy to employ such rough-and-ready methods to approximate a natural cycle for Thorson & for Egg, I recently discovered that (since the semi-major axes of both moons were known) it was possible to find the rotational period of Perseus & Bellerophon through a more scientific method - the equation required may be found at the other end of the link below.
https://en.wikipedia.org/wiki/Semi-major_and_semi-minor_axes#Orbital_period
The problem is that while I have the semi-major axis for both moons, I'm not sure if I have the right standard gravitational parameter for Planet Sphinx; I've been using 13.171 (per the surface gravity mentioned in 'Honorverse Tech Bu9') but suspect that this has flawed my results (since the orbital period given for Perseus was 51.12 and the one given for Bellerophon was 62.45, which seems off - given the longest calendar month on Sphinx is only 39 days).
Could any fan more mathematically adept than I am please help me work out where these calculations have gone wrong and how one might right my mistakes? I'm rather at my wit's end (a common situation where higher mathematics are concerned) and would greatly appreciate any assistance.
Thank You in advance to any interested parties for your consideration.
