# I may have made an error in calculating my spin-orbit resonance

I have a very warm planet named Phoenix I'm worldbuilding that's 1.2 times the mass of Earth, with a density somewhat smaller at 5.2 g/cm^3, orbiting at a distance of 0.1 AU from it's star in 10.2 Earth days. It was important to me to put it around a relatively high mass Class M star, about 0.32 Msol, due to how the flora and fauna would behave and develop from this kind of star; in short, a restricted amount of insolation usable for photosynthesis but an abundance of thermal energy powering the atmosphere and ocean led to the development of autotrophs that can convert mechanical oscillation to chemical energy. However, I thought I could be clever and introduce day-night cycles by putting the planet in spin-orbit resonance, giving the world circulation cells not centered around the subsolar and antisolar points. I settle on a 7/2 resonance, put in some eccentricity to make it plausible, and call it good.

Fast forward to my building up of the alien cultures on the planet, and I want to make the 7-day cycle their main time keeping unit. I rediscover the difference between solar days and sidereal days, and promptly panic about how to salvage what I've built up. I keep crunching numbers but I just can't get a grasp on this: how do I make a seven day solar year without completely dismantling one of my core concepts; close, hot orbit; a slow day that creates a single cell for each hemisphere; and spin-orbit resonance that prevents tidal locking? I'm hoping to avoid an arbitrary length of time like our weeks and named months are.

• There is no question mark in this question... OK, the planet has a 7:2 spin to orbit resonance. There are 3½ sidereal days per orbit, or 2½ solar days, for a total of 5 solar days every two orbits. The inhabitants use periods of whatever n solar days as their basic timekeeping cycle. Why would there be any relationship between n and 2, 5, or 7? Here on Earth most of us use cycles of 7 solar days which is a number that has no relationship to any natural phenomenon whatsoever. (And historically the Romans used 8 day cycles, just to show how arbitrary that is.) Commented Jul 6 at 23:41
• @AlexP This basically answers all my questions, thank you! My main concern was my work on the culture and mythology already relies heavily on the number 7 being the number associated with the heavens and indivisibility, and I didn't want to scrap that. Looks like a 9/2 resonance would satisfy my needs quite well; again, thank you! Edit: I was probably having a brainfart in hindsight, you showed it was incredibly easy to figure out.
– GJC
Commented Jul 7 at 21:01
• I'm delighted that you found an answer via @AlexP's comment - but I sincerely hope you didn't miss his first point. I'm here because your question is listed in the vote-to-close review queue. It might not matter to you, but this was (and is) a badly formatted question posted to a site that specifically exists to host quality questions with broad value. I won't vote to close, but when next you post, please do us the courtesy of putting as much thought into your question as you obviously did into your world. Thanks.
– JBH
Commented Jul 8 at 6:30