When humans finally manage to colonise another planet, there will be some significant differences between life on that planet and life on Earth. One of them is the calendar. Why would the Earth’s calendar be inadequate?
First, the orbital period of the new planet will be different than Earth’s 365.25 days. Second, the length of the day is going to be different. Third, with these two basic pieces of information, the year will start at different seasons, and midnight would happen at different times of day. It would make no sense.
So, what we need to do is create a new calendar and timekeeping system. I’m going to use my fictional world of Ariadne as an example. I have yet to figure out the calendar, so I’m doing it on the fly as I write this post.
First of all, we need to determine the distance of the planet from the star, which is Beta Comae Berenices. To do this, we need an equation. We’ll start with the equation that is used to determine the temperature of a planet (and rearranged to solve for distance D).
D = (Ts^2Rs/2Tp^2)((1-a)/(1-τ/2))^1/2
D is the distance to the star, Ts is the temperature of the star, Tp is the temperature of the planet, Rs is the radius of the star, a is the albedo of the planet, and τ is the optical depth of the planet’s atmosphere. Going through this, I want Tp to be equal to 288 Kelvin, which is similar to Earth’s. The albedo should also be similar to Earth’s which is 0.39. And the optical depth should be similar to Earth’s, considering the atmosphere is very similar. Therefore, that should be 0.6. The temperature of Beta Comae Berenices is 5,935 Kelvin, which is slightly hotter than the sun. The star is also slightly larger than the sun, 1.106 times the size, and therefore has a radius of 770,154,252 metres. Plug all these in the equation, and we get a distance of 152,657,589 km, which is slightly larger than the distance of the Earth from the sun.
Now, to determine the orbital period of the planet, we need the mass of the star, the orbital radius, and the mass of the planet. We’ll use Kepler’s Third Law for this. To simplify this, I used this very handy tool to calculate the period. The semimajor axis is set to 152,657,589 km, the mass of the planet is 1.028 Earth masses (as it’s 2.8% more massive than Earth), and the mass of Beta Comae Berenices, which is 1.15 times the mass of the sun.
We have a result of 0.961094 Earth years, or 351.046 days.
Now, as for the calendar, I’m going to be making up some numbers a bit here. I’ll keep the numbers the same for the planet and star, but the year will be 351.1 days. This means that the day on Ariadne is slightly shorter than Earth’s day by 13 seconds. That’s all. For the clock, a standard 24 hour clock with 60 minutes can continue to be used, though it’ll have to be adjusted a little.
As for the calendar, to get a nice round number of days per month is a bit difficult. However, based on a 351 day year, a 12 month calendar with 29 day months is possible. There are an extra 3 days, though. They could be distributed around to 3 other months, but I’d like to do something special. At the beginning of each year, there will be a 3 day month. It’ll be a 3 day period for people to celebrate the colonisation of the world.
Now, to account for that extra 0.1 days, we can add leap years every 10 years. Add an extra day on the decade to the holiday month, so on every 10th anniversary, there’s an extra long holiday.
As the year is slightly shorter, people’s ages will increase a bit faster. So, a 50 year old person on Earth would have an age of 52 on Ariadne. It won’t make a big difference, though. However, colonists will have to figure out a new birthday based on this new calendar. That can be calculated by regressing the calendar into negative years to find the birthdate. The landing date will start with year 1, holiday month day 1.
Another matter is to name the months. This will come at a later date, as the colonists haven’t arrived at the planet yet! They’ll have time to name them.
I hope you found this post informative. This is going to be Ariadne’s standard calendar, and it will be described with names in the future.
I Read Encyclopedias for Fun 
Okay, hats off…you managed to find a way to have Math equations in a post about writing a sci fi fiction.
You focus on world building. I’ll stick to being detailed with my characters 😉
It is a very nifty walk through! Detailed as always.
Oh, I’ll definitely focus on characters, but I just have fun with the world building. That’s how it all started.
Wow, that was in-depth and an equation and everything! That’s impressive. I avoid any kind of equation like the plague, but I get why this one would be useful 😀
And this was a simple equation! In fact, the equation I used only gives a rough guess. A much more complicated equation is needed to produce a more accurate number.
This is one thing I’ve been working on for the Kingdom Chronicles for quite a while. Except it gets a little more complicated because the Vagans run their lives by a sidereal-lunar calendar, counting solar years only because the Uhuu-mal do. Anyway, I’ve been working the reverse way to figure out where the planet would be: build the planet and its cultures, then expand out to the star systems and galaxies around it. Kudos on the math tho, I might jot that down for later.
Go right ahead. I’ve used that equation in university, but I was reminded of it recently in an online course I’ve been taking about searching for earth-like planets.
Good luck with your calendar. It sounds a bit more complicated than what I did.
Just from that alone, I’m interested in reading this story, especially the way incorporated traits of the planet into people’s everyday lives by giving them the celebration period. It’s that kind of worldbuilding that makes me so envious.
Loved this post, absolutely loved it.
Thanks! Funny how a little astrophysics can result in some culture.
That’s exactly what I was thinking – and precisely the kind of thing I love. :]
Well, I hope to get a lot more interesting world building going on. I need to get all of my files I backed up last month onto my new computer, which includes a map I’ve been working on.
Just wanted to say thanks for this post. I spent about four hours tinkering with it and the Orbital Period calculator, trying to fit my base idea for my planet and sun (and calendar) into the equation so that everything fits. Finally got it! Probably would have been quicker if I’d made much use of math since college, but very helpful anyway.
Glad it helped. It’s partly why I wrote it. I also made a few other recent posts about worldbuilding that may be of interest, as well.
Reblogged this on The War of Memory Project and commented:
I just wanted to reblog this to help anyone who’s as nuts about creating their own planet and solar system as I am. Spent way too long dinking with the calculations today, but that’s just because I haven’t solved an equation since college.
Interesting piece – I’m impressed at the level of rigour in world building.
Interesting that you got a result that was so similar to Earth. Is this a likely outcome of the maths when looking at habitable planets?
I was a bit surprised that I got a year that was a bit shorter than the Earth’s, considering the star is larger and hotter than the sun. But a higher gravity would explain it, anyway. However, since this star is so similar to our sun, the results would be similar. If it were bigger and hotter, it would be farther out. If it were smaller and cooler, it would be closer, and likely have a shorter year. In the expanded universe of this series, if I take it to interstellar travel in the future, I’ll have to figure this out.
Reblogged this on The Way of the Storyteller:.
This is beautiful! I’ve been researching how to make a calendar year for a fictional planet for a few weeks now. I’ve been doing so in anticipation for the game “No Man’s Sky”. In the game you can explore planets and every planet rotates around a star. It also rotates on an axis. My goal was to create a calendar year for the planet I originally start on. In the game it’s possible to carve out the ground, so I hope to eventually make a sundial pertaining to that planet. This post helped me better understand how to achieve my goal. So, thank you!
You’re welcome! I’m glad it could help someone.
I’m also looking forward to the game. When I saw videos about it last year, I thought this is the game I’d been waiting to see for my entire life.
The 13 aditional seconds on each day, will in a year turn to 1,2675 aditional hours. A day on this planet has 23 hours and 47 minutes aproximately. In 19 years, that will be 24,0825 aditional hours. So, in each 19 years, a day has to be gotten off. But that will keep resting 15,97 seconds, or aproximately 16 seconds.
But those additional 13 seconds are in comparison to the Earth’s day. I mentioned that the clock itself is adjusted to take that into account. Anyway, I’m not trying to make this exact to many decimal places, just a more general guide about how this can be done. If someone is ambitious, they can take it down to many decimal places to create a more accurate calendar. But as this is fiction, I’m satisfied with what I got.