# Calendar in Binary Star System



## Noldona (Feb 2, 2015)

I am working on building a fantasy world in a binary star system. My current goal is to determine the calendar of the world. I am having trouble finding the formulas to calculate things such as daylight length, seasons, etc. for the system. Hopefully, someone will be able to point me towards a resource for these formulas or help me determine the values. Here are some of the specifics of the system.

The system is a binary star system consisting of a G2 V star as the primary star and a K1 V star as the secondary star. The stars orbit each other in a period of 79.91 Earth years with a periapsis of 11.2 AU and a apoapsis of 35.6 AU. The primary star has a velocity of 5.01 km/s, while the secondary star has a velocity of 6.05 km/s.

Orbiting around the primary star is an Earth sized planet with an oribit velocity of 28 km/s, periapsis of 1.08 AU, apoapsis of 1.11 AU, and a rotation velocity of 465.1 m/s. The planet ecliptic is at about 67.5 degree off from the solar ecliptic.

The planet is orbited by 3 moons, however I have already found the formulas for determining their orbital periods. I just mention it in case their existence affects any of the other calculations.


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## johnsonjoshuak (Feb 2, 2015)

That's way more science than I was prepared for when I came into this thread lol

When I'm figuring out my orbits, I just go paper and pen. As far as rotation, isn't that kind of arbitrary/based on mass etc? 

Here's something tho Kepler's laws of planetary motion - Wikipedia, the free encyclopedia


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## Noldona (Feb 2, 2015)

Sorry for the heavy science, but I like my worlds to be sort of realistic. Makes for a more believable world. I have a program which I used to build a simulation of the stable orbits of the solar system which is where I got all of the figures for distances and such. However, the program does not give me figures for day/night length, sunrise/sunset, season lengths, etc. The are the figures that would be important to an individual living on this planet.


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## Terry Greer (Feb 2, 2015)

An interesting problem.

I don't have any formulae, but I can look at it from a different angle.

Daylight length at least is largely down to the rotation of the planet - which is entirely in your hands. 

Seasons will also depend on your plant's axial tilt and not just on the orbits - which is near enough circular to make relatively little affect (after atmosphere and biological climate feedback have been taken into account).

The main axial tilt is what will drive the seasons. If its negligable then there won't be much in the way of seasons, and the more its tilted the more of the planet will be affected by those seasons.

E.g. the tropics aren't affected hugely by the earth's current axial tilt of 23 degrees - but if we were tilted over as much as Uranus (97 degrees) then the entire planet would have severe seasons. 

But far and away the biggest climate effect will be the planet's rotational speed (which transfers heat from the lit to the dark side), the atmosphere (including any seas or other thermal reservoirs that store heat and release it slowly) and the biology itself (which acts to maintain its biosphere and also absorbs heat/energy and replenishes the atmosphere using a feedback system. Our sun's heat output has changed markidly over the earth's history, and despite this the life living on it has managed (overall) to maintain the climate within fairly narrow bounds through these feedback systems.

The secondary star is an orange dwarf and is pretty distant at 11 to 35 au which means it's energy output will probably not add significantly to the seasons - but it would illuminate the night a fair bit - especially when close.


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## Noldona (Feb 2, 2015)

As the world is intended for a standard medieval fantasy roleplaying campaign, I could cheat a bit and say the planet has a similar axial tilt and rotation speed as the earth. As the planet is slightly farther away from its star then Earth is from the Sun, doing such would give it a slightly longer day coming in at somewhere around 26 hours for a sidereal day. The solar day (which would be more important to the inhabitants) would be closer to 28 hours though. Also, since you say that the secondary star would not affect the seasons much, and the orbital distance and star type are basically the same as the earth, my seasons would probably be similar to the earth.

This really just leaved how to determine sunrise/sunset times for both stars as they would both provide sufficient light to the planet. And since the stars orbit each other and the planet only orbits 1 star, I would like to also calculate when 1 star might eclipse the other.


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## Queshire (Feb 2, 2015)

It's for a fantasy role playing campaign? Go with 24 hours.

Realism is important and cool, but when you're dealing with a group as small as a role playing group it needs to give way to practicality. I don't see them remembering a random bit of trivia like day length no matter how impressive the math is to reach it, and if that trivia affects their game without adding to it,  for instance messing up the timing of their plan since they defaulted to 24 hours by habit instead of doing 28 hours then they would start to get annoyed.

Now if the 28 hour days added something cool to the story like having magic get boosted during those extra 4 hours it might be a different story, but having the days be 28 hours without anything else is just a dull fact.

Edit: Also the stars would Eclipse each other whenever the plot says so. Trust me, your job will be much easier if you have some wiggle room to adapt to the players inevitably going off the rails.


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## Terry Greer (Feb 2, 2015)

The distance the planet is to the star has no bearing on the day length (ie. the time it takes the planet to rotate about its axis). It can be anything you like. The earth's rotation has slowed down over time as the moon has 'stolen' gravitational energy and receeded. 

The time of sunset and sunrise will vary depending on where you are on the planet and its orbital tilt - just like it does on earth. When its endless summer in the Antarctic - its endless night in the Arctic. The only time you get 12 hours day night everywhere is at the spring and autumn equinox. 

It's worth mentioning that the Orange dwarf even at closest approach is well beyond the equivalent of Saturn, and it's smaller and less luminous  than our own sun. So a world like our earth lit just by that would be a dull orange twilight at best. This companion would, like our own moon, and its rising would get progressively later every day. (by about 1/370th of the day length (assuming 360 days in the year). 

Assuming the length of the year is roughly the same and the main sun always occludes its more distant companion the eclipse will be about every 1.0125years (or about 1 year + around 4 or 5 days). As the angular size of the sun is about half a degree, this means that it will take approximately just over half a day for the eclipse to occur.

These are rough calculations as I don't have the formulae to make them exact, but they should be fine for a fantasy setting.

You don't need it to be accurate really - but I'd draw a diagram, of this on  abig bit of paper - it will help you get your head around it and using a protractor you can then easily figure out how close they'll be in the sky together in any one week. If you do this for about 12 positions (all on the same chart) you can just linearly interpolate between them and it will be close enough.


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## Noldona (Feb 2, 2015)

I feel that the more realistic the world is, the better it is for gaming in. I've always been annoyed by random dungeons populated by monsters that make no sense. Why would trolls build a dungeon in a specific fashion or one at all instead of using a cave? I don't think they would build something. It would make more sense for them to move into the ruins on an old keep. That keep would then be built in a specific fashion due to the previous inhabitants building it that way. In the same sense, the main races living in this world would have their own religions, lore, calendars, etc. It makes sense that they wouldn't use the standard earth calendar or even necessarily split the day into the same time groups as we do. While the eventual goal of the world is to be a campaign setting, my plan is to write history and backstory for the world. I want someone to be able to look at it and feel like this world could actually exist somewhere in the universe. This is why I am worried about figuring out the timing for different things.


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## Saigonnus (Feb 2, 2015)

As a former DM, I feel for your desire to have the gaming world be realistic. I had everything in the solar system mapped out, the world we played in all drawn out on sheets of paper. I know the planet has an axial tilt of 30%, giving it some some fairly severe weather occasionally and that it take 400 days to circle the distant star. I also know it take 30 hours for a single day/night cycle. I also know where things were in relation to everything else and had a binder filled with the info for specific kingdoms, cities, cultures and what not. 

Truthfully though, the specifics for all of that astronomy never really came up in the campaigns we ran in the world at all. It did give a sense of realism though, when I would describe a vast star filled sky with three moons chasing each other the heavens. I think ultimately it will come down to how you use the information you have. If you go on long periods of info dumping, give your players a thick stack of papers to read before the game and you'll take something away. Remember; like with a novel, they have to suspend their beliefs somewhat anyway and sometimes hard facts robs them of that. 

I do agree with some of the points you'd made about premade dungeons and the like, how some random monsters are found within, when it makes no sense that they are there. Trolls for example tend to prefer a moist, swamplike environment and even if said castle, underground complex were built by someone else, as long as it fits that criteria, they would reside there. Ultimately you are the DM and can choose something else to inhabit the space if it doesn't seem right. That is part your job... Use these different threads to weave a memorable story.

I think if you stick to the information you make about the specific cultures, races, kingdoms etc... It will feel realistic enough.


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## Noldona (Feb 2, 2015)

Terry, you are right that rotational speed determine the sidereal day length (time to complete 360 degree rotation) not the orbital distance. However, the average inhabitant on the world would be more interested in the solar day (time to which the sun reaches the same point in the sky). This length is affected by the orbital distance and orbital velocity.

For the sunrise/sunset times, I understand the difference based upon location on the planet. This is why I was hoping to find formulas so I could calculate out what the times would be. As for the orange twilight periods, this could lead to some interesting plot ideas and cultural things as the length of that twilight period would change during the course of the year. So knowing the length of time it lasts at different points of the year could be useful as well.

As for drawing the diagram, I'm confused on how that would work, especially since the star orbits are on a different plane then the planet orbits. If you could provide some more information on how you do this, that would be helpful.

Saigonnus, I have been GMing on and off for about 15 years now in several different system so I know you are completely correct. I am sure a majority of the work I am going to be putting into this world will never be seen or even cared about by the players, but for me world building is half the fun of being a GM. Plus, having a rich backstory is a great source of ideas for adventures, as you are probably well aware of. Are there any programs, systems, or references you used to figure out all the details for your world?


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## Terry Greer (Feb 3, 2015)

I see what you mean now - but its easier to go the other way and decide how many days you want in your planetary year first. 
You can get the orbital period from a formulae in he link below - that will give you how long a year is.

Then your best bet is to decide how many days you want in that year - because then its easy to figure out the day length.  You need to make a descision on one value otherwise there are two many unknowns.

These formulae might help for the orbital period:

Kepler's Laws Tutorial

The number of days in a year though (siderially) is up to you. The solar day is then equivalent to 1 day more or less (depending on which way the planet orbits) averaged over the year by the number of days.

E.g. if the siderial year you want to be equivalent to 100 days  and it takes 2000 hours for the orbital year.
then:
A sidereal day = 2000/100 hours = 20 hours.
The number of solar days in the year is however either 99 or 101 (1 more or 1 less) depending on the direction of the orbit.

This means an 'average' solar day is either 2000/101 (19.8 hours) or 2000/99 (20.20) hours.

It's easy to swap in whatever values you have to this - but its you who have to decide the number of days you want to cram into that year - a formulae won't give it as it depends on the radial velocity of the planet and is arbitary.

I hadn't realized you'd put the stellar orbits at a different angle to the main planet's orbital plane. That really does make it much harder to figure out without a formulae so a diagram and an approximation wouldn't help much.  

When it comes to figuring out the day length based on latitude then it gets more complicated - try this:

Length of Day and Twilight

Though I think you're overworrying about the details a bit -


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## Terry Greer (Feb 6, 2015)

I do understand the drive to produce detailed believable worlds - I've been there - and do admire it when its carried off with style.

I have to add the best work I've seen on creating a believable world setting goes to '*Harn*' by N Robin Crosby. Probably the most beautifully and intricately crafted medieval fantasy world I've ever seen. 

It's a pretty standard medieval world in many ways with cultures that are based on well known sources, but its done superbly.

The detail is extensive and unique and its hugely worth a look to anyone interested in creating worlds for their stories or role playing. I mean REALLY recommended.

There are literally dozens of regional modules and expansions, but for the overall book and world information you should seek out a copy of Harn World.

Maps in the Kethira suppliment show the geology, culture spread and languages, migrations, climate and trade winds and ocean currents! Other illustrations show the solar system that the main planet is part of and the night sky - an many other things.

The detail is stunning and its easy to customize for personal use. For example in any map (such as a city map) it would be done in 3 flavours.
1. Full colour 'painting' for generating atmosphere and buy in.
2. An annotated one with points of interest - for the DM's eyes only.
3. A black and white line drawing with nothing marked - for the players to use for exploration (or the DM if they wnt to customize their own version).

It was a labour of love that took many years.
Mr Crosby died a few years back, but the pdfs are still available and its still sld in a few places such as *DrivethroughRPG* Drivethrough rPG and their own *Kelestia website* 

A small thumbnail preview of some of the gazeteer stuff can be found here:
HÃ¢rnWorld Maps | Kelestia.com. 

Do an image search on Google and you'll see what I mean.

Here's a link to the Kethira module here (and you can get a preview):  

Kethira - Columbia Games Inc. | Columbia Games Inc. | Harn Classics | RPGNow.com


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