Astonomical Calculations

[kristof65]

This isn't technically a Traveller question, but I know there are a lot of people here with the astonomical and math knowledge to help me figure out what I need to know.

I'm working on my fantasy campaign, and I'm trying to calculate how often solar and lunar eclipses occur for the portion of the world my campaign falls in. Unfortunately, the "optimizations" I made to my worlds calendar have really hampered me in figuring out how to tweak the formulas/methods needed to calculate eclipses. I'm probably just going to wing it, but decided to go ahead and ask, because I'm sure someone here* is smarter than me, and could whip the calculations out quickly.

What I have is an earth sized world, orbiting at approximately the same distance around the sun once every 365.25 days (exactly - to make my calendar easier). The moon is also the same size/distance as our moon, with the same orbital inclination, but orbits once every 28.096 days (365.25/13 actually) unlike the 29.5 days or so ours does. Again, to make my calendar easier. The region in question is at approximately the same latitudes as continental US and roughly the same size - since its a fairly small region when compared to the world size, I don't think I really need to know how often eclipses occur everywhere, just in that region.

I'm guessing that since I kind of rounded off the numbers for my world, that eclipses should have similar regular patterns, but for the life of me, I can't figure out what, particularly when it comes to the lunar eclipses.

Thanks in advance,
Chris H



*more likely several someones, if not the majority of you.

 

[GamerDude]

I'm working on my fantasy campaign, and I'm trying to calculate how often solar and lunar eclipses occur for the portion of the world my campaign falls in.

Kris,

If you go to the Wikipedia page on lunar eclipses (http://en.wikipedia.org/wiki/Lunar_eclipse) is nice with picture examples and such.

On it there are links to pages that discuss these cycles, Eclipse cycle (http://en.wikipedia.org/wiki/Eclipse_cycle) and Saros cycle (http://en.wikipedia.org/wiki/Saros_cycle). The Eclipse cycle page goes through the math I believe you are looking for.

I hope these pages help you.

 

[kristof65]

I pored over that page, and several other pages on lunar eclipses around the web before I even posted here.

Thanks, though.

 

[EDG]

Try this - obviously you'll have to tweak the numbers to match your system, but it seems pretty complete. If you want to figure solar eclipses then you'll need to figure out the size of the lunar shadow cone. I guess you'll have to assume that the moon's orbit is not inclined to the planet's equator as well:

http://www.eso.org/public/outreach/eduoff/aol/market/experiments/middle/skills202.html


Or, you can use an astronomy visualisation program like Celestia and set up the system there (and your viewpoint on the planetary surface), and actually time the duration of the eclipses.

 

[GamerDude]

I pored over that page, and several other pages on lunar eclipses around the web before I even posted here.

Thanks, though.

You are quite welcome. I hope EDG's solution is of more help than mine was.

 

[kristof65]

I'm not looking for durations though - I'm looking for frequency.

 

[EDG]

I'm not looking for durations though - I'm looking for frequency.

So you are

I think it will depends on the inclination of the orbits of the planet around the sun and of the orbit of the moon around the planet. If everything is on the exact same plane, then you will always get one solar eclipse and one lunar eclipses for every orbit of the moon around the planet (one at full moon when it's in the planet's shadow, and one at new moon when the moon is directly between the planet and star). And the eclipses will always be visible only from the equatorial regions since that's where the shadow will be cast.

If any of the orbits are inclined though, then that changes where the shadow is cast, and whether or not the moon crosses the shadow much at all (and that also depends on the orientation of the moon's orbit in space too).

So it's complicated . I guess you'll have to draw it out somehow and use trigonometry to calculate things. if you're still stuck I would suggest asking on the BAUTforums (despite being called the "Bad Astronomy and Universe Today" forums, they have discussion boards for Good astronomy questions like this - just ask on the Q&A board).

 

[GamerDude]

if you're still stuck I would suggest asking on the BAUTforums (despite being called the "Bad Astronomy and Universe Today" forums, they have discussion boards for Good astronomy questions like this - just ask on the Q&A board).

Thanks for that link EDG. I think I'll go there and take a look-see. I might just be able to glean something from it.

 

[Rikki Tikki Traveller]

May I suggest an APPROXIMATION:

Once every 2.4 years you get a Lunar Eclipse (2 years and 4 months)

Any particular spot on the map will get a Solar Eclipse every 25.3 years. (25 years and 3 months)

Saves doing the calculations and still makes them noteworthy when they appear.

 

[BP]

What I have is an earth sized world, orbiting at approximately the same distance around the sun once every 365.25 days (exactly - to make my calendar easier). The moon is also the same size/distance as our moon, with the same orbital inclination, but orbits once every 28.096 days (365.25/13 actually) unlike the 29.5 days or so ours does. Again, to make my calendar easier. The region in question is at approximately the same latitudes as continental US and roughly the same size - since its a fairly small region when compared to the world size, I don't think I really need to know how often eclipses occur everywhere, just in that region.

I'm guessing that since I kind of rounded off the numbers for my world, that eclipses should have similar regular patterns, but for the life of me, I can't figure out what, particularly when it comes to the lunar eclipses.

kristof65, I did this once for an imaginary system - and it took several pages (I'd definitely have to write a progam now-a-days).

The RW approximations of Sol-Earth-Luna are often based on the 'Saros' eclipse cycles - documented back in babylonian times IIRC (some theories even said stonehendge can be used to predict). And in RW - this cycle varies over time (to be more correct there are some ~40 families to be calculated to get it 'right'). As EDG mentioned - complicated.

You've nicely given the relevant figures (365.25/13, position, etc.), but, unfortunately, I don't think the rounding you've done helps this - these are periodic (trig) functions that don't generally gain simplicity in this respect. Even ignoring eccentricies of orbit, wobble, oblateness, tidal effects, penumbra/umbra based on primary wavelengths, etc., the solution is still non-trivial.

Since you are matching a Sol-Earth-Luna system so closely, why not just use existing systems - here's two online/java types: NASA one and U.S. Navy one.

P.S. You can do these calcs by hand (w/trig tables/slide/calc) - or by using continued fractions and the like (if you want to use approximation tricks) - but its quite tedious. I.E. Way to much to explain in a post.

 

[GamerDude]

The approximations mentioned sound good to me. I mean just how scientifically accurate does the setting have to be. kristof65's world is so close to our reality what harm would it be for him to use the frequency etc of our own lunar eclipses and such?

This was a very early debate on these forums about how much 'science' should be brought into RPG's and one person quite nicely pointed out "not so much that it interferes with or slows down the game".

I commend kristof65 in his desire for scientific accuracy, his game must be a blast to play in.

 

[EDG]

RTT - where did you get those approximate numbers from? Presumably they must be based on something - are they just approximations to reality?

I would have to say though, if the numbers for kristof's system are that close to Earth's, then he may as well just use the same timing as for Earth.

 

[Rikki Tikki Traveller]

EDG: I made them up as I wrote. There have been TWO total solar eclipses in my birth town in ~46 years (my life time), so that was how often I decided solar eclipses occur (I just added a random month).

Lunar eclipses was a "SWAG" (Scientific Wild-Ass Guess) based on about how often they seem to occur (from my memory).

However, I do agree that using real life timing would be better and "close enough".

I once tried to do a similar thing with TWO MOONS. One on a "weekly" cycle and one with a "monthly" cycle. Never got it figured out though.

 

[kristof65]

Thaks for the replies, guys.

For the most part, my world started off being a "clone" of earth, so to speak, and everything was the same as earth - after all, this campaign got it's start in high school over 20 years ago. As I began detailing certain things, they got tweaked - one of the first things was the calendar, and I made it 13 months of 28 days each with a special holiday day making up the 365th day. The 13 months were literally based upon the cycle of the moon - each month starts on the new moon.

This worked fine until several years of play and my continuing education revealed that I can't use the earth's moon cycles exactly, because they are actually longer than 28 days. It was at that point when I realized that if I wanted to continue to use "real data" for my approximations, I need to have a leap year, too - which i did by making the holiday two days long every four years.

Up until now, this has been sufficient.

But now the group now has a werewolf among them - and in my world, werewolves are significantly weakened during lunar eclipses - which was something I threw in years back when the PCs needed to defeat a particularly powerful werecreature. With a player now actually playing a werewolf, I need to determine when the lunar eclipses are, because they can affect him. And doing the lunar eclipses means knowing when the solar eclipses are, too. Those things led me to realize I might need to be a little more accurate than just picking some random arbitrary numbers.

To further complicate matters, in a previous campaign, set 400 years ago, a significant adventure happened that revolved around a solar eclipse. Two of the current players also participated in that campaign. So I need to work out a cycle for it that will coincide with what those players remember and let me know if any solar or lunar eclipses will occur during the time frame of this campaign. If I was working with a whole new batch of players, I'd just wing it, but I need to be consistent.

So thanks for the compliment on scientific accuracy GamerDude, but it's more about consistency than accuracy - you know, the type of consistency where if a Tavern named the Cup and Sword is in the village of Thames the first time the PCs pass through, then the next time they pass through Thames, it better be there, or a story as to why its not.

Anyway, I'm now realizing with your guys input that this is a really, really complex math problem that is probably better to just backward engineer. I think I'll just ignore the placement of my planet, sun and it's moon, and derive some numbers for the eclipse cycles from the earth's cycles that sound about right. If any of my players want to figure out the math like our ancients did, they can be my guest.

Since it's a fantasy world, I guess it really doesn't matter if the world is 93.3 million miles from it's sun, or 93.4; nor does it really matter if the moon is orbiting a 5 degree inclination versus a 6.1234 degree one. What really matters are the events themselves.

Thanks again, guys.

 

[BP]

... need to be a little more accurate than just picking some random arbitrary numbers.

... need to be consistent.

In effect - believable to your group. Since just about everything in RPGs is, somewhere along the line, arbitrary - the key becomes 'believability'. Sometimes this runs head on into reality. Most of the time it is just a matter of being consistent - which is generally more important than accuracy or rationalization. I've spent a lot of research time making things 'realistic' - and a lot less time actually playing them - i.e. wasted time on realism (my own eclipse calcs were a prime example) .

...What really matters are the events themselves.

Well put. And its real cool that you have held a gaming group together for so long! Enjoy.