Sounds like a fun system. There's a debate going on about multiple moon systems that you might be interested in here. I like the idea of the weird astrophysical set-up having an effect on the magic of the world.
My journey to revising my world began one evening at work while idly browsing Wikipedia on nearby star systems (I had gotten there from a slashdot article on an exoplanet).
Now quick aside, there's a seen in the movie Krull where you have the setting of the two suns that I always thought was cool and awesome and from teenage years I had had my world be in orbit of a binary star pair. Naturally twice the sun meant twice the orbit for the same solar energy, so the calendar was expanded out to this weird setup where humans counted in half years of 360 days since there was 8 seasons in any orbit (two suns in sky, summer, one winter right).
Wild, fantastical to be sure, but that day I started reading up on what the truth of a planet in a binary star system would be like and, honestly, the science truth is even more amazing and fantastical than the fantasy I had concocted. So I co-opted it.
The lesson I took from this that I'll be applying to my mapping is realistic accuracy, even in a fantasy setting, can add more to the depth and feel of that setting than it will ever detract. The more real the "real" things of a setting are, the more fantastic the fantastic things can be, IMO.
And eventually some stellar cartography will be in order for my setting. As it stands here's the cosmos of the setting as we would understand it - that's important to note since the people of the world still firmly believe it is flat and the stars of the universe orbit their world...
Carthasana is the third planet of the larger of two stars in a binary star system. The star it orbits is the same size as our sun. Carthasana's orbit is slightly more perturbed than ours and takes 365.7629 days to complete - this means the calendar has skip years rather than leap years: every fourth year a day is skipped to keep the solar calendar in sync. Carthasana has one true moon and two asteroids it has managed to capture in orbit around it. The nearest asteroid appears as a very bright star in the morning or evening sky of -5 magnitude. It's orbital period is 10 hours. The asteroid out has a 4 day orbital period and a maximum magnitude of -4. Carthasana's moon is the same size as ours (for reference a full moon has magntiude of -12.6).
The other star in the binary pair is called the cold sun since it lies too far away to provide any appreciable warmth (It does provide the fraction necessary to offset the effect of Carthasana's slightly further orbit from its sun though). Seasons do not pass with respect to it. This said it is still a -20 magnitude object (the sun being -26.73 by comparison) - or about 100,000 times as bright as a full moon. This means the presence of the star in the "night" sky turns it from black to a deep blue color and blotting out stars in the sky with magntitudes less than 3 (about the same effect as light pollution in modern urban environment).
It takes 80 years for the stars to complete a revolution around their shared center of gravity. This means that sunrise and sunset times for the cold sun change slowly over that 80 year cycle on Carthasana - if the two suns rise together on Midwinter it will be 80 years before they do so again.
Half the year is lit well enough that armies can move. This will affect the history of the world. Throwing fantasy considerations back into mix I've ruled that at least some kinds of undead are linked to the light of the cold sun.
Part of my setting revision will be writing software that can track these movements and let the DM know how much light is available at any given time in the year - since the night and day isn't a clear indicator as not all "nights" are dark, and nights when neither cold sun nor moon is in the sky are rare indeed.
Having a technical basis for the system with a predictor should prove very useful. You didn't mention if the two stars had the same spectral output. We had another thread not so long back for what happens with creatures who can see outside of human visible spectrum. This might add more flavor into the mix when certain creatures come out or hibernate depending on which star is out.
We also had another thread talking about eclipses too. With a binary and two asteroids you must have them frequently. Perhaps with an 80yr orbit those eclipses could last longer than ours and a 10hr asteroid might have quite sudden light dropping eclipse effects lasting mere seconds...
If the seconds star at mag -20 is out by itself then presumably you would be able to see that asteroid as a dark shape going across the sky.
An eclipse requires the occulting object to have a visible disk, which neither asteroid has, and that that disk have an apparent size equal to or greater than the blocked star. Carthasana's primary moon, Balcra, has this property like our own moon - it is exactly 40 times smaller than the sun, but 40 times closer. The cold sun can also be eclipsed as it just barely has a discernable disk to the unaided eye about 1/40th to 1/20th the size of the sun.We also had another thread talking about eclipses too. With a binary and two asteroids you must have them frequently. Perhaps with an 80yr orbit those eclipses could last longer than ours and a 10hr asteroid might have quite sudden light dropping eclipse effects lasting mere seconds...
No. BTW, my reference on both the asteroids is the fact I've observed both with an unaided eye and with a telescope our own International Space Station. The magnitude given is brightest possible, a good deal of the time the station is much dimmer. The asteroids are a bit further off though and unlike the ISS they orbit out far enough to escape being eclipsed themselves at least on some nights, though they do wink out at night as they get eclipsed. However, when the cold sun is out when this happens they just fade away, lost in the scattered blue light created by the cold sun.If the seconds star at mag -20 is out by itself then presumably you would be able to see that asteroid as a dark shape going across the sky.
If the nearest asteroid has a period of 10hrs then that makes it about 20,000 km away. If your asteroid was 175km long then it would have the same diameter as our moon at about 30 arc minutes. So if you think the asteroid is too small to eclipse stuff then fair enough but I was thinking of something pretty big. Even if this asteroid was say 10km across then it would still have 1/15th the moon diameter which is still a discernible blob shape in the sky. Hope my math is right here I have seen the ISS plenty of times and its bright but pretty point like without a scope. Well its just my wild imagination making the asteroid vast enough to be worthy of a trip from Bruce Willis I guess.
This pic is our asteroid sizes compared to our moon
so given that our moon is 20x farther than your asteroid orbit then odds on that any of these would be pretty blobby.
Tagging this thread for future discussion and reference... The setting I am trying to design was based on a binary system... but I never got it all straightened out... I had also intended to put a planet in "habitable zone" orbit of each star, so when the early sci fi stage of the setting (I was crazy and working on a mideval fantasy, 1920s+fantasy, 2100s+ fantasy, and something way futuristic with fantasy...) happened the first "colony supportable" world would actually be within reasonable reach.
Anyway the asteroids are mainly there to make astrology interesting. For that role they do not need to exceed a kilometer or so in size.