Planet and moon orbits

[á?t ç?d ?ovér]

I am a conlanger and conworlder. This means that I create worlds, civilizations that inhabit the worlds, languages spoken by people on those worlds (which is what I'm most interested in), land features of those worlds, etc. Incidentally, you too would be an alt code lover if you worked with languages that frequently use characters like á or ç.

Many of the features in the worlds I create are fictional and/or fantasy (for instance, the creation myth of one of the world's civilization's is completely true within the context of the world, much like Tolkien's story The Silmarillion is true within the context of Middle Earth). But I still like to have realistic details where I can. Which brings me to planet and moon orbits.

I'm currently working on a world called Arzhaná. It orbits a sun, called Exïnes, and has two moons, Sfantángi and Zhaumpadhei. There are other planets in this solar system as well. I would like to make this system capable of existing in a universe with physical laws similar to our own, and not do anything completely unrealistic like having an icy-cold planet close enough to a hot star that it orbits it in a day. I would like to have enough details to make this system in the space simulator program Celestia.

I have some details about this system:
Arzhana's surface gravity is 2.48% more than Earth's.
Sfantángi is the smaller of the two moons, is closer, and is tidally locked with Arzhana. Zhaumpadhei is larger, and is not tidally locked with Arzhana. It appears bigger than Earth's moon, but only slightly.
The length of a year is 373.6103 Earth days.
Arzhana's radius and density is similar to Earth's, but not exactly the same.
Arzhana at the right distance from the star to support life similar to what lives on Earth.

These are features I would like to have, but I'm willing to get rid of them if they conflict with any of the above features:

Exïnes is a red star.
The moon Zhaumpadhei has a small moon of it's own. It is just barely able to be seen from Arzhana.

Other than the above, I am willing to make up whatever details I need to create a system that will work in the physical world. But since I don't know those details, I'm asking this board.
Any help is appreciated!

[Ricimer]

Actually, there's nothing that strikes me as contradictory in your statements.

Its a little different in size and density, okay, and so you have a small variation in gravity. No problem there. Now, if that was the 2.48x earth gravity, instead of %, as I first read, there'd have been a small problem. But it isn't so we won't worry about it.

By the way, how'd you whip up such a small difference? I really don't think that would matter at all.

Two moons, no problem. Smaller one is tidelocked, that works pretty well, since smaller objects have less angular momentum to bleed off. Of course, the tidal forces (that cause the tide lock, thus the name) are less, but you've got it closer. So you're within the bounds of possibility.

Second moon, once again, no problem since apparent size depends on physical size and distance. Take for example how our sun looks to be the same size as the moon, despite it being ~1 million miles across. It is, of course, over 100x more distant, so that shrinks it to fit.

Now, here's where things are going to be a bit different:

You have a red star, but ~ 1 earth year. That changes the parameters of the star, or the orbit a bit.

A red star will put out less light per meter than the sun. So a red star, the same size as the sun, doesn't give off as much energy. As such, the planet has to be closer to get the same amount of heat as earth. That speeds up its orbit, assuming the stars have the same mass.

So, the star must be less massive, which fits with the redder idea, and the planet be a lot closer. How much closer depends on how red you go. So, how red is red? Is it a yellow red, an orange red, or red red? This is an interesting balancing act even though as you go redder, the star gets less massive, and the planet must get closer to a) get the same energy b) have the same year. But A) and B) vary differently, hmm, I could wrack my brain for a relation between subsolar blackbody temperature and orbital period for a given mass star (which depends on how red you choose). But its late, and that quantum mechanics homework...yeah, that says it all, quantum mechanics homework.

Another note, just for any biology you whip up. Red light is less able to free electrons, regardless of intensity (in many materials it just can't) so this will effect the photosynthesis processes of plants. They'll be a lot bluer, since they need to absorb and use red more. They'll likely have more fiolage too, and probably a little slower growth.

[Master258]

[quote="á?t ç?d ?ovér"]I am a conlanger and conworlder. This means that I create worlds, civilizations that inhabit the worlds, languages spoken by people on those worlds (which is what I'm most interested in), land features of those worlds, etc. Incidentally, you too would be an alt code lover if you worked with languages that frequently use characters like á or ç.[quote]


Has ever got you thinking that maybe were're just a creation of another conlanger and conworlder?

[á?t ç?d ?ovér]

Actually, there's nothing that strikes me as contradictory in your statements.

Basically, what I'm trying to do is create a table like this:

Arzhana
Mass: similar to earth
Density: similar to earth
Radius: similar to earth
Surface gravity: 102.48% of Earth's
Distance from sun at perhelion:
Distance from sun at (the opposite of perhelion):
Surface gravity:
Rotation period: similar to earth
Eccentricity of Orbit:
Inclination:
Period:373.6103 Earth days

Sfantángi
Mass:
Density:
Radius:
Orbital period:
Rotation period:
distance from arzhana at closest point:
distance from arzhana at farthest point:
Eccentricity of orbit:

Zhaumpadhei
Mass:
Density:
Radius:
Orbital period:
Rotation period:
distance from arzhana at closest point:
distance from arzhana at farthest point:
Eccentricity of orbit:

Shaumpadhei's moon
Mass:
Density:
Radius:
Orbital period:
Rotation period:
distance from Zhaumpadhei at closest point:
distance from Zhaumpadhei at farthest point:
Eccentricity of orbit:

Exïnes
Stellar type:
Surface temperature
Mass:
Radius:
Density:
Color:

I want to fill in the remaining details in such a way that the system works,that the planet is at the right difference from the sun to support life as we know it, and that the few specific things I want that I mentioned in my first post occur. I chose these details because they're what you need to model a star system in the program Celestia, which is what I'd like to do with my conworld.

By the way, how'd you whip up such a small difference? I really don't think that would matter at all.

I just made that figure up. I also just made up the year length figure.

[JohnOwens]

Well, just for some examples, I figured the orbits for a planet in the habitable zone of Betelgeuse, a red supergiant, and Proxima Centauri, a red dwarf. I got an orbit of about 220 years for Betelgeuse, and about 3/4 day for Proxima Centauri. So typical red dwarfs and red supergiants won't work, you'll have to look for something in between (which means just about ANYTHING red). I'll see if I can dig out some more modest examples.

Added: Getting warmer (so to speak), Alpha Centauri B is an orange-red dwarf, K0-1V, and for its habitable zone, I get about 250 days, 2/3 year. So it would seem it should need something just a bit larger than that, maybe a K1IV orange subgiant or M0IV red subgiant would do. If anyone knows any examples with mass & luminosity to work with? Otherwise I'll poke around a bit more myself.
Ook! Gamma Cephei (which happens to actually have a known planet orbiting it) is a K1IV, but putting something in its habitable zone gives an orbital period of about 6 years. I guess what we're looking for is either a high-end KV-class orange dwarf, considerably bigger than Proxima Centauri, or a M0IV red subgiant, cool enough to let the planet orbit close enough to shorten the year up.

Added: OK, I finally found a candidate in the right ballpark, HIP 29958/GJ 9210/LTT 2513, an M0IV red subgiant about 93 +/- 19 light years away. The only mass I could find for it was rather vague, 0.5 solar masses, but with its brightness, that makes its habitable zone orbit at about 0.91 AU, with a period of about 450 days. That should be close enough that it can be tweaked a bit by assuming the luminosity is equal to 29958's (0.844 times solar luminosity) while upping the mass a bit. Hmm, let's see... 1.475*10^30 kg makes it work for your number of days exactly. But that makes the mass 0.741 solar masses, so it would be a bit brighter than 29958, most likely, pushing the habitable zone further out....
But anyway, that's close enough that you might be able to take it from there.

[á?t ç?d ?ovér]

A bluish star would also be acceptable, but it's my understanding that blue stars are so short lived that they would nova before intelligent life could evolve. I'm just looking for a star some other color than the sun's yellow, really, to make it more interesting.
Arcturas is orange, right? What would an orbit in it's habitable zone be? And how did you compute that JohnOwens?

[JohnOwens]

What would an orbit in it's habitable zone be? And how did you compute that JohnOwens?

If you know it's luminosity compared to the Sun's, then the easy way to find the habitable zone is just to take the square root of the relative luminosity and figure the planet has to be that many AU from the star. The tricky part can be figuring out the luminosity; sometimes, you only have a visual magnitude and a rough distance to figure it out from, you go through the logarithm process, yadda yadda, wave your hands, *poof*! you've got an absolute magnitude to compare to the Sun's.

P.S. In cased you missed it, see the final addition to the above post, about the red subgiant; if I find any better ones, I'll post below here henceforth.

Added: You can rule out Arcturus, I'm afraid; it's a red giant, but its mass seems to be only 1.0-1.5 solar masses, while its luminosity is about 180 times the Sun's, putting the habitable zone at about 13.4 AU (the square root of 180), for an orbital period around 14,600 to 18,000 days long, depending on that mass. (Use P=sqrt((4*pi*r^3)/(G*M)) at this point, or the simpler P=sqrt(r^3/M), using years, AU, and solar masses for the units.)

[JohnOwens]

Added: You can rule out Arcturus, I'm afraid; it's a red giant, but its mass seems to be only 1.0-1.5 solar masses, while its luminosity is about 180 times the Sun's, putting the habitable zone at about 13.4 AU (the square root of 180), for an orbital period around 14,600 to 18,000 days long, depending on that mass. (Use P=sqrt((4*pi*r^3)/(G*M)) at this point, or the simpler P=sqrt(r^3/M), using years, AU, and solar masses for the units.)

Hmm, looking at it that way gives me a good idea for how to simplify it as much as possible. Once you have the relative luminosity, call it L, use the years, AU, solar masses as above, you'd get P = sqrt(sqrt(L)^3/M), or if you like the expanded form, P^2*M = sqrt(L)^3. That makes it a bit simpler to isolate the mass, M = sqrt(L)^3/P^2, or the luminosity, L = (3rt(P^2*M))^2. Those might be a bit more easily useable.
Oh, and to make it easier, your year = 1.022911 Earth years, so that's what you want for P.

P.S. Anyone know the standard ASCII representation for an nth root? :-?

[milli360]

P.S. Anyone know the standard ASCII representation for an nth root? :-?

What's wrong with x^(1/n) ?

[á?t ç?d ?ovér]

If you know it's luminosity compared to the Sun's, then the easy way to find the habitable zone is just to take the square root of the relative luminosity and figure the planet has to be that many AU from the star. The tricky part can be figuring out the luminosity; sometimes, you only have a visual magnitude and a rough distance to figure it out from, you go through the logarithm process, yadda yadda, wave your hands, *poof*! you've got an absolute magnitude to compare to the Sun's.

Are you saying that the habitable zone of a given star is at the distance where the star's apparant magnitude is the same as the sun's apparant magnitude from earth?

[JohnOwens]

If you know it's luminosity compared to the Sun's, then the easy way to find the habitable zone is just to take the square root of the relative luminosity and figure the planet has to be that many AU from the star. The tricky part can be figuring out the luminosity; sometimes, you only have a visual magnitude and a rough distance to figure it out from, you go through the logarithm process, yadda yadda, wave your hands, *poof*! you've got an absolute magnitude to compare to the Sun's.

Are you saying that the habitable zone of a given star is at the distance where the star's apparant magnitude is the same as the sun's apparant magnitude from earth?

Exactly, that's one way of putting it. Visual magnitude should be around -26.8. I've been thinking about how much leeway there is in that. Given that you'd have a range where the closest part of the zone has planets only habitable at the poles, the farthest part has planets only habitable near the equator, and the possibilities of different albedos (anyone know the difference in albedo between land & sea?), you could stretch it out a bit, probably at least to where you could get by in the m_v (visual magnitude) 26.6-27.0 range. That gives about +/- 20% of the power/area of what Earth gets, which ought to be a tolerable range. Taking the square root of that, you might be able to get away with distances about +/- 10% from the distance that gives you exactly the same m_v as the Sun from Earth, which means you could change the year length by about +/- 15% (which might make that HIP 29958 just barely doable with a 373.6103 day long year, 15% less than 450 days gives 383 days, but it'd be mighty toasty).

[Brady Yoon]

And habitable zones grow increasingly larger with the star's luminosity. For example, a star with a luminosity of 100,000 times the solar would have an enormous habitable zone, extending many times past Pluto's orbit. Also, a habitable zone is a 3 dimesional area. Just a couple things to consider. :wink:

[Ricimer]

Brady, while the habitable zone may be a 3-d volome, the planets orbit is still a 2-d plane, and will likely be along the stars equator (due to the formation process, and conservation of angular momentum).

Another note on the habitiable zone: Eccentricity can play a big role. What john says is perfectly valid for near circular orbits.

But you can really play around and have a highly eccentric orbit. The temperature on the planet will vary a lot over the year, but the average temperature can still be quite moderate.

[rebeccalb]

[quote="Master258"][quote="á?t ç?d ?ovér"]I am a conlanger and conworlder. This means that I create worlds, civilizations that inhabit the worlds, languages spoken by people on those worlds (which is what I'm most interested in), land features of those worlds, etc. Incidentally, you too would be an alt code lover if you worked with languages that frequently use characters like á or ç.

Has ever got you thinking that maybe were're just a creation of another conlanger and conworlder?

If you believe in God, then yes.