Hello I'm new. I'm attempting to create my own solar system, that would work in the real universe, but would obviously be fictional. I've done a good bit of researching for various things involved, but I have a few questions which I could use some clarification on. A few details about my solar system before I get to the questions:

Star - Class K (main sequence)

Planets - 5 (2 terrestrial, 3 gas giants)

Info - The second planet from the star is the only one in the habitable zone. It is roughly twice the size of Earth, with a similar atmosphere. It has two moons, the first one is roughly the size of Mars, also with an Earth like atmosphere, and the second is roughly the size of Ceres with no atmosphere.

Questions:

1. My question pertains to the physics involved, as that is not my strong suit. Would that be sustainable? I see no reason it wouldn't assuming the moons orbit at a far enough distance to keep their orbits from degrading to the point where they'd collide with the planet.

2. I want the atmosphere to be close to a purple hue. From what research I've done, looking at star types and atmospheric composition, a Class K star with a planet that has an Earth like atmosphere should achieve that result, is that correct?

3. Regarding the previous question, if that is correct, then what color would the star appear to be from the planets surface?

The K star is going to cause problems - the habitable zone is close enough to the star that any large planets are going to get tidelocked pretty quickly (by "twice the size of Earth" I presume you mean twice the mass of Earth?). And if the planet is tidelocked to the star, that means that it can't have any moons because they would have spiralled into the planet during the tidelocking process (or maybe they are still spiralling in toward the planet if the system is really young).

AFAIK the planet's sky would be blue because of rayleigh scattering of the star's light - IIRC it doesn't matter what the star colour or atmosphere composition is, that doesn't change the blueness. Though it might change the 'brightness' of the blue, so a redder star might make a sky that is darker blue. I'm not the expert on this, IIRC grant hutchison knows a lot more about this side of things.

The star itself would still look like our own sun (i.e. blinding orb in the sky), but with a slight orange hue. The colour be more noticeable when the sun is low on the horizon, where it'll be a lot redder than our own sun. But even a red M V star is only as "red" as an incandescent light bulb.

Additionally to EDG-'s comments:
A terrestrial planet of that size has a greater chance of having a denser atmosphere than Earths. It would be a fine balance to get it "Earth-like".

Interesting bit about the tidelocking, thanks for that info. What type of star do you think would allow a planet of that size to exist in it's habitable zone without that occuring and have the two moons work?

As to the atmospheric color, research I have done suggests that the color of the atmosphere will indeed be different, for an Earth like planet, if the star type is different due to the wavelengths of light emitted by different stars, causing different scattering effects in the atmosphere resulting in alternate colorization. Here is a particular article I found that discusses the differences in atmospheric color that might occur with alternate star types:

http://www.orionsarm.com/whitepapers...en_worlds.html

As for the size I was actually thinking twice the equatorial diameter, and I have no idea how much mass that would be in relation to Earth.

I love science, but I hate math, it is bothersome. :-)

I considered that, I actually made up a mock list of all the planetary characteristics for my planet, but it is guess work that is not supported by real physics.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

I posted a reply addressing some of your points, but it had a link in it so I guess it will show up once a mod okays it.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

In a work of fiction you can be 'the system builder' This solar system has had a few billion years to settle down and stabilize a tad. Ejecting unbalanced and tidal locking other bodies as the mechanics dictate. Your outlined system sounds perfectly possible and given the appropriate rotational forces would be sustainable. You seem to grasp the reality of fact and from there can license yourself to make up a working different system. You want the sky to be slightly purple. It can be. The absorption and refraction of visible light is what gives a atmosphere its hough. Hough (you) decide.

Thanks. Another possibility I just considered was a binary planet instead of the terrestrial with the two moons. That might be interesting, though would likely be more problematic in determining how days and nights work exactly, as depending on how they orbit each other they could end up constantly eclipsing one another.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

At twice the radius, 8x the volume as Earth. Assuming the density is the same, it would have 8x the mass and twice the surface gravity.

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Hmmm... we should be able to handle twice the surface gravity, wouldn't be pleasant, weighing twice as much, but it is doable. How bout the atmospheric pressure?

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

Do not forget gravitational compression of the planetary interior.

However, you might play with intrinsic density of the planet. The uncompressed density of Mars and Moon is lower than that of Mercury, because they are more rock and less iron than Mercury and Earth.

As for atmospheric pressure, note how Earth has less atmosphere than Venus, despite having more gravity.

That is true, just because the planet is bigger doesn't mean it would necessarily have more atmospheric pressure.

Also I'd want there to be a good amount of iron in the core so that a sustainable magnetic field would be present to shield the planet from cosmic radiation. Which obviously means the planet would need to be geologically active for the core to be spinning and creating said magnetic field. Given the size of the planet it would likely take longer to cool off than the Earth as well.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

You think so? If the star is on the high end of the range for a type K, I really don't think tidal locking is all that inevitable. For instance, a K star ranges from 0.5 to 0.8 times the mass of the Sun and 0.1 to 0.45 times the luminosity of the Sun. If the hypothetical star has 0.45 times the Sun's luminosity, then for the planet to have the same solar constant as Earth, it needs to be SQRT(0.45) = 0.67 AU from the star. That's just a little bit closer than Venus is to the Sun, so I doubt it would be tidelocked.

On the other hand, if the hypothetical star is a low mass type K with a luminosity of only 0.1 times the Sun, the planet's distance would be about SQRT(0.1) = 0.32 AU. In this case I think tidelocking is far more probable.


I think you might be okay with a type K but it probably should be on the large end of the mass range, such as a K1 or K0* star. I'd consider something perhaps 0.75-0.80 times the Sun's mass and 0.37-0.45 times the Sun's luminosity. (Note that the mass-luminosity relationship is L ~ M^3.5)

* Edit: Changed "K8 or K9" to "K1 or K0" - See EDG's post #19 below.

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With a moon the size of Mars orbiting would that not counteract the tidelocking? Also since the moon, being within the habitable range as well with an atmoshphere, be habitable as well? The gravitational fluxuations may allow the core of the moon to remain liquid, or may be within the planets gravitational field, so the atmosphere would not be stripped like Mars is. There then would be the possibiliy for water, and life.

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Ooooo, I think I thought a thought. Ooo I did, I did, I did think a thought.

How big of an orbit would the main moon require around the planet, and how big of an orbit for the second moon?

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Science may set limits to knowledge, but should not set limits to imagination.
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Ooooo, I think I thought a thought. Ooo I did, I did, I did think a thought.

There are three tidelocking possibilities to consider:

1) The moon is tidelocked to the planet.
2) The planet is tidelocked to the moon.
3) The planet is tidelocked to the star.

My gut feeling is that #1 is highly probable; the other two I'm not so sure about. #2 and #3 are, of course, mutually exclusive. Again going strictly by my gut, I think #2 is more likely than #3 unless the planet is very close to the star. If we have large type K star with the planet some 0.6-0.7 AU away, my feeling is that the planet would likely not be tidelocked to the star (though I could easily be wrong). Whether or not the planet and moon are mutually tidelocked (#1 and #2) I suppose depends largely on the distance between the bodies and the age of the system.

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Lots of good information here, thanks very much. :-)

That's the idea. I'm actually going to have the planet in the middle of an ice age, while the moon is in more of a sub-tropical state.

That is something I'm curious about as well.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

If the larger Mars sized moon was farther out, and the Ceres sized moon was closer to the planet, would that cause the Ceres sized moon to be more likely to be tidelocked while the Mars sized one would not?

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

Ah... I forgot all about the small moon; I got fixated on the big one. I think the odds are very high the small moon would be tidelocked to the planet, but not the planet to the small moon. Regarding the large moon, if it and the planet were close to one another, I think there may be a good chance they'd be mutually tidelocked - like Pluto and Charon - particularly if the system is old. If the large moon were further away, we might have a situation like Earth and its moon. I'm not sure what conditions have to be met to have the large moon not tidelocked to the planet.

What do you want your situation to be? Do you want the moon and planet tidelocked? How old do you want the system to be? Somewhere I've seen a method for estimating the amount of time needed for two bodies to become tidelocked. If I can re-discover the method, perhaps we can engineer your system to be what you want it to be. And if you can't have everything you want, perhaps we can figure out where you need to compromise.

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Unfortunately I think your gut is wrong, Bob.

I've crunched the numbers on similar scenarios and worlds can get tidelocked pretty easily to K V stars (at least within 3 Ga). I'll have to check on the specifics, but larger worlds get tidelocked to the stars more quickly, and they get tidelocked faster if they're closer.

Tides gets complicated if moons and stars are involved, but the moons will lock first and then the planet will lock to the star.

Also the large end of the mass range for a K V star is K0/K1, not K8/K9 (that's closer to the M V end).

I'd like for the larger moon to not be tidelocked to the planet, or vice versa. But the smaller moon being tidelocked is fine.

If they both have to be tidelocked for it to work then so be it though.

What star type would you recommend for this set up to work properly then?

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

Drat, I can never remember which direction the numbering goes - I always have to look it up. I decided to chance it this time and got it wrong. That'll teach me.

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I just ran some calculations using this method:
http://en.wikipedia.org/wiki/Tidal_locking#Timescale

In the first scenario I used a star with a mass of 0.8 Suns. Using the L~M^3.5 relationship, the star has a luminosity of 0.46 Suns. For the planet to have the same solar constant as Earth, its semi-major axis is 0.68 AU. I used a planet with two times Earth's diameter and 8 times Earth's mass. I assumed an initial rotational period of 12 hours and used Q=100. Using the described method, this yields a time to tidal lock the planet to the star of 7.5 billion years. Of course this method yields a result with considerable uncertainty.

In the second scenario I used a star with a mass of 0.5 Sun and a luminosity of 0.09 Suns. The planet data is the same as before except the semi-major axis is 0.30 AU. In this case the planet becomes tidal locked in only 140 million years.

This seems to show that a low-mass type K star (K9) will tidal lock a planet in its habitable zone very quickly. A high-mass type K star (K0) will obviously take much longer to tidal lock a habitable zone planet. An Earth-aged planet (~5 billion years) may not yet be tidally locked, but it would seem its rotational period will at least be significantly slowed.

If I continue the calculations for a range of star masses we get the following:

Star mass - Semimajor axis - Tidal lock time

0.5 x Sun - 0.30 AU - 141 million years
0.6 x Sun - 0.41 AU - 640 million years
0.7 x Sun - 0.54 AU - 2.5 billion years
0.8 x Sun - 0.68 AU - 7.5 billion years
0.9 x Sun - 0.83 AU - 20 billion years
1.0 x Sun - 1.00 AU - 48 billion years
1.1 x Sun - 1.18 AU - 108 billion years
1.2 x Sun - 1.38 AU - 233 billion years

For comparison, performing the calculations for Earth, the tidal lock time is about 73 billion years.

This seems to suggest that for a large Earth-like habitable zone planet to have a fast rotation period, the star needs to be at least a low-mass type G star.

Alternatively, I fixed the mass of the star at 0.8 Suns and the semi-major axis at 0.68 AU. I then calculated how long it takes planets of different sizes to tidal lock. I assumed the planet's density is the same as Earth.

Planet mass - Planet radius - Tidal lock time

0.1 x Earth - 2957 km - 30 billion years
0.2 x Earth - 3726 km - 21 billion years
0.3 x Earth - 4265 km - 18 billion years
0.4 x Earth - 4694 km - 16 billion years
0.5 x Earth - 5057 km - 14 billion years
0.6 x Earth - 5374 km - 13 billion years
0.7 x Earth - 5657 km - 13 billion years
0.8 x Earth - 5914 km - 12 billion years
0.9 x Earth - 6151 km - 12 billion years
1.0 x Earth - 6371 km - 11 billion years

So it appears a small planet around a type K0 star could retain a short rotation period for a long time.

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According to the same method I used in my previous post, the distance between the bodies has a tremendous influence on the length of time to become tidal locked. I used a planet 8 times Earth mass and a satellite the size and mass of Mars. As before I used an intial period of 12 hours and Q=100. Here is what I got:

Semimajor axis - Tidal lock time

500,000 km - 470 thousand years
1,000,000 km - 30 million years
1,500,000 km - 340 million years
2,000,000 km - 1.9 billion years
2,500,000 km - 7.3 billion years
3,000,000 km - 22 billion years
3,500,000 km - 55 billion years

I don't know how old you want your system to be, but if it is anything like Earth-age, it looks like you're going to need a semi-major axis of about 2.5 million kilometers or more to keep from being tidal locked. I don't think this will be a stable orbit. I tried entering this scenario in Gravity Simulator using a 0.9 Sun-mass star, a star-planet semimajor axis of 0.83 AU, and a planet-moon semimajor axis of 2,500,000 km. The moon almost immediately broken out of planet-centered orbit and went into a star-centered orbit.

It seems that to have a stable orbit you will almost certainly have to settle on having the moon tidal locked to the planet.

The formula in this web page is described as estimating the tidal lock time for a small body to a large one. I don't know if you if you can use the formula to estimate the reverse, i.e. the tidal lock time for the larger body to the smaller. I have, however, used to formula to calculate this and I get following:

Semimajor axis - Tidal lock time

500,000 km - 650 million years
600,000 km - 1.9 billion years
700,000 km - 4.9 billion years
800,000 km - 11 billion years
900,000 km - 22 billion years
1,000,000 km - 42 billion years

If using the formula in this way is valid, then it seems to indicate that an orbit over about 700,000 km may result in the planet not being tidal locked to the satellite. Furthermore, I entered a 1,000,000 km orbit into Gravity Simulator and it appeared to be stable, although I ran the simulation for only about 50 years.

In conclusion, I think to have your moon in a stable orbit it must be close enough to the planet that it will most probably be tidal locked. If you want your planet not to be tidal locked to the satellite, the satellite will probably have to be at least 700,000 km or so away from the planet. I think I'd set the range at about 750,000 to 1,000,000 km.

Interestingly, it looks like I can also use the formula to estimate the planet's period of rotation as a function of time. If the semi-major axis is 800,000 km and the initial rotation period is 12 hours, the planet's rotation period over time is:

Initial - 12 hours
After 1 billion years - 13 hours
After 2 billion years - 15 hours
After 3 billion years - 17 hours
After 4 billion years - 19 hours
After 5 billion years - 22 hours
After 6 billion years - 27 hours
After 7 billion years - 34 hours
After 8 billion years - 45 hours
After 9 billion years - 69 hours
After 10 billion years - 147 hours
After 11 billion years - 28.95 days (tidal locked to satellite's period)

Of course, as the planet slows down, the satellite moves away to conserve angular momentum. The formula used doesn't seem to have a provision for the changing semi-major axis. I'll probably have to integrate the problem over time, assuming a closer initial orbit and then increase the semi-major axis according to conservation of angular moment as the rotation periods decrease. I don't have anymore time to work on this today, but I'd like to continue later when I get the chance.

Something I need to know to have a target to shoot at is the age of the system. How old do you want this planetary system to be? Also, do you have a preference for the duration of the planet's day?

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Wow! I really appreciate all the calculations Bob B., all that info gives me a lot of things to consider.

I was thinking 5 billion years for the age of the solar system. As for the duration of the planet or moon's day, I don't really have a set figure in mind, as long as it is not horrendously long, like 75+ hours or anything.

For the star type I'd like to go with the high mass (0.9 x Sun) K0 star.

Which in your opinion would be better for the planet and moon to sustain Earth like atmosphere's:

1. Keep the planet and moon sizes as they are with them tidelocked to one another.

or

2. Decreases the planet's size a bit so that the planet and moon actually orbit a common center of gravity, like Pluto and Charon do.

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"True genius shudders at incompleteness, and usually prefers silence to saying something which is not everything it should be." - Edgar Allen Poe

This is nowise obvious. Where do you see any signs of recent hermeologic activity? And Mercury is slowly spinning, and tidelocked - yet possesses a nice hermeomagnetic field.

Note that despite having less gravity, Mercury is nearly as dense as Earth, so intrinsically denser. The surface acceleration of Mercury is equal to that of Mars although it is far smaller.

Suppose that you had a body the size of Mars, and with intrinsic density of Mercury, so denser than Mercury or Earth. It would have stronger gravity and higher escape speed than Mars, so it would have greater escape speed, and could hold a dense atmosphere in habitable zone...

I'm going to try working on this problem later today after I get home. I think I can set it up in a spreadsheet so I can advance the simulation in small time increments. This should allow me to factor in the changing semi-major axis. I'll see if I can find a set of initial conditions that evolves over time to yield the conditions you stipulate above.

I don't know if I can get this completed in one day. It may run into the weekend.


I think a 0.9 x Sun mass star will be G type. According to the information I've seen, K stars are about 0.5 to 0.8 x Sun and G stars are about 0.8 to 1.1 x Sun. A 0.9 x Sun star will probably be about a G5 or G6. The Sun is a G2.


I'm no expert on atmospheres so I really can't give much advise here. However, technically the planet and moon will orbit a common center of gravity no matter how big they are. It's possible, however, that the center of gravity lies within the body of the larger mass. In your case -- planet diameter = 2 X Earth, planet mass = 8 X Earth, and satellite mass = 1 X Mars -- the break even point is a semi-major axis of about 961,500 km. Less than this number and the COG lies within the planet. Of course, as you say, decreasing the mass of the planet will move the COG closer to the satellite.

If I can get this spreadsheet idea working, I should be able to experiment with a whole bunch of different scenarios. Ideally, I'll be able to enter the size and mass of the bodies, their initial rotation periods, and the initial distance between them. Hopefully at that point the spreadsheet will give the changing conditions over a series of time steps so I can see how the system evolves. I'll probably be able work with only two bodies at a time, i.e. star-planet or planet-moon. I think it is too mathematically challenging at this point to try to factor more than two bodies.

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Interesting stuff. One thing that hasn't been mentioned is changing the initial spin rate of the planet/moon. If you use 12 hours, then you will get tide locked fairly quickly.

The Earth, for instance, seems to have had an initial spin rate of just 6 hours, which gives it more time before becoming tidally locked. Try using 4, 3, or 2 hours initial spin rate and you'll see you can make them spin freely for a lot longer, without changing any other parameters.

Bob B., I'd be really interested to see this spreadsheet you're working on, it would certainly save a whole lot of calculating.

BTW there is another formula for Tide locking that I think is better. It was discussed in this thread: Tidal Locking, need to understand it (see page 2 for the formula provided by EDG). You might want to use that formula for your spreadsheet, instead of the one on Wiki.

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I'd certainly be happy to share it, assuming I can get it working.

Is this the following the formula you're referring to?

I don't know how this formula compares to the results of the Wiki formula, but I think I like it better. Having the result in dW/dt certainly lends itself better to what I want to accomplish with the spreadsheet.

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Yeah that's the one. It seems to be compatible with the Formula from Wiki, but it gives exactly twice the answer of the Wiki one, we couldn't quite figure out why though. Other then an arbitrary decision on the part of the creators not to place a "divide by 2" sign on it.

I have it written down like this, in a more complete form. You probably won't need this, but I'll put it up for others wishing to use it (at least I think this is the complete form, I may have made some mistake).

dW/dt = (9/4) [(G.Ms^2.R^3)/(a.Mp.Q'p.A^6)]

dW/dt = Decrease in rotational angular velocity (radians per second)
G = Gravitational constant
Ms = Mass of star (kg)
Mp = Mass of planet (kg)
R = Radius of planet (m)
a = Moment of inertia factor of planet (0.3 - 0.4)
g = Surface gravity of the Planet (m/s^2)
u = Rigidity of the Planet (Nm-2)
p = Density of the Planet (kg/m^3)
Q = Dissipation function of the Planet
Q'p = Q*(1 + (19.u/2.g.p.R))
A = Semimajor axis of planet (m)

wi = Initial Spin rate (radians per second)
wf = Final Spin rate (radians per second)
t = Age of the system (seconds)
oP = Orbital Period (seconds) (Year length)
rP = Rotational Period (seconds) (Day length)
tlock = Time taken to become Tidally Locked (seconds)

To calculate tidal locking time...

tlock = (wi - (2*pi/oP))/(dw/dt)

To calculate the day length, given the age of the system (if tidally locked, day length will be same as orbital period)...

wf = wi - (dw/dt * t)
rP = 2*pi/wf

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Do not mess with distances and Gravity Simulator at this step! Just estimate the constraints on orbital periods.

First, the so-called Hill radius. Moon orbits the Earth in 1/13 of year. The outer retrograde satellites of Jupiter have considerably smaller ratio of satellite to primary orbit, but those are inclined and eccentric orbits of questionable stability. 1/13 is a comfortably safe ratio.

Now estimate the orbital period of planet. For K0, 0,45 solar luminosities and 0,9 solar masses, I get a period of about 0,58 years. Slightly shorter than Venus, which is not tidelocked. So, the planet would not tidelock to the star.

Keeping the same Hill sphere safety margin, you could comfortably get a satellite at 16 day orbit. But this is close enough to tidelock. Moon, at 27 days, is tidelocked. Mercury, at 88 days, is tidelocked (but in 3:2 lock). Iapetus, at 79 days, is tidelocked. However, Hyperion, at 21 days, is not tidelocked.