Creating a Sci-Fi World - Thea (Questions & Answers)

[MattRob]

I'm currently working on a sci-fi story, which largely revolves around a single world (which the current name for is Thea, you'll see why when I describe it...).

Okay, I understand I've got some hard questions, so I've cut them into 5 labeled sections. Any help is vastly appreciated! :)



#1. - Planetary formation and dynamics

This Thea is the moon of a gas giant, Salacia (Well, I say gas giant, though it has a significant rocky core)...
I had to stretch some numbers to get a desired effect, but I want to know if this is too unbelievable...
Parent Body Mass: 6 Earth mass
Thea mass: 0.295 Earth mass
Thea Orbital Semi-major axis: 2,187,982 km
Orbital period: 152 days

I realize it's a large orbit, for a very large moon. It's around Tau Ceti, a very old star system, so I wonder if an Earth-Moon sort of relationship wouldn't lead to this, except the body that hit Salacia to form Thea hit in such a way that the moon is in a higher orbit? Could this, coupled with the fact that it's retrograde orbit would slowly expand it's orbital altitude, plausibly lead to this extreme orbital altitude?





#2. - Orbital stability

Also, the Salacia-Thea system needs to orbit Tau Ceti at the outer range of the habitable zone. I'll do all the hard work of calculating gravitational strengths at different distances, but at what point is the moon orbiting so far out that the sun would make the orbit unstable?
(i.e., if 90% of the gravitational force a moon experiences is from the planet it orbits, it will most likely be stable. But if 99% of the gravitational force it feels comes from the star, wouldn't that de-stabalize it's orbit around the planet? If so, at what % does it's orbit start becoming unstable?)





#3. - relationship of pressure and density under compaction from gravity

This is probably the most interesting one:
the relationship in-between atmospheric density and pressure.
So, IIRC, I think human tolerance for atmospheric pressure is ~6 atm max...

Thea's gravity is 74.5 % G.

So if the atmosphere has 6x as much density at the surface, would it only have ~4.47x as much pressure?
(Because pressure comes from gravity compacting the air, is the relationship proportional or exponential?)




#4. - gasses under compaction of gravity.

And now orbital altitudes...

On Earth, ~140 km is the lower end of a safe orbit.
So... I need to know what the lower end of a safe orbit would be over Thea, and my question is; are my assumptions correct, close to correct, or just plain wrong?:
So, in order to get 6x as much atmospheric density at the surface, would I need 36x as much atmospheric mass, because air pressure trying to expand into space would resist the compacting force of gravity?
And so then, would the atmosphere stretch 6x higher because of the increased mass(Since 6 is the square root of 36)?
(setting the low orbit for Thea at 840 km)


#5. - aerodynamics...

Say, an aircraft has a stall speed of 212 mph on Earth (stall speed of shuttle), what would it's stall speed be on Thea, which has 6x as much atmospheric density, 0.745G, and 4.47x atmospheric pressure?

I'm thinking... Would it be:
212 * 0.745 / (0.5 * (6 + 4.47)) mph?
That is, I'm multiplying gravity in G's, and dividing the average of atmospheric pressure and density.



Big thanks to anyone that replies! It's quiet an undertaking!
And I'm sorry I couldn't explain why I'm making things certain ways, I think the idea may possibly be unique, so I don't want to give up trade secrets :P

Once again, many thanks to anyone who takes up the challenge!

 

[Travis_King]

First a question:

Is your character a scientist or cosmologist or astrophysicist who will be detailing the formation and phsyical characteristics of this world throughout the book? Does your story depend on the accurate calculation of orbital period and atmospheric density?

If you build a relatively plausible system, let the reader decide how the thing formed, or why the orbit is so high, or why low orbit is at 800km. Unless you are writing a science textbook, you shouldn't need this stuff. I mean, sure, you could have your character talk about theories as to why the system is the way it is, but you won't need any calculations unless you want to bore the reader.

But anyway:

1) Anything is possible with orbits, its just a matter of initial conditions. Let the reader make those up themselves; again, as long as it is plausible (i.e. you don't have a moon rolling on the surface of a planet!)

2) If it is orbiting a planet, it is primarily experiencing the gravitational pull of that planet. If it is in the habitable zone, it is not going to fly away or get sucked into the sun. The moon is being stabilized in orbit around the Earth. If the moon, a relatively large moon compared to Earth, can stay in a stable(ish) orbit around Earth which does not have the mass of a Gas Giant, then I think you are safe.

3) The pressure due to atmosphere:

The rest I think you are over thinking. But if you insist, just look up the equations for stall speed and and factor in your variables.

 

[DrStupid]

The system is not stable. Here are the parameters:

Thea:
Mass = 1.76233·10²⁴ kg
Semi-major axis = 2.187982·10⁹ m
Velocity = 1046 m/s

Salacia:
Mass = 3.5844·10²⁴ kg
Semi-major axis = 1.078·10¹¹ m
Velocity = 30797 m/s

Tau Ceti:
Mass = 1.532·10³⁰ kg

and here is the corresponding simulation:

http://tinyurl.com/6htfzg2

 

[Travis_King]

You put in the wrong parameters in your simulation.

Try This

Basically, your planet would orbit Salacia in the same plane at 1.2 million km with a slightly slower orbital velocity

edit: Cool applet though. I like it.

 

[DrStupid]

You put in the wrong parameters in your simulation.

Try This

Unfortunately the URL is read only. The program don't update it. Maybe I will change that some day but currently you would have to do this manually. The data format is:

http://www.drstupid.de/Newton.html?{Stepwidth},{Substeps},{Display Size},{Timer Delay};{Mass},{Sx},{Sy},{Sz},{Vx},{Vy},{Vz},{Name}[;{Mass},...]

Basically, your planet would orbit Salacia in the same plane at 1.2 million km with a slightly slower orbital velocity

Of course the orbit will be stabilized by reducing the Semi-major axis but the value of 2,187,982 km was given by MattRob. Changing it would result in another system.

 

[Travis_King]

Oh, good call.

try this

This is the best orbit I could make.

 

[DrStupid]

This is quite stable:


Thea orbiting Salacia with a semi-major axis of 1.6 Mill. km


But I think more than 2 Mill. km is impossible.

 

[MattRob]

First a question:

Is your character a scientist or cosmologist or astrophysicist who will be detailing the formation and phsyical characteristics of this world throughout the book? Does your story depend on the accurate calculation of orbital period and atmospheric density?

If you build a relatively plausible system, let the reader decide how the thing formed, or why the orbit is so high, or why low orbit is at 800km. Unless you are writing a science textbook, you shouldn't need this stuff. I mean, sure, you could have your character talk about theories as to why the system is the way it is, but you won't need any calculations unless you want to bore the reader.

So far, yes, a xenobiologist (which, after an interstellar colonization and decades of prospecting a second one on an exoplanet rich in oxygen, is a much larger field than it currently is :tongue: ). Though I definitely wouldn't want to put highly technical info such as this... Certain things will come up. Like for instance, the moon, Thea, is facelocked, and day length is a major point in the plot, so it will be known. From this, the reader will be able to know the orbital radius. The technically-minded one might think it a bit odd, work it out, then suddenly realize why some of the other characters said Thea is in an unusually high orbit... It is! ;)
(Then that reader will get a really captivating feeling, he'll suddenly become a lot more immersed in it all when it feels so real, and he knows that the writer knows what he's doing!)

Also, it helps the entire process along, makes things more tangible, and is just nice to know. For a well-written novel, the vast majority of the information isn't even written, but only supports the written pages.

You certainly have a good point though, too much technical info will kill a story very quickly, except for a very small audience.

But anyway:

1) Anything is possible with orbits, its just a matter of initial conditions. Let the reader make those up themselves; again, as long as it is plausible (i.e. you don't have a moon rolling on the surface of a planet!)

2) If it is orbiting a planet, it is primarily experiencing the gravitational pull of that planet. If it is in the habitable zone, it is not going to fly away or get sucked into the sun. The moon is being stabilized in orbit around the Earth. If the moon, a relatively large moon compared to Earth, can stay in a stable(ish) orbit around Earth which does not have the mass of a Gas Giant, then I think you are safe.

3) The pressure due to atmosphere:

The rest I think you are over thinking. But if you insist, just look up the equations for stall speed and and factor in your variables.

I've got the stall speed issue figured out...

1) A very good point, that I may actually use. Reality has a neat way of surprising scientists. In this case, astrophysicists. To have everything be "Realistic", would really be very unrealistic, because it's quiet rare that everything is just as we humans think it will be ;)

2) - mostly addressed by subsequent posts.

3) Incredibly helpful! Thank you, greatly!

The system is not stable. Here are the parameters:

Thea:
Mass = 1.76233·10²⁴ kg
Semi-major axis = 2.187982·10⁹ m
Velocity = 1046 m/s

Salacia:
Mass = 3.5844·10²⁴ kg
Semi-major axis = 1.078·10¹¹ m
Velocity = 30797 m/s

Tau Ceti:
Mass = 1.532·10³⁰ kg

and here is the corresponding simulation:

http://tinyurl.com/6htfzg2

That's not a cool applet.
That is an AWESOME applet.
Thank you for posting!

How did you decide on Salacia's SMA? It will need to be somewhat towards the outer region of the habitable zone, since the atmosphere is so thick... But not too far. I actually'd prefer the planet was more on the "hot" side, with the poles only a bit warmer than Earth's.

This is quite stable:


Thea orbiting Salacia with a semi-major axis of 1.6 Mill. km


But I think more than 2 Mill. km is impossible.

I increased Salacia's mass by 10x, that seems to work.

But in terms of keeping the orbital period as close to the original as possible... This is better.

 

[DrStupid]

How did you decide on Salacia's SMA?

${\rm SMA}_{{\rm Salacia}} = {\rm SMA}_{{\rm Earth}} \cdot \sqrt {\frac{{L_{TauCeti} }}{{L_{Sun} }}}$

It will need to be somewhat towards the outer region of the habitable zone

OK, with the above mentioned formula Salacia will be placed in the center of the habitable zone and according to http://astro.berkeley.edu/~kalas/disksite/library/kasting93a.pdf the outer edge of Sun's current habitable zone for earthlike planet might be up to 1.37 AU. That would be 1 AU for Tau Ceti. But the habitable zone shrinks with time and Tau Ceti is much older than Sun. On the other hand the evolution of the habitable zone of small stars only depends on the geology of the planet (see Werner von Bloh, Siegfried Franck, Christine Bounama, Hans-Joachim Schellnhuber: Maximum number of habitable planets at the time of Earth’s origin: New hints for panspermia? Origins of Life and Evolution of the Biosphere 33: 219 [2003]). As Thea is not a planet but a moon orbiting a heavy planet one could imagine that its geologically aging is delayed by the tidal forces of Salacia.

To cut to the chase it is very difficult to estimate the outer radius of the habitable zone of Tau Ceti. If you place Salacia and Thea in the center of the HZ you will be on the safe side.

since the atmosphere is so thick...

The surface temperature of a planet is mostly determined by the composition of the atmosphere and not by its thickness. But nevertheless it is a good idea to give Thea a thick atmosphere. As Thea has a slow rotational period there would be strong temperature differences between day and night. A thick atmosphere (and maybe much liquid water on the surface) might reduce these variations.

But not too far. I actually'd prefer the planet was more on the "hot" side, with the poles only a bit warmer than Earth's.

You may choose your favorite climate by varying the mount of greenhouse gases (especially by the carbon cycle) and as climate is very complex you do not need to explain it to the reader.

I increased Salacia's mass by 10x, that seems to work.

Now it is really a gas giant and not a gas dwarf or super-Earth only )

 

[tony873004]

I like your applet too. I just finished making our solar system:

http://www.drstupid.de/Newton.html?86400,40,8e12,0.04;1.98891691172467E+30,0,0,0,0,0,0,*Sun;3.30192458710471E+23,51133344656.0555,7108282382.821,-4106119172.87816,-16122.3350253907,50420.113009442,5599.66878886643,*Mercury;4.86862144253118E+24,-64473240745.1065,-87045921701.702,2518724678.89452,27897.55356446,-21007.5774723024,-1899.001972596,*Venus;5.97369125232006E+24,114558592141.443,-99301639200.8153,9079439.93210793,19037.4677206211,22406.1640142303,-1.26454804849274,*Earth;6.41863349674674E+23,-21596759703.7356,235621115182.237,5468398392.37033,-23214.1805545805,-153.422100113155,565.050858690756,*Mars;1.89900183351053E+27,679212531224.287,-316015739323.215,-13868380251.9134,5345.41396465112,12462.3353558017,-171.656675912955,*Jupiter;5.68603461771861E+26,-508899920462.921,-1407407100083.7,44661630023.3694,8569.21915105331,-3303.06514216686,-283.905117754286,*Saturn;8.68409661853903E+25,-2289161086511.92,1514715248709.31,35264570310.829,-3801.79263259362,-5988.22245966695,26.8062780801559,*Uranus;1.02456847416779E+26,3178795223134.61,3124935362413.42,-137614160267.487,-3836.39683223281,3919.99603303816,7.83094751917401,*Neptune;1.47086282036213E+22,5237767903888.93,-2756602006395.19,-1219991932208.19,2868.52150982362,3456.42397581264,-1196.55658675529,*Pluto;7.34777534869879E+22,114335458485.279,-99022096789.8218,16806039.3355042,18189.6530651192,21712.2215087267,-100.182648168635,*Moon;9.47157243163967E+20,-205053460566.022,323195520099.715,48388654987.2948,-15465.2923462682,-11047.5847559938,2486.43227941913,*Ceres;2.14309312931087E+20,218639790605.12,231449439137.69,-179815242692.363,-18157.5110993609,7828.1100712785,-3809.94720724681,*Pallas;2.66762641270863E+20,79063657883.4206,376147425878.87,-20660496023.4075,-17227.4015836272,3613.05225075037,1990.95310079199,*Vesta

 

[tony873004]

...at what % does it's orbit start becoming unstable?...

In a prograde direction, objects are stable out to about 1/3 of the way to the edge of the Hill Sphere. The Hill Sphere formula is:

r= a cuberoot (m/(3M))

So plug in your planet's semi-major axis (or better yet, its periastron value) for a, the planet's mass for m, and the star's mass for M. This gives you your Hill Sphere radius around the planet. Your moon, in a prograde orbit, will be stable out to about 1/3 of the distance. Here's an online calculator I made so you can play with this formula easily: http://orbitsimulator.com/formulas/hillsphere.html

 

[DrStupid]

I like your applet too. I just finished making our solar system:

http://www.drstupid.de/Newton.html?86400,40,8e12,0.04;1.98891691172467E+30,0,0,0,0,0,0,*Sun;3.30192458710471E+23,51133344656.0555,7108282382.821,-4106119172.87816,-16122.3350253907,50420.113009442,5599.66878886643,*Mercury;4.86862144253118E+24,-64473240745.1065,-87045921701.702,2518724678.89452,27897.55356446,-21007.5774723024,-1899.001972596,*Venus;5.97369125232006E+24,114558592141.443,-99301639200.8153,9079439.93210793,19037.4677206211,22406.1640142303,-1.26454804849274,*Earth;6.41863349674674E+23,-21596759703.7356,235621115182.237,5468398392.37033,-23214.1805545805,-153.422100113155,565.050858690756,*Mars;1.89900183351053E+27,679212531224.287,-316015739323.215,-13868380251.9134,5345.41396465112,12462.3353558017,-171.656675912955,*Jupiter;5.68603461771861E+26,-508899920462.921,-1407407100083.7,44661630023.3694,8569.21915105331,-3303.06514216686,-283.905117754286,*Saturn;8.68409661853903E+25,-2289161086511.92,1514715248709.31,35264570310.829,-3801.79263259362,-5988.22245966695,26.8062780801559,*Uranus;1.02456847416779E+26,3178795223134.61,3124935362413.42,-137614160267.487,-3836.39683223281,3919.99603303816,7.83094751917401,*Neptune;1.47086282036213E+22,5237767903888.93,-2756602006395.19,-1219991932208.19,2868.52150982362,3456.42397581264,-1196.55658675529,*Pluto;7.34777534869879E+22,114335458485.279,-99022096789.8218,16806039.3355042,18189.6530651192,21712.2215087267,-100.182648168635,*Moon;9.47157243163967E+20,-205053460566.022,323195520099.715,48388654987.2948,-15465.2923462682,-11047.5847559938,2486.43227941913,*Ceres;2.14309312931087E+20,218639790605.12,231449439137.69,-179815242692.363,-18157.5110993609,7828.1100712785,-3809.94720724681,*Pallas;2.66762641270863E+20,79063657883.4206,376147425878.87,-20660496023.4075,-17227.4015836272,3613.05225075037,1990.95310079199,*Vesta

I am surprised that the call works with that many bodies. Is there a limitation for the length of an URL?

By the way: It's not a Java Applet but simply JavaScript and HTML pseudo graphics. The numerical core (Runge-Kutta-Nyström) is located in http://www.drstupid.de/NewtonSimulation.html