# Pandora (Borderlands): Is this planet possible?

LuckyStampede
I'm a big fan of the Borderlands series (Well, 2 and on, 1 was kinda meh), and as I understand it, the developers had astrophysics consultants to make the world work right. However, in the only interview I've found about the research, Anthony Burch (the head writer) gave an inaccurate description of the planet in-game. So here's what I have gathered about the nature of Pandora from in-game information and observation:

1) It has a highly eccentric orbit, giving it planet-wide seasons. Planetary summer lasts 3 earth years, planetary winter 7.

2) During perihelion summer, it is tidally locked to its star. We can tell this because the star is not in the sky during gameplay (more on that later). It may or may not be tidally locked during its aphelion winter, no evidence one way or the other so far.

3) Either way, the day side of the planet is almost the same each orbit, but may shift slightly over time.

4) The habitable zone does shift slightly over time, as one area that was a major shipping port is under deep freeze in this cycle (suggesting a trailing edge to the habitable zone), while another area that was tropical, wet, and had seas is a desert this cycle (suggesting a leading edge)

5) As noted, liquid water and a breathable atmosphere exist on this planet. However, the state of the water, and which areas are wet and dry zones, is not stable.

6) Gravity is slightly less. Not enough to cause atrophy on long-term residents, but enough so that a normal human who gets intense regular exercise can run faster and jump farther than they could on earth.

7) The planet has one moon, which is unusually large and/or close to the planet compared to our moon. The moon rotates and goes through phases rapidly. It is hard to get an accurate measure of the period (due to the fact that the game's time scale is off), but the rotation and phase shift are not in synch.

8) The habitable zone is relatively small due to these extreme conditions. The area the game takes place in is on the "night" side of the planet during perihelion, where it receives reflected light from the moon. The moon's phases act as a day/night cycle for the habitable zone, and presumably the amount of reflected light is one of the contributing factors to a region's climate.

9) Life exists on this planet, but in an extreme state befitting its extreme environment. Species are able to go dormant for very long periods of time (either by hibernation or dormant eggs). There are multiple successor species for when a different environment exists in a region, and any woody plants are invasive species.

That's all I got for now. If you need any more information, I can try to find it. It strikes me as plausible, if highly unlikely, but I don't know very much about the subject so I'd like some help if you can.

The issue most readily apparent here is that having both of either 1) a tidally locked planet & high-eccentricity orbit, or 2) a tidally locked planet (to the sun) & a large moon is pretty much impossible.

The first is impossible because a high-eccentricity orbit means that the planet would need to vary its rotational speed depending on where in the orbit it is at the moment.
The second is impossible because the planet would tidally-lock to the moon much, much faster than it would to the star, and this precludes simultaineous tidal-lock to the sun, unless the moon is very, very far. How far exactly would depend on other details of the sytem, but from what I remember when I calculated this for another guy, it may very well put the moon beyon the gravitational influence of the planet.
The only way it could work is if the moon were recently captured, but then it's unlikely to be in a nice circular orbit, and the capture would likely screw the habitability of the planet big time.

LuckyStampede

Anyway, so you mean those are impossible to have together, but merely unlikely to have separately? If that's the case, one my assumptions could be wrong. Would one of these scenarios work?

1) Pandora is only tidally locked when it's in perihelion summer. Its spin changes as it moves away from the star. As noted, the habitable zone shifts between summers, leaving some areas dry that were previously wet, and some areas that were subarctic completely frozen over.

2) Is it possible that the moon (called Elpis) has such rapid spin due to the change in tidal forces from the sun? Such as, when the planet moves away from the sun, it may become tidally locked, while when Pandora comes back to perihelion, the planet itself becomes tidally locked while the moon starts spinning rapidly?

Oh, also, I never said this part, but during the perihelion summer at least (when the games take place) the moon is also geosynchronous. I wish we had a view of everything during the winter so we could tell the difference.

I think it's worth noting that both the planet and the moon are very volcanically active. I'm not sure how this bit of info relates, but one side of the moon also seems to be far more active than the other. When that side comes into "night," you can see it's completely covered in glowing fault lines and volcanoes. Why would one side be more active than the other? Also, this apparently is not entirely a natural phenomenon, as both Pandora and Elpis have been subject to reckless core mining, resulting in an event called "The Crackening" on Elpis and smaller-scale increase in volcanic activity on Pandora. Though core mining increased volcanic activity, I think that its prevalence to begin with relates to the massive tidal forces both would have to be under.

Another thing worth noting I believe is that it was originally settled by humans during aphelion winter. It's actually more habitable (if inhospitable) to humans during that time. It's during the perihelion summer that things went bad for the original colonists. It's stated due to hostile fauna awakening, but I don't think things were doing very well on the side facing the sun either.

Oh, another thing I just noticed: The Pre-Sequel (yeah, that's a thing now) takes place on the moon itself, but it's during the aphelion winter. During this time, the planet and moon seem to have a mutual tidal lock, or at the very least, the moon doesn't spin anywhere near as fast as it does during the summer.

So, is any of this useful and make it more plausible? I also want to post several views of the sky from Pandora, and the biomes that exist there, which I will do in the next post

LuckyStampede
Here's a few images that might help.

Here you can see the volcanic activity clearly under a number of conditions. The H-shaped space station is, of course, not a natural feature, and though it is pretty dang big, it's apparent size and distance are both highly deceptive.

The "craters" are not actually natural features either, as this view from the station itself shows: The circular formations were left by an alien civilization that is now virtually extinct. They used Pandora and Elpis as a dumping ground for dangerous alien superweapons, including monstrous creatures that were sealed away in stasis. No telling what effect the aliens and monsters had on the planet's development, so it's probably best to assume no influence beyond what's readily apparent.

And here's a view of Pandora from Elpis

Finally, here's a view of the sky from different regions, and a brief rundown of the climate:

Never actually gets "day," only seems to ever be twilight. This is the region during the previous cycle (note lack of Helios Station). No telling what it looks like now.

A very strange biome. Very wet and swampy, clouds blanketing the sky most of the time. The sun is barely visible on the horizon, but looking in that direction at all it's blindingly bright, even through the cloud cover. The moon is...I need to reinstall it and check, but IIRC it's rarely visible and lower in the horizon than the previous biome. Also, much of it takes place in a vast cavern with a very high ceiling and the sunward side completely open. Waterfalls come from cracks in the ceiling.

Giant monster notwithstanding, this is the most hospitable biome observed. Subtropical with liquid seas. Presumably, what the desert looked like last cycle.

Completely dry desert region. Was coastal and tropical last cycle, now the oceans are dry. I thought I'd show two views so the hint of sun on one horizon and the location of the moon were both visible.

Finally, the moon in the arctic areas. Note how the sky is much dimmer even in lunar day than in the desert regions. Also, there seems to be an aurora here at night.

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DrStupid
1) It has a highly eccentric orbit, giving it planet-wide seasons. Planetary summer lasts 3 earth years, planetary winter 7.

2) During perihelion summer, it is tidally locked to its star. We can tell this because the star is not in the sky during gameplay (more on that later). It may or may not be tidally locked during its aphelion winter, no evidence one way or the other so far.

3) Either way, the day side of the planet is almost the same each orbit, but may shift slightly over time.

This is possible with n:1 resonance and an orbital eccentricity of 1-1/n.

LuckyStampede
Uhhh...kay. Sorry, not actually my field at all, I'm just a dabbler in...everything. When I took interest in this subject, I had to look up terminology to make sure I was using it right, so this goes WAY over my head. Can you define what that means using layman's terms, or direct me to a (preferably free, and not CPU-melting) program that would help me visualize it?

DrStupid
Can you define what that means using layman's terms

n:1 resonance means n-1 days per year and an orbital eccentricity is defined as

$e = \frac{{r_{\max } - r_{\min } }}{{r_{\max } + r_{\min } }}$

with the minimum distance from the central star rmin and the maximum distance rmax.

n=1 would be a tidal locked planet on a circular orbit.

n=2 results in one day per year and an orbital eccentricity of 1/2. That means the maximum distance from the central star is three times the minimum distance. This orbit looks like this:

http://tinyurl.com/p567wz9

LuckyStampede
n:1 resonance means n-1 days per year and an orbital eccentricity is defined as

$e = \frac{{r_{\max } - r_{\min } }}{{r_{\max } + r_{\min } }}$

with the minimum distance from the central star rmin and the maximum distance rmax.

n=1 would be a tidal locked planet on a circular orbit.

n=2 results in one day per year and an orbital eccentricity of 1/2. That means the maximum distance from the central star is three times the minimum distance. This orbit looks like this:

http://tinyurl.com/p567wz9

Neat! Thanks for the explanation. Is there any way to get the moon on there, and/or make the celestial bodies unrealistically larger so they're easier to see?

Also, are questions about the ecology and climate of Pandora more suited to another subforum?

LuckyStampede
And I just realized I have another question:

How does the moon have phases if:

1) The planet is tidally locked to the star

2) The moon is geostationary.

I don't know how that would work. Is it possible, then, that one of my base assumptions is completely wrong? After all, we only see a relatively tiny portion of the world. It could easily be just a polar region on a world with an extreme tilt, hence the appearance of a tidal lock (it is never explicitly stated in game, I'm going from observations). Still doesn't explain the rapid phases of the moon. An extreme axial wobble maybe? I'm at a loss.

Not about this scenario in particular, no. But lots of people post in the SF writing section of the forum wanting to design their solar systems with a degree of plausibility, so similar scenarios appear every now and then.

The man himself talks about his game here:
http://www.rockpapershotgun.com/2012/07/16/borderlands-2-interview/
I actually created the physics for the way the planet works, and the planet has this elliptical orbit around its star. The habitable side of the planet actually faces against the star, so you don’t actually see the sun, ever. Meanwhile the moon has this sort of geo-synchronous position in the sky, so it’s always in the same spot in the sky. The moon has a crazy fast rotation, it takes about 20 minutes for it to spin. One side of the moon is a furnace, like a nuclear furnace, where it’s reacting and it’s super-hot, and it splashes a lot of extra light onto the planet. On the other side it’s very cold and dark, and so when the moon spins, when the hot reactive side warms up the atmosphere and it gets hot, it feels lighter outside. When you get the cold side it’s not dark, because you’re getting the ambient light from the nearby star, but it gets dim, with a sort of cold feeling, and you can also see these beautiful auroras in the sky. From that particular position I hadn’t actually looked at the light cycle from the moon spinning, and I was checking that out, so that’s what I was doing down there.
Which means it's just not a setup that is possible. You can't have a planet locked to the star and the moon at the same time. The only way this could work is if the moon were in one of the lagrange points - L2 (http://en.wikipedia.org/wiki/Lagrangian_point). But this point is a)unstable and b)relatively far away, whereas the moon is very close c)exactly behind the planet (at least partially in the shadow).
The "phases", as you can see, are explained as not actual phases but differences in emissivity of lunar surface. The "radioactive" side supposedly providing light - which is another dodgy idea, as the light we can see on the pictures is of the white, stellar variety (blue sky, white colour items look white, etc.) whereas light from the glowing surface is at best reddish.
The point being, it looks like a made-up physics model that was never supposed to be accurate or feasible. That is, if the actual forces were modelled as well, it would all fall apart in a manner of days.

DrStupid
1) The planet is tidally locked to the star

The planet can't be tide-locked to the star. There is only a temporarily co-rotation in perihelion.

2) The moon is geostationary.

When I tried to calculate this I found an error in my previous result. The formula for resonance and orbital eccentricity should be

$n^2 = \frac{{1 + e}}{{\left( {1 - e} \right)^3 }}$

and therefore

$e = 1 - \frac{1}{n} \cdot \left( {\sqrt[3]{{\sqrt {n^2 + \frac{1}{{27}}} + n}} - \sqrt[3]{{\sqrt {n^2 + \frac{1}{{27}}} - n}}} \right)$

The distance of a geostationary moon would be

$D^3 = \frac{{m_p + m_m }}{{n^2 \cdot m_s }} \cdot a^3$

with

a = semi-major axis or the planetary orbit
mm, mp and ms = masses of the moon, planet and star as well as
n = ratio between sidereal year and day

A stable moon orbit must be at least within the minimum Hill sphere (in perihelion). With the common mass of moon and planet (in order to estimate the upper limit) this results in:

$D^3 = \frac{1}{{n^2 }}\frac{{m_p + m_m }}{{m_s }} \cdot a^3 = \frac{{\left( {1 - e} \right)^3 }}{{1 + e}}\frac{{m_p + m_m }}{{m_s }} \cdot a^3 < \frac{{m_p + m_m }}{{3 \cdot m_s }} \cdot a^3 \cdot \left( {1 - e} \right)^3$

As this would require e>2 there are no such orbits. The moon can't be geostationary.

LuckyStampede
Not about this scenario in particular, no. But lots of people post in the SF writing section of the forum wanting to design their solar systems with a degree of plausibility, so similar scenarios appear every now and then.

The man himself talks about his game here:
http://www.rockpapershotgun.com/2012/07/16/borderlands-2-interview/

Which means it's just not a setup that is possible. You can't have a planet locked to the star and the moon at the same time. The only way this could work is if the moon were in one of the lagrange points - L2 (http://en.wikipedia.org/wiki/Lagrangian_point). But this point is a)unstable and b)relatively far away, whereas the moon is very close c)exactly behind the planet (at least partially in the shadow).
The "phases", as you can see, are explained as not actual phases but differences in emissivity of lunar surface. The "radioactive" side supposedly providing light - which is another dodgy idea, as the light we can see on the pictures is of the white, stellar variety (blue sky, white colour items look white, etc.) whereas light from the glowing surface is at best reddish.
The point being, it looks like a made-up physics model that was never supposed to be accurate or feasible. That is, if the actual forces were modelled as well, it would all fall apart in a manner of days.

Well, I take that with a grain of salt because he's mainly in charge of plot and dialogue, and what he describes blatantly contradicts what we see in the game. There is a glowing side, but it's not the side that provides light, as the moon rotates far faster than it goes through its phases, and it goes through its phases very fast. It is slightly brighter when it's nighttime and the glowing side of the moon is facing the planet, but it's a small variation compared to the reflected light.

LuckyStampede
The planet can't be tide-locked to the star. There is only a temporarily co-rotation in perihelion.

When I tried to calculate this I found an error in my previous result. The formula for resonance and orbital eccentricity should be

$n^2 = \frac{{1 + e}}{{\left( {1 - e} \right)^3 }}$

and therefore

$e = 1 - \frac{1}{n} \cdot \left( {\sqrt[3]{{\sqrt {n^2 + \frac{1}{{27}}} + n}} - \sqrt[3]{{\sqrt {n^2 + \frac{1}{{27}}} - n}}} \right)$

The distance of a geostationary moon would be

$D^3 = \frac{{m_p + m_m }}{{n^2 \cdot m_s }} \cdot a^3$

with

a = semi-major axis or the planetary orbit
mm, mp and ms = masses of the moon, planet and star as well as
n = ratio between sidereal year and day

A stable moon orbit must be at least within the minimum Hill sphere (in perihelion). With the common mass of moon and planet (in order to estimate the upper limit) this results in:

$D^3 = \frac{1}{{n^2 }}\frac{{m_p + m_m }}{{m_s }} \cdot a^3 = \frac{{\left( {1 - e} \right)^3 }}{{1 + e}}\frac{{m_p + m_m }}{{m_s }} \cdot a^3 < \frac{{m_p + m_m }}{{3 \cdot m_s }} \cdot a^3 \cdot \left( {1 - e} \right)^3$

As this would require e>2 there are no such orbits. The moon can't be geostationary.

Thanks. Even though my eyes gloss over the equations and my brain just says "mathy mathy math" (creative writing major here), sounds legit. I don't think we've completely invalidated the idea yet, so let's assume that it's still plausible, I'm just wrong on some of my base assumptions.

What conditions could create the appearance of what I'm describing, over a relatively short time (a few days at most), and a relatively small geographical area?

DrStupid
What conditions could create the appearance of what I'm describing, over a relatively short time (a few days at most), and a relatively small geographical area?

Let's take a star like Vega, a planet like Venus and our Moon. This meets condition 6.
A planetary orbit with a perihelion of 4 AU and an aphelion of 8 AU would meet condition 1 and maybe 4, 5, 8 and 9.
A planetary rotation of 5 Earth-years would meed conditions 2 and 3.
A distance of 38000 km between moon and planet (and therefore 10 times the visual size of the moon and a "month" of 20 hours) meets condition 7.

This system looks like this: http://tinyurl.com/o8kros3

Do note, if that's not immediatelly apparent, that the above includes a moon that is not geosynchronous.

Is there any way to get the moon on there, and/or make the celestial bodies unrealistically larger so they're easier to see?
Have you heard of Celestia?
http://www.shatters.net/celestia/
It's a free planetarium software. You can create add-ons including creation of whole new systems. It's a bit of work to get one's head around, but nothing too hard. As a side effect you'll learn something about orbital parameters.