Scale of Pandora

[pukapa nari]

...
Those data allow us to estimate the orbit period of Polyphemus to about 490 earth days:
Orbital radius                 r ~1.875 *10¹¹ m (inhabitable zone)
Solar Mass ACA             M ~2.19 *10³⁰ kg
Gravitational constant    G = 6.67428 *10^-11 m³ kg^-1 s^-2

   t_orbit = SQRT(4 * π² * r³ / G * M)
          = 42213845 s
          = 489 earth days
          = 1.34 earth years

That is the time in which Polyphemus rounds it's sun and most likely also the length of a Pandoran year

Kaltxì ma Tsu'roen
You forgot the mass of Polyphemus!
The formula is :  torbit = SQRT(4 * π² * r³ / G * (M+m))

I took the volume close to Saturn and a density between Saturn and Jupiter ...
so I got a mass for Polyphemus of 8,015 * 10²⁶ kg
I come up to a  Polyphemus-year of 476 days ...

Several of Polyphemus' moons have a diameter larger than 6437 km (ASG p14)

Diameter of Pandora (11447 km) is more than 6437 too ...

but what is more ... if you have mass of Pandora and Polyphemus, you just need the radius of Pandora's orbit to
calculate the time, Pandora needs for one turn arround Polyphemus...

we cannot place Pandora too close to Polyphemus, but also not too far from it, for it's mass is not a little and it may
drift away from Polyphemus!!
I think a radius bigger than 1 * 10⁶km seems to far as soon as it would be more than 0.5% of the distance
Polyphemus - ACA though Polyphemus' diameter allready is more than 15% of that orbit ...
As you know, it takes a "week" for Pandora to pass Polyphemus' shadowside ... so the nearer we place Pandora to
Polyphemus, the faster it goes and the shorter is the period for the whole circulation ... and also of the rotation of
Pandora itself   

At that radius of 1 * 10⁶km you get 10 earth days for Pandora to orbit Polyphemus ...

Now have a closer look to the diameter of that orbit and the diameter of Polyphemus ...
When Pandora rotating along the night side of Polyphemus, it takes a week (7 days) ... means seven times the expression
of day and night ...
So we can say:  Pandora is rotating 7 times in this period ...
Now lenght of the orbit is  π*r² ... = 6.280.000 km
Polyphemus' shadow is nearly his diameter ... ~115.000 km
as you see, that this period is less than 2% of the whole period to orbit Polyphemus
so if Pandora rotates 7 times at the night side of Polyphemus it has to rotate more than 380 time while orbiting Polyphemus ...
this means that one rotation takes 10 earth days / 380 times = ~38 earth minutes ...!!

So: on Pandora 19 minutes daytime and 19 minutes nighttime !! 

I really wonder why Grace thought Jake cannot make that one night in the jungle ...
19 minutes is quite short

Conclusion: There is a mistake in the perfect universe of Cameron ... unfortunately 

Everyone can check out this things on internet - Cameron has so many professionals, why didn't he
solved this problem a little better :s

The easiest may be, to place Polyphemus outside the (us known) inhabitable zone ... as soon as NASA also is
thinking of life existing out of the inhabitable zone in our solarsystem ... (eg. on Europa, a moon of Jupiter)

[Tsa'räni]

You make a lot of assumptions and at least some of them are wrong.  To start with, using your numbers, the hill sphere for Polyphemus is going to be something like 7.4 * 10^6 km.  That means an acceptable orbital distance of Pandora around Polyphemus can be, at most, 7.4x your estimated max number.  And that's going to make a large difference in your calculations.

I don't have time to look over the rest of it, or adjust for that mistake, but I'm guessing Cameron and his astrophysicists have this figured out to a reasonable level.

Edit - This is an extremely simple way to look at hill spheres, as there are plenty of other factors that come into play.  But it's accurate enough to show one of problems in your calculations.

[pukapa nari]

I don't think that my calculation is such wrong ...
The only assumption is the distance between Pandora and Polyphemus and the density of
Polyphemus, 'cause there is nothing said about it ...
but these two assumptions will be close enough, for it was derive from dimensions of that
mentioned planets and their moons !!

other numbers are all from Cameron's wikia or wikipedia.org !!

You said yourself the orbital radius of Polyphemus is 187.000.000 km (I had same results)
If the hill sphere for Polyphemus is 7.4 * 10^6 km, it would be 4% of it's orbital radius ... quite a lot 

The moons in our solar-system all are smaller then Pandora too... it is even bigger then Mars or Mercur !!
And there still are another 13 moons arround Polyphemus ! 

It is also said in the ASG that "Pandora rotating along the night side of Polyphemus within a week" !!
If this was really a long time, Pandoras orbital radius would exceed those 7.4 * 10^6 km too!
... for if it is  7.4 * 10^6 km, on Pandora-day would last 100 earth-minutes ...!!

still very less


Maybe the only mistake Cameron made, is not to tell about the Pandora day and years ...
If he told it, maybe noone would proof it, if it's right or not ...

[Tsa'räni]

Well, you can't debate a hill sphere calculation with hunches.  It is what it is, and the hill sphere radius for what you listed is what I gave.  That's just how it is.  An acceptable orbit would extend out to 7.4 * 10^6 km without leaving Polyphemus' influence.

Now, since I have a little more time, if you can point me to the place in the ASG where it talks about orbiting through Polyphemus' night side in week, I'll address the rest of your points.

I'm sorry, but there just isn't much basis for what you're claiming as far as I can see.

Edit - And I used Earth's semi-major axis for the orbital distance, which is just under 150 million km.  If I used your 187 million km, the hill sphere would be even larger, though only by a bit.

Edit 2 - And also, using the wiki or anything like that, which takes heavily from the "official" game, is shaky ground at best.  The game has so many mistakes that I don't think anything in there can be trusted.  The Na'vi don't even seem to have queues.

[Tsa'räni]

Instead of editing the post again, I'll make another.  I've found where you're getting this information, but it's not in the ASG.

http://james-camerons-avatar.wikia.com/wiki/Polyphemus

Now, even though the source at the bottom doesn't list the official game, I'd bet anything it comes from there.  Because there is nothing like this quote in the ASG...

"Pandora resides just outside the main radiation belts of Polyphemus, except for a week, when rotating along the night side of Polyphemus."

To start with, this sentence does not necessarily mean it only takes a week to pass through Polyphemus' shadow.  It could actually mean several things - the sentence is vague, at best.  And second, as I mentioned in the other post, this does not come from the ASG.  I'd bet anything it comes from the game, and in a game where Na'vi don't have queues, any new information is suspect.

So it's really much ado about nothing.

[pukapa nari]

Edit - And I used Earth's semi-major axis for the orbital distance, which is just under 150 million km.  If I used your 187 million km, the hill sphere would be even larger, though only by a bit.

Ok, Earth's semi-major axis for the orbital distance is under 150 million km... that's in the so called inhabitable zone...
But for ACA you needed 150 million km * 1.25 'cause ACA is brigther than our sun...
isn't it ?  (look at some posts from others above)

Edit 2 - And also, using the wiki or anything like that, which takes heavily from the "official" game, is shaky ground at best.  The game has so many mistakes that I don't think anything in there can be trusted.  The Na'vi don't even seem to have queues.

I have no game at all but I may ask then: why do they mix all the data thogether on Camerons wikia

[Tsa'räni]

150 million or 187 million km - it doesn't really matter.  I stated I used 150 million for clarity.  In the ASG it states the orbit of Polyphemus around ACA is similar to that of Earths.  The point is pretty much moot unless you want to grind out details, which this isn't about.

As for the wikia, it's not "Cameron's" as far as I know.  Anyone can edit that site.  It's a group of people that have attempted to compile all available information into once place.  Sadly, they don't seem to get that you can't trust a game that has so many glaring errors compared to the movie that many fans simply turn away in disgust.  In fact, we're not even sure we can trust all the info in the ASG, because there appear to be some errors there.

In the end, even that is a moot point.  You're basing all this off a sentence (the one I quoted) that is very vague.  It doesn't necessarily mean it takes one week to pass through Polyphemus' shadow.

[Roiki]

When Pandora rotating along the night side of Polyphemus, it takes a week (7 days) ... means seven times the expression
of day and night ...
So we can say:  Pandora is rotating 7 times in this period ...
Now lenght of the orbit is  π*r² ... = 6.280.000 km
Polyphemus' shadow is nearly his diameter ... ~115.000 km
as you see, that this period is less than 2% of the whole period to orbit Polyphemus
so if Pandora rotates 7 times at the night side of Polyphemus it has to rotate more than 380 time while orbiting Polyphemus ...
this means that one rotation takes 10 earth days / 380 times = ~38 earth minutes ...!!

So: on Pandora 19 minutes daytime and 19 minutes nighttime !!  

I don't really know how you came up with this, but if it were to make one orbit in 36 minutes, it would have to move at speeds of over 2700km/sec, and that's just no possible.

With that orbital length and using saturns mass as the mass of polyphemus and radius of 1,000,000 km, it's orbital speed would be 6.16km/sec making one orbit the length of 283 hours, or about 12 days. Since pandora is tidally locked, this would be the orbital time around it's own axis as well.

Granted there is lots of assumptions, but that's all we have to go now, the possible semi-major axis of pandora can be somewhat hypothesized, this image reminded me of Titans orbit, which is 1,2 million kilometers, and it has an atmosphere. If it were closer than 400 000 km, tidal heating would most likely render the planet heavily volcanic(like is the case with Io).

[Tsa'räni]

Since pandora is tidally locked, this would be the orbital time around it's own axis as well.

Do you have a source for that?  I once thought I'd read it was tidally locked, but have since been unable to find anything saying that (meaning it's not in the ASG as far as I can tell).

[Roiki]

It's not stated anywhere, but it's an observed astronomical phenomenon and gravitational effect. Even our moon is tidally locked to earth, so is every other moon in our solar system. The gravitational effects of the parent body over time causes the orbiter to decelerate until its own rotation is equal to it's rotation around the body that it orbits around. More can be found here.

If pandora for some reason or another wasn't tidally locked, it would seriously challenge the natural laws in avatars universe, throwing them out the window. But again, absence of proof isn't proof of absence.

[Tsa'räni]

Yeah, I know what tidal locking is.  There are mechanisms that could prevent the moon from being currently tidal locked.  This debate was had a while ago and we settled on either being possible with the given information.

[Roiki]

From the top of my head i can't remember that discussion, i have to look it up.

Still i can't think of a single plausible reason why it wouldn't be tidally locked, since their size diffenrece is considerable the gravitational forces of the parent would induce tidal locking inevitably.

[pukapa nari]

@Roiki:
I never said, Pandora orbits Polyphemus in 36 minutes ...
The result in my post was, that Pandora rotates one time in 38 minutes but orbits Polyphemus
in ~10 earth days ...

When Pandora is tidally locked, it cannot take one week rotating along the night side of
Polyphemus, for there is no impression of day and night while that period ...
So this would be totally contradictorily!!!

But anyway ... as the data form Camerons wikia is contradictorily, you never will be able
to find out the "truth" ...


 

[Eric Vanasse]

http://www.pandorapedia.com/   when you click on this link it shows a welcome video which explains stuff about pandora and such, but at 36-37 seconds it quickley show the ACA (alpha centuari A) the biggest star in the 3 star system (which houses the solar system where pandora is). it shows the star and the orbiting planets, if you pause it at the right time, you should be able to get a good view of the solar system that you are asking fro, also from what i have read Pandora is roughly 3/4 the size of earth which makes sense considering the lower gravity. i hope the video helps

[pukapa nari]

Ma Eric,

that picture is too small ... you only see Alpha Centuari A, Polyphemus and three or for other
Planets, orbiting ACA ...
You also see some circles ans tiny moons arround Polyphemus, but they don't move at all ...
really very strange, for they do have to move quite fast, as it looks like a time-lapse!!
(see how fast the other planets move) ...

really pitty contradictorily, ... :s
 

[Muzer]

http://www.pandorapedia.com/   when you click on this link it shows a welcome video which explains stuff about pandora and such, but at 36-37 seconds it quickley show the ACA (alpha centuari A) the biggest star in the 3 star system (which houses the solar system where pandora is). it shows the star and the orbiting planets, if you pause it at the right time, you should be able to get a good view of the solar system that you are asking fro, also from what i have read Pandora is roughly 3/4 the size of earth which makes sense considering the lower gravity. i hope the video helps

I read somewhere (don't remember where) that gravity on Pandora is about 0.8G (though I may have mis-remembered this), so assuming masses are approximately the same, you can see it would have 0.8 times the volume of the earth (that's if mass and gravitational field strength are proportional - are they? I don't know). Then you could probably use the formula for the volume of a sphere to find out approximately the diameter.

[Nìwotxkrr Tìyawn]

Mass and gravity are proportional. Mass and volume are not proportional, so you can't find out volume nor diameter based on mass unless you know the average density of the planet.

[Muzer]

Yeah - how likely is it that Pandora and the Earth have approximately the same density?

[Nìwotxkrr Tìyawn]

Especially with all that unobtainium.