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Old 01-13-2011, 03:45 AM
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Default Routine ISVs en route to Pandora

I've been encountering different interpretations for how many ISVs are still en route to Pandora and at what rate they are arriving. Today, I finally got out a pen and paper (and Pandorapedia) to work it out. I thought I would share my results here to serve as a reference for others. If you disagree with any assumptions, calculations, or results, please share your thoughts here so that we can arrive at a consensus.

This is the page I used as my main reference. (I find Pandorapedia to be much more self-consistent and reasonable than the wiki):
ISV Venture Star | Pandorapedia: The Official Guide to Pandora | Own AVATAR on Blu-ray & DVD Now!

From the first paragraph, we know that the ISV Venture Star is part of a twelve-vehicle fleet that forms an "endlessly looping supply chain," meaning that at any moment in time, some ISVs are in transit to Pandora and some are in transit to Earth.

The ISVs currently en route to Pandora are just part of this "routine" supply loop; however, they cannot simply "turn around" when they receive word that circumstances at Hell's Gate have changed. They carry just enough fuel to allow them to decelerate from 0.7c when approaching Pandora. While in orbit, they must refuel in order to accelerate back up to 0.7c in the opposite direction. ("Power source" section.)

In order to calculate the rate at which ISVs are arriving, we must know the duration of the "endless supply loop" cycle. In the "Mission profile" and "mission duration" sections, we see that each leg of the round-trip is 6.75 earth-years long (in an inertial reference frame) and that there is also a 1-year loiter in orbit around Pandora.

In addition, I have chosen to assume that there would be a 1-year loiter in orbit around Earth as well. This is my own assumption; I can't find any references to how long ISVs remain in Earth's orbit. My reasoning is that the same considerations that necessitate a 1-year loiter around Pandora would also necessitate a similar loiter around Earth (getting people in and out of cryosleep, loading and unloading cargo, checking the vehicle and systems for damage, extra time to allow for a safety margin, etc). However, there's no reason that the Earth-loiter has to be exactly the same length as the Pandora-loiter.

**EDIT: The assumptions concerning the duration of the Earth-loiter have been revised. Please see post #22 for updated conclusions.**


Based on the chosen assumptions, however, the total duration of a complete cycle is 6.75 + 1 + 6.75 + 1 = 15.5 years.

If we further assume that the twelve ISVs are spaced equally throughout this cycle, each ship is ahead of the one behind it by (15.5 years) / (12 ships) = 1.29167 years (or 1 year, 3.5 months).

If you draw a diagram of the different phases of the cycle and how the ships are spaced throughout it, you'll see that at any given moment there is either 5 ships en route and 1 orbiting, or 6 ships en route and 0 orbiting (with the same being true for Earth, by symmetry). The first scenario is true 77% of the time; the second scenario is true 23% of the time.



I am going to make the assumption that the ISV Venture Star was a little over 3 months into its expected 1-year orbit when the big battle took place. Due to the forced evacuation, it probably leaves orbit ahead of schedule, unless it needs the entire year to refuel, or it's necessary to maintain some minimum distance from the ISV ahead of it. Regardless, the next ISV would be arriving about 1 year after the big battle. After that, four more ISVs will arrive at intervals of 1.29167 years (1 year, 3.5 months). The last “routine” ISV will arrive a little over 6 years after the battle.

Note that it's not logistically necessary for these ISVs to have any rendezvous with Pandora's surface at all. They can simply refuel and turn around, and refueling is accomplished using repurposed, unmanned Valkyries that act as automated gas harvesters, collecting hydrogen and deuterium from Polyphemus' upper atmosphere. Whether or not the personnel would try to shuttle down anyway is another question for a separate topic.

In summary, here are the assumptions I made in my calculations. (Asterisks indicate assumptions not found in Pandorapedia):
Quote:
1) There are 12 ISVs total, including the ISV Venture Star that brings Jake and Norm to Pandora.
2) The journey between Earth and Pandora takes 6.75 earth years (in an inertial reference frame).
3) Each ISV spends 1 year in orbit around Pandora during each round-trip.
4) Each ISV spends 1 year in orbit around Earth during each round-trip.*
5) The ISVs are spaced at equal time-intervals throughout the "endless supply loop." *
6) The ISV Venture Star is a little over 3 months into its expected 1-year loiter when the battle occurs.*
And here are my conclusions:
Quote:
1) There are five ISVs en route to Pandora during the events of the movie (not including the Venture Star).
2) Each ISV is 1 year, 3.5 months ahead of the one behind it.
3) The first ISV would arrive about a year after the battle.
4) The fifth ISV would arrive about 6 years after the battle.
Comments and criticisms are welcome!
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You came back
How do you make up after you've done the unforgivable? Jake and Neytiri have a conversation in the wake of Hometree's destruction, during their first real moment alone following his return as Toruk Makto.

The Last Train Home
Fourteen years after the war, a lone spaceship appears in the sky. The former members of the Avatar program watch its approach expecting the worst, fearing for their adopted home. Then the ship lands. And suddenly, nothing makes sense anymore.

Five seconds too late
This is a different kind of Jake/Neytiri romance, the story that would've unfolded had she been delayed for just five seconds while trying to reach him following the fight with Quaritch.

Last edited by Sothis; 01-27-2011 at 06:13 PM.
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