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Flight Incorporated has just recently posted these advertisements:

Buying Fuel for High Prices!

Buying fuel for our spaceships
Fuel in possession/fuel needed in gallons: $\Delta = 1000/\infty$
Current Bank Balance: $100,000,000,000.00

Required Balance = $\infty$ as fuel required is infinite
We will pay 1 gram of AN:92 per gallon of fuel.


Oxygen needed!

We need compressors... and oxygen tanks! You will be paid in brass-plated troughs with your name on a plate. Under the plating is a layer of plastic. Engraved on the bottom is our company name and logo.


The following was posted on Flight Inc.'s website.

Pilot's Guide

Remember to strap in your seat belts! Mass and speed increase simultaneously. Time is dilated. Communications will be offline, as no form of communication travels fast enough. Prepare for a breathtaking tunnel view.
Time to destination is: $cyears=year$
$C$ is the undisputable speed limit, proposed by the maker of $e=mc^2$ What we're doing is impossible, but that's never stopped us!


Technical Guide

Classical engine runs off of hydrogen. Liquid fueled rocket needs two tanks for propellant and oxidizer. System cannot be distorted by mass increase.

What do they need the fuel for and what are they being paid in?

Note: No knowledge of science fiction is required to solve this. Tear every line apart :)

Trouble deciphering our ads?

AN is an abbreviation for something related to materials. (Atomic Number) Basic science knowledge is required. We don't buy from people who don't know science. We love the periodic table... Who cares about speed limits, even those universe-wide?


Hints

AN is an abbreviation for Atomic Number. This puzzle is related to Einstein, relativity, and classical physics. The speed that they are trying to go to (or near it) does weird things to a spacecraft.

Huge Spoiler:

They are trying to travel at the speed of light. The oxygen is related to combustion and the hydrogen is the fuel.

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  • 5
    $\begingroup$ They need it for their spaceships, and one gallon sells for $c$. Easy game :-P $\endgroup$ – Joe Dec 5 '14 at 14:31
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    $\begingroup$ By the way, do you mean time is diluted or dilated? $\endgroup$ – Joe Dec 5 '14 at 14:35
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    $\begingroup$ @Joe That's part of the puzzle. $\endgroup$ – QuyNguyen2013 Dec 5 '14 at 18:43
  • $\begingroup$ "No knowledge of science fiction is required" - what about a knowledge of physics? $\endgroup$ – Rand al'Thor Dec 16 '14 at 15:43
  • $\begingroup$ @rand al'thor Yes $\endgroup$ – QuyNguyen2013 Dec 16 '14 at 16:31
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They are most probably

Going to attempt to reach the speed of light (almost)

Going by the start:

Buying fuels for high prices:

The $\Delta $is the ratio of the amount of fuel they currently have and the fuel they need (which is $\infty$, as stated), and they currently have 1000 gallons, which by their current bank balance costs $10^8$ dollars, which is the order of speed of light(which is $3*10^8$ m/s approx). As many have already pointed out, AN:92 refers to uranium, whose 1 g has approx $6.54*10^{21}$ atoms, which may be the price paid per 1 gallon of fuel.

Oxygen needed:

They need it...uh...to breath? Or to burn the fuel, probably. Your name plate may go in their wall of fame or something. Still not able to figure this one out.

Post on their website:

Pilots guide:

Increase of mass and speed refers to the increase of mass by a factor of $\gamma$ which is $ m=\frac{m_o}{\sqrt{1-\frac{v^2}{c^2}}}$ where $\gamma$ is equal to $\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. Time is also dilated by the factor of $\gamma$, which is called time dilation. Communications will of course be offline because no known means of communication is faster than speed of light. The tunnel view refers to the view which you will get from inside the spaceship. Everything will look so fast as if you are in a tunnel. The time to the destination $cyears=year$ also refers to Time dilation, and this could be used to take out the speed of the spaceship which they have designed currently (or they have made). Time dilation occurs by a factor of $\gamma$, so here $c=\gamma$. $\implies v=\sqrt{c^2-1}$, which is very close to the speed of light. This is the velocity of the spaceship by which you will travel. C is of course the speed of light, and the velocity is really high, and almost impossible to attain. And all of this was given by none other than the maker of the relation $e=mc^2$, Albert Einstein.

Technical guide:

Actual space exploration vehicles run by hydrogen fuel cells, which gets converted into water in the electrochemical reactions. The tanks maybe for storing this water. This is another reason as to why they need compressors and oxygen, to use these fuel cells for propulsion, as the fuel cells also need oxygen in the reactants side. Due to mass increase, they may need special tanks or something.

In short,

You are getting an opportunity to go to space by a huge amount of fuel and are going to reach the speed of light (roughly). Since the speed of the spacecraft will be so much ($\sqrt{c^2-1} $ is very near to c), the mass will increase, time will dilate and length will contract. In short, you might not even come back and see what they were gonna pay you with. Sounds fun, doesn't it?

It was quite easy ;)

P.S. How is all this basic knowledge of science? Relativity is really complex, and weird as well.

EDIT:

The oxygen and the compressors are required for combustion of the loads of fuel they are buying from you, as the O.P. has pointed it out.

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  • $\begingroup$ Can I know why I got a down vote? $\endgroup$ – Rohinb97 Apr 1 '15 at 8:31
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Answer:

They're planning to travel at infinite velocity (aka. warp ten). They're willing to pay the speed of light per gallon for fuel. I know this sounds a bit off, but read the explanation.

Because:

As some have theorized, infinite velocity would cause a vessel to exist at all points in space simultaneously. With infinite velocity comes infinite fuel consumption. As a fun side note, existing at all points in the universe at the same time means that all fuel in the universe would exist inside of the fuel tanks. This means that the trip would essentially use up all fuel in the universe and then still not have enough.

Where C comes in:

C in physics stands for the speed of light. This reinforces the fact that velocity will pay for fuel, the fuel grabbed from the entire known universe.

The only way it would work:

Since there isn't enough fuel in the known universe, other universes must be drained as well. In fact, infinite universes must be. Therefore, all fuel in the multiverse would be consumed, infinite mass would create a universal black hole, and the ship would be destroyed unless it was permanently transphasic and had a permanent energy source using energy that the engines can't.

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    $\begingroup$ Not sure. Travelling at speed c also stops time. So you have plenty of fuel but no time to burn it. $\endgroup$ – Florian F Dec 5 '14 at 14:58
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    $\begingroup$ @FlorianF "Burn the fuel!" // "We can't Captain, we have no time!" $\endgroup$ – Joe Dec 5 '14 at 15:05
  • $\begingroup$ Hmm... Time to ponder for sixteen hours, watch two specific star trek episodes, and edit my answer. $\endgroup$ – Travis Don Kindred Dec 5 '14 at 15:11
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    $\begingroup$ So, Uranium. Atomic Number 92. $\endgroup$ – Travis Don Kindred Dec 5 '14 at 20:54
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    $\begingroup$ I researched brass heavily thinking it was a weakpoint, but I got nothing. It may be time for another hint. $\endgroup$ – Travis Don Kindred Dec 10 '14 at 13:37
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Easy one ;)

The important point is the Pilots Guide:

The pilots guide referes to Albert Einstein and furthermore to the so called Einstein-Rosen-Bridge. These are theoretical one way traversable Wormholes. But to transfer you need near lightspeed -> you need near infinite amount of fuel to accelerate any mass to near lightspeed -> Time will be diluted and for the crew of the spaceship it will take VERY short to reach the other side.

Buying Fuel for High Prices!

As the need for infinite amount of fuel can only mean that the payment is much less worth than the fuel or consists of this fuel one possibility comes to mind. AN as the Acid Number. Ranges about 92 mg KOH means it is some kind of oil. If partial oxidation is used to get Hydrogen it is common to use some sort of oil for the process. So you gimme 1 Gallon of oil and I give you 1gram of oil. Good deal?

Oxygen needed! & Technical Guide

As burning an unlimited amount of fuel you need also a unlimited amount of oxygen. Payment will be plaquetes like http://en.wikipedia.org/wiki/Lunar_plaque as this is tradition for space adventures

So the answer is:

They are shooting someone through a wormhole and you get paid less than you invested.

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  • $\begingroup$ Everything but the fuel and the pilots guide is correct. $\endgroup$ – QuyNguyen2013 Dec 10 '14 at 21:00
  • $\begingroup$ Funny so the one true thing is the plaquet... I was mostly unsure about this. $\endgroup$ – EvilFonti Dec 11 '14 at 8:59
  • $\begingroup$ Just dropping some thoughts about the missing part AN may refer to Antimony, and 92 to Uranium. Apparently Antimony-Uranium oxide is some sort of potent catalyst for something. If nothing else at least Antimony has an interesting story about how it got its name. $\endgroup$ – dmg Dec 16 '14 at 20:44
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Most likely not the correct answer, but I had thought of

Uranium enrichment using lasers

Explanation

CO2 is the fuel for the laser (so oxygen is required) and the payment is enriched uranium (Atomic number 92). The pilots guide refers to lasers moving at the speed of light. The brass troughs refers to laser etching. Some lasers run on hydrogen fluoride instead. It doesn't answer why infinite fuel is needed though.

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Answer:

They're paying for fuel using Uranium in an attempt to have their spaceships reach the speed of light.

Explanation about the fuel:

AN:92 refers to atomic number 92, which is Uranium.

Explanation about what they need the fuel for:

The speed of light is the "undisputable speed limit" referred to in the pilot's guide. As you approach the speed of light, your kinetic energy ($\frac{1}{2}mv^2$) increases. According to $e=mc^2$ this energy also has mass, so as you approach the speed of light your mass increases (also mentioned in the pilot's guide).

The only part I'm not sure about:

The technical guide mentions that the "system cannot be distorted by mass increase". I'm not sure if this has any significance other than explaining that the spaceship won't break because of the increased mass.

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  • $\begingroup$ The mass thing refers to changing mass. $\endgroup$ – QuyNguyen2013 Feb 21 '15 at 1:05
  • $\begingroup$ What about the oxidizer ? $\endgroup$ – QuyNguyen2013 Feb 21 '15 at 19:21
  • $\begingroup$ @QuyNguyen2013 Is it more complicated than you need an oxidizer in order to burn fuel when you're in space? $\endgroup$ – Rob Watts Feb 21 '15 at 20:50
  • $\begingroup$ No, you got it. $\endgroup$ – QuyNguyen2013 Feb 22 '15 at 2:53
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I just think it could be a black hole.

This answer cannot explain many things, but it explains:

  1. oxygen "compressors"

  2. "tunnel view"

  3. Einstein and Relativity

  4. Supreme Time Dilation.

I cannot comment as my reputation is too low, but this question was interesting, and I decided to try...

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  • $\begingroup$ Sorry, no. How do you go the speed of a black hole? $\endgroup$ – QuyNguyen2013 Feb 22 '15 at 23:32

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