## Vocabulary

**• Carbon (C): **Element with a mass of 12 g/mole

**• Hydrogen (H): **Element with a mass of 1 g/mole

**• In-Situ Resource Utilization (ISRU): **Taking advantage of a planet’s natural resources to supplement a space mission

**• Low**** ****Mars**** ****Orbit**** ****(LMO):**** **The minimum altitude above the Martian surface necessary to maintain a stable orbit

**• Mars Ascent Vehicle (MAV): **A spacecraft that lands on Mars and is used by astronauts to get back into Martian orbit

**• Mole:**** **a standard of measure of the amount of a substance

**• Oxygen (O): **Element with a mass of 16 g/mole

**• Propellant**** ****Mixture**** ****Ratio:**** **The oxidizer to fuel ratio that makes up rocket propellant

**• Rocket**** ****Propellant:**** **The combination of rocket fuel and oxidizer used to propel a rocket forward

**• Sabatier**** ****Reaction:**** **the chemical reaction that turns hydrogen into rocket propellant

## Narrative

In the book, and now movie, “The Martian,” the protagonist is stranded on Mars with only a slim hope of rescue, assuming that he can science the –er– *heck *out of his situation. Without giving away too much of the plot, he uses an MAV to blast off from the surface of Mars into LMO. The only problem is that it landed with no return rocket propellant, and, therefore, the rocket fuel and oxidizer tanks are empty! There is a small amount of liquid hydrogen (H_{2}) rocket fuel on board, but it’s not enough to get back into orbit. So how did our intrepid astronaut S.T.E.M.–user manage to get back into orbit? The answer: by using methane as the rocket fuel. But where did the methane come from? That answer: In-Situ, Brutus?

The hydrogen is used along with the Sabatier Reaction to create rocket propellant and needs a lot of carbon dioxide (CO_{2}) to work. Since CO_{2}; is plentiful in the Martian atmosphere, methane (CH_{4}) and oxygen (O_{2}) can be extracted and used as rocket fuel and its oxidizer. We are literally making rocket propellant out of thin air! Methane is also an easier fuel to store for a longer duration than the standard fuel of liquid hydrogen used in most rockets. Now there is no need to bring along said propellant on missions, therefore, allowing for a larger cargo capacity to the Martian surface. Nice!

## Analysis

The ingenious chemical reaction that the MAV uses is as follows:

2*H _{2}* + 3

*CO*→

_{2}*CH*+ 2

_{4}*O*+ 2

_{2}*CO*

In English, the above translates to two hydrogen molecules plus three carbon dioxide molecules yield one methane molecule, two oxygen molecules, and two carbon monoxide molecules.

That’s a total of 4 hydrogen, 3 carbon, and 6 oxygen atoms on both sides of the equation. To make the math easier, we’ll use molar units and go with kilograms:

Hydrogen: 4 x 1 = 4 kg

Carbon: 3 x 12 = 36 kg

Oxygen: 6 x 16 = 96 kg

________________

Total: 136 kg

The amount of methane and oxygen produced is:

*CH _{4}* =

*C*+ 4

*H*= 12 + 4(1 )= 12 + 4 = 16

*kg*

and

2*O _{2}* =

*O*+

_{2}*O*= 2

_{2}*O*+ 2

*O*

*= 2(16) + 2(16) = 32 + 32 = 64*

*kg*

Therefore, for every 2 kg of hydrogen brought to Mars using ISRU techniques, 16 kg of methane and 64 kg of oxygen can be produced and stored for future use. This process reduces to 8 kg of CH_{4} and 32 kg of O_{2} for every kilogram of H_{4}:

1 *kg **H _{2}* → 8

*kg*

*CH*+ 32

_{4}*kg*

*O*

_{2}We now have a propellant generation equation.

## Example

The MAV uses 15,080 kg of propellant and a propellant mixture ratio of 2.77:1 to hurl itself into Martian orbit. How much hydrogen should the MAV bring?

First, we need to determine the proportion of methane and oxygen of the propellant.

*Fuel =* *P**ropellant / (Mixture Ratio + 1)*

*CH _{4}* = 15080 / (2.77 + 1) = 15080 / 3.77 = 4, 000

*kg*

and

*Oxidizer** *= *Propellant *− *Fuel*

*O _{2}* = 15080 − 4000 = 11, 080

*kg*

This now becomes a classic proportion problem where we set up two fractions that are equal to each other, then cross–multiply.

1 *kg** **H _{2}* / x

*= 8*

*kg*

*CH*4000

_{4} /*kg*

*CH*⇒ 8

_{4 }*x*= 4000 / 8 ⇒

*x*⇒

*x*

*= 500*

*kg*

*H*

_{2}The same kilogram of hydrogen also generates 32 kg of oxygen. The amount of oxygen generated therefore becomes:

(500)(32 *kg** **O _{2}*) = 16, 000

*kg*

*O*

_{2}Therefore, using our just–derived propellant generation equation:

500 *kg **H _{2}* → 4, 000

*kg*

*CH*+ 16, 000

_{4}*kg*

*O*

_{2}Since the rocket only needs 11,080 kg of oxygen, the difference can be used for breathing and other necessities.

## Conclusion

Generating and storing rocket propellant using ISRU is a nifty way of saving weight for any spacecraft that operates on the Martian surface and needs to blast off back into Martian orbit. In this case, not only do we get to make rocket fuel, but we get to make the very air that we breathe. Kinda takes your breath away, in a manner of speaking! Maybe there’s something to this in–situ stuff after all.

*For a more in-depth treatment of this high school project by Joe Maness & Rich Holtzin visit www.stemfortheclassroom.org.*