# Introduction

Terraforming other planets is a long-standing human goal. With the ever-increasing threat of global nuclear warfare, the need for a back-up planet has become more real. Mars is a great candidate for terraforming due to its similarity to Earth and its relatively close proximity. Humans could effectively solve two problems at once by terraforming Mars using radioactive material. Our project will investigate the amount of energy needed to terraform Mars and to see if radioactive material can realistically provide that amount of energy.

Before bombarding Mars with nuclear weapons, we have to decide what terraforming would entail and what we would consider to be habitable conditions. We intend to addresses several key questions: What does “habitable” mean for a planet? And how much additional energy does Mars require to be habitable?

For the purposes of this project, we have decided to set a surface pressure of 1 bar and a surface temperature of 300 K +/- 50 K as our terraforming goals. An Earth-like surface pressure is important for the human body and most of our human technology and practices. Mars also has reduced gravity compared to Earth, so an increase in surface pressure would further help humans adjust to a terraformed Mars. We have a somewhat wide temperature range because humans have the technology to survive those temperatures. There are also accurate in situ temperature measurements from the various spacecraft at Mars, so we can more accurately discern the energy difference between Mars today and our Terra-Mars by using temperature as our benchmark.

We are using a very simplified model of Mars for our calculations. We are approximating Mars as a spherically symmetric, Earth-like terrestrial planet with a metal-rich core and a liquid mantle. We are assuming net heat flow moves radially outwards because the core is the hottest portion of the planet. The moment of inertia of Mars ($$I/MR^2$$ = 0.366) indicates that the interior Mars is less differentiated than Earth, so we can assume a constant density within each layer of our simplified model of Mars.

Figure 1: Diagram of our simplified model of Mars. The core has a radius of 1500 km, the mantle has a radius of 1830 km, and the crust has a radius of 3390 km.

# Atmosphere

Before delving into calculations, we had to make several key assumptions and determine our desired terraforming conditions. We assumed the atmosphere to be an isotropic ideal gas, and chose to fix the terraformed surface temperature at 300 K. Using our 1 bar surface pressure terraforming condition, the ideal gas law, and scale height equation, we calculated surface conditions for TerraMars and compared those values to Mars’s current surface conditions.

We also chose the chemical composition of our new TerrAtmosphere. Mars’s current atmosphere is 96% CO$$_2$$, so it would be unrealistic to make the surface air breathable to humans using water vapor alone. Since we are estimating the minimum amount of energy required to terraform Mars, we decided to fix our TerrAtmosphere goal and calculate the additional mass and energy needed to obtain our desired TerrAtmosphere composition of 70% C0$$_2$$, 26% H$$_2$$0 vapor, and 4% everything else, including nitrogen, oxygen, and argon. This is certainly a large amount of water vapor, but it would allow for precipitation and potentially conditions for the possibility of bringing terrestrial plants to Mars.

 Mars Today Terra Mars Atmospheric Chemical Composition $$^1$$ 96% CO$$_2$$, 1.93% Ar, 1.89% N$$_2$$, 0.145% O$$_2$$ $$^3$$ 70% CO$$_2$$, 26% H$$_2$$O vapor, 4% other Average Surface Pressure $$^1$$ 6.36 x 10$$^{-3}$$ bar $$^3$$ 1 bar Surface Atmosphere Density $$^1$$ 0.020 $$kg/m^3$$ $$^2$$ 2.025 $$kg/m^3$$ Surface Temperature $$^1$$ 210 K $$^3$$ 300 K Atmospheric Scale Height $$^1$$ 11.1 km $$^2$$ 13.3 km Temperature at one scale height $$^2$$ 182 K $$^2$$ 220 K Total Atmosphere Volume - $$^2$$ 1.9283 x 10$$^{18}$$ m$$^3$$ Total Atmosphere Mass $$^1$$ 2.5 x 10$$^{16}$$ kg $$^2$$ 3.905 x 10$$^{18}$$ kg

In the table above, the superscripts preceding each quantity indicates the source: $$^1$$ quantity from NASA Mars Fact Sheet, $$^2$$ quantity calculated by Sahana, $$^3$$ fixed terraforming condition.

Our terraformed atmosphere would be significantly more dense and thicker than Earth’s current atmosphere. The atmosphere of Mars would require an additional 3.8 x 10$$^{18}$$ kg of mass to reach our terraforming conditions. This amount of water vapor is slightly larger than the estimated total mass of the north polar ice cap. Terraforming the atmosphere of Mars will require vaporizing ice from both the north and south polar ice caps.

The subsurface conditions of these regions are not well understood, but the polar ice caps are composed primarily of water and CO$$_2$$ ice. We examined several topological models of the polar ice caps and visually estimated the amount of water ice available to vaporize at each pole. Of the 3.8 x 10$$^{18}$$ kg of water ice needed, we can theoretically obtain 1.74 x 10$$^{18}$$ kg of ice from the north pole and the remaining 2.13 x 10$$^{18}$$ kg of ice from the south pole.