Title: Final Project - Part 3
Course: ASTRON103: The Evolving Universe: Stars, Galaxies, and Cosmology (001) DHH SU18 > Section: Week 7

Hunt for a New Home

The time has come for us to begin making the steps to leave our beloved Earth. We must find a new planet around another star that can host a new colony of humans and life!

For this project, you will go through the steps of planning for a new exoplanet colony, starting from identifying an ideal stellar type, analyzing their light curves for transiting planets, determining properties of these planets to find a suitable Earth-like counterpart, and planning a journey of first explorers.

This project is slightly different from your previous two in that each week, you will have to complete and submit one new element. In total there will be 4 parts to this project spread out over 4 weeks.

Part 3

This part of the project is due at the end of Week 7 on Sunday, August 5th at 11:59PM.

By now, you should have hopefully identified 5 planets around 5 potential host stars for a new colony. Below, we have provided the actual planet parameters that make up these planets that should be close to the ones you found last week in Part 2.

This week, you will dive deeper into these planets and determine which one is best suited for a future colony of humans. To do so, you will need to determine what the habitable zone of each star is and see whether the planet lies within this zone.

Tasks

1. For each of the 5 star-planet systems, determine the inner and outer radius of the habitable zone.
  1. To do this, refer to the guide below that walks you through line of thinking needed to calculate this.
2. Submit your habitable zone inner and outer radius measurements analysis in the web form here.

Final Project - Part 3: Habitable Zone

Habitable Zone Guide:

We treat a star as if it were a perfect light radiator, a blackbody source, which is an idealized representation of how light is radiated by dense objects. We make this approximation because the amount of power radiated per unit area from a blackbody only depends on its temperature that we denote as T.

The radiated power per area (e.g., watts per square meter) of a blackbody can be written as power, P
P = σT^4

Where the Greek letter σ (lower case sigma) is a numerical constant that ensures the units come out properly, specifically the Stefan-Boltzmann Constant (refer to Astronomy Chapter 5.2).

If the temperature T is in units of Kelvins (K, 0 C (where water freezes) = 273 K) then the value of the constant σ is 5.7x10^-8 W m^-2 K^-4.

We can then determine the total power from a star (or its Luminosity) if we know the star's radius (R_star). We simply multiply our power from above with the surface area of the star:

L = P * 4 π R_star^2

The power falling on a meter^2 on the surface of a planet at a distance D from the star is

p = L/4πD^2 [watts/m2]

This just means the the power from the star is spread out evenly on the surface of a sphere with a radius equal to the distance of the star from the planet (D).

Equilibrium on the Planet:

A planet can also act as a blackbody - absorbing light from its host star and radiating away that energy as a blackbody.

The sunlight falls on the projected surface of the planet, which looks like a disk with radius R_pl (radius of the planet). Thus the area absorbing sunlight is just π R_pl^2, the area of a circle with the radius of the planet.

If the planet absorbed all of the sunlight then the Energy absorbed by the planet is

P_pl(abs)0 = (π R_pl^2)p = (π R_pl^2)( L/ 4πD^2) watts.

The fraction of sunlight reflected is given by the albedo that we give the symbol A. If all sunlight is absorbed then A=0 (none reflected) and A=1 is everything reflected. Planets typically have A of a few tenths, so for this project you will assume that A = 0.2

So corrected for this reflected light, we have the total power absorbed by the planet as our result above multiplied by (1 - albedo) or (1 - 0.2 = 0.8)

P_pl(abs) = (0.8) (π R_pl^2)( L/ 4πD^2) watts.

Just like with a star, the planet can now re-emit this energy out as a blackbody. To have equilibrium, or balance, the planet has to emit all the energy it absorbs.

P_pl(emit) = P_pl(abs)_ = (0.8) (π R_pl^2)( L/ 4πD^2) = σT_pl^4 (4π R_pl^2 )

We now have all the information we need to calculate the Temperature of a planet around a star at different distances from a star.

You can combine these formula above and solve for the distance to the star (D) after plugging in your various star and planet parameters and assuming the two limiting cases for the temperature of the planet (the boiling point of water - the inner radius; the freezing point of water - the outer radius).