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Blog

Finding a Habitable Exoplanet

1/21/2025

Comments

 
With the inclusion of Kepler's Laws in our new high school earth science standards as well as the new IB Physics curriculum, I was very interested in a practical investigation that students could interact with data in the same way that an astronomer would and apply these concepts to an authentic situation.

In looking through many different resources that are out there, I came across a cool framing from New Visions for Public Schools. This activity is a remix from a storylined investigation in their "Discovering New Worlds" unit.
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Finding a Habitable Planet (pdf)
File Size: 4528 kb
File Type: pdf
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Standards Covered:

​NGSS
ESS1.B: Earth and the Solar System
Kepler’s laws describe common features of the motions of orbiting objects, including their elliptical paths around the sun. Orbits may change due to the gravitational effects from, or collisions with, other objects in the solar system.

Minnesota | 9-12 Earth and Space Science
9E.2.2.1.1 Use mathematical and computational representations to predict the motion of natural and human-made objects that are in orbit in the solar system.
​Emphasis is on  Kepler’s laws of planetary motion and Newtonian gravitational laws governing orbital motions, which apply to human-made satellites as well as planets and moons.
In this activity, students are provided with data about 10 different exoplanets and their host stars to investigate and determine the best candidate for supporting life outside of Earth.

Background

The Circumstellar Habitable Zone (CHZ) is the region around a star where water could exist on the surface of an Earth-like planet. Water is understood to be vital in the formation of life due to its many important functions in biochemistry. Although the region is a spherical shell that surrounds a star, it is often shown as a ring in diagrams looking down onto the plane of a star system. Realize that the CHZ is closely related to the inverse-square law – how energy quickly falls off with distance from a star. Thus, the size and location of the CHZ change over time as a star evolves. For our Sun at present, the CHZ ranges from 0.97 AU to 1.37 AU but this range varies from star to star.

Tools

The following tools allow students to make sense of the raw data provided without needed to get to deep into the math of everything. These supports could be removed for more advanced students to provide more calculations.
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Blackbody Spectrum PhET
​Use this site to analyze stellar spectra for peak emission/temperature data for stars 
Note: this could be replaced with Wien's Law if you would rather have students calculate the temperature from the peak wavelength rather than using a simulation to change the temp until the spectrum matches

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Kepler's 3rd Law Calculator
​Use this site to calculate an unknown stellar mass, orbital period, or semi-major axis using Kepler’s 3rd Law

Note: this could be replaced Kepler's 3rd Law if you would rather have students calculate Semi-major axis by hand. (M x T ² = a ³)

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Habitable Zone Calculator
​Use this site to calculate the inner and outer radii of the habitable zone of a star. Be sure to hit “return” after each new value

The planet orbit is not required to get the inner and outer radii but provides a nice check if the orbit falls in the habitable zone.

The List of Possibilities

​Students receive a curated list of 6 stars that have had exoplanets discovered in their system. Some of these stars have more than one planet so students have 10 exoplanets in total to determine which ones have orbits in the habitable zone and could potentially support life
Kepler-18
Kepler-186
Kepler-442
TOI-2257
HD-20782
Trappist-1
Kepler-18 b
Kepler-18 d
Kepler-186 b
Kepler-186 d
Kepler-186 f
Kepler-442 b
TOI-2257 b
HD-20782 b
Trappist-1 b
Trappist-1 h

The Data

Star Spectra

In lieu of "raw data", a simulated spectrum for each star has been created in PhET. From this, students can either use PhET to match the spectrum by changing the temperature or calculate the temperature using Wien's Law (peak wavelength = 0.0029/T). This stellar temperature will be needed to determine the habitable zone around the star.
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Kepler-18 Spectrum
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Trappist-1 Spectrum

Planet Light Curves

Each time a planet passes between its star and the earth, the star’s brightness drops slightly, this transit data can be used to determine the orbital period and distance of each planet
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Kepler-18 b Light Curve
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HD-20782 b Light Curve
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Trappist-1 b Light Curve
Original Images
All light curves were created using this desmos tool that I threw together for this activity. You can download the individual graphs below
kepler-18b.png
File Size: 220 kb
File Type: png
Download File

kepler-18d.png
File Size: 183 kb
File Type: png
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kepler-186b.png
File Size: 230 kb
File Type: png
Download File

kepler-186d.png
File Size: 248 kb
File Type: png
Download File

kepler-186f.png
File Size: 242 kb
File Type: png
Download File

kepler-442b.png
File Size: 258 kb
File Type: png
Download File

toi-2257b.png
File Size: 281 kb
File Type: png
Download File

hd-20782b.png
File Size: 262 kb
File Type: png
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trappist-1b.png
File Size: 268 kb
File Type: png
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trappist-1h.png
File Size: 210 kb
File Type: png
Download File


Data Dashboard

Since there is a lot to determine about the stars and their exoplanets in order to determine which candidates fall in the habitable zone, it is useful to collect the data in a couple of organized tables.
Stars
  • The temperature can be determined from the stellar spectra
  • The habitable zone is calculated using the "Habitable Zone Calculator" tool with the star's radius and temperature as inputs
Star Name
Mass (Suns)
Radius (Suns)
Temperature (K)
Habitable Zone
Kepler-18
0.972
1.108
 
 
Kepler-186
0.544
0.523
 
 
Kepler-442
0.610
0.60
 
 
TOI-2257
0.33
0.31
 
 
HD-20782
0.96
1.17
 
 
Trappist-1
0.090
0.119
 
  
Planets
  • The period can be read as the time between minima on the planet's light curve graph
  • The semi-major axis is calculated using the planet's period and host star's mass. This calculation can be done using Kepler's 3rd law or an online calculator
  • Determining if the planet is habitable is a matter of comparing the semi-major axis (which is the average distance to the star) to the host star's habitable zone. If it falls with in the inner and outer radii, the planet is consider a potential habitable candidate.
Planet Name
Eccentricity
Period (days)
Semi-Major Axis (AU)
Habitable? (Y/N)
Kepler-18 b
0.0
 
 
 
Kepler-18 d
0.0
 
 
 
Kepler-186 b
0.0
 
 
 
Kepler-186 d
0.0
 
 
 
Kepler-186 f
0.04
 
 
 
Kepler-442 b
0.04
 
 
 
TOI-2257 b
0.5
 
 
 
HD-20782 b
0.95
 
 
 
Trappist-1 b
0.01
 
 
 
Trappist-1 h
0.01
 
 
 

Analysis

In the end, students will find that 3 of the 10 planets have a semi-major axis that falls inside their host star's habitable zone but there is more to the story. The following analysis questions guide students to look at the role that eccentricity has in an exoplanet's habitability.
  1. Of the ten planets assessed, which fall within the habitable zone?
  2. Of the planets that fall within the habitable zone, what is the eccentricity of each of their orbits?
  3. Click on the links for the stars of the potentially habitable exoplanets from the list below. As you drag the image around, notice the orbit of the planet relative to the green band marking the habitable zone (the planet’s current location is marked with the planet’s name). What impact does the eccentricity of a planet’s orbit have on its habitability?
  4. Based on everything that you’ve learned in this lab, if you were to choose one habitable planet from the 10 candidates provided, which one would it be and why?
It is clear when looking at a planet with a highly elliptical orbit like HD-20782, that the average distance from the star isn't always enough to assess an exoplanet's habitability

After investigating the orbit shape for the 3 possible candidates, students should be able to narrow this list down to just one planet that remains in the habitable zone of its star for its entire revolution.

That planet is:
​​Kepler-442 b
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Files

This activity was made as a google doc. See below for a pdf and editable google doc version of the student facing materials as well as the solutions with the tables fully completed
Finding a Habitable Planet (pdf)
File Size: 4528 kb
File Type: pdf
Download File

Finding a Habitable Planet (editable)
Finding a Habitable Planet - KEY (pdf)
File Size: 4542 kb
File Type: pdf
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Finding a Habitable Planet - KEY (editable)

​Notes

The following are some of the slides that I used throughout the topic to introduce the concepts needed for this exoplanet project
Star Color (pdf)
File Size: 2387 kb
File Type: pdf
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Star Color (Google Slides)
Discovering Exoplanets (pdf)
File Size: 2119 kb
File Type: pdf
Download File

Discovering Exoplanets (Google Slides)
Kepler's 3rd Law (pdf)
File Size: 823 kb
File Type: pdf
Download File

Kepler's 3rd Law (Google Slides)

Click for more Astrophysics resources ​⬇

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    Joe Cossette

    Father, Physics Teacher, Knowles Fellow, Friend, Techie, and Musician

    "Learning to teach teaches me to learn"


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