Scientific Explanation of the Algorithm to Determine Exoplanet Habitability

Our algorithm determines the habitability and detectability of exoplanets by incorporating astrophysical models and observations. It evaluates each exoplanet's position within the habitable zone (HZ), surface temperature, angular separation, and contrast ratio based on NASA's Habitable Worlds Observatory (HWO) parameters. This approach is based on research into direct imaging, radiative equilibrium, and exoplanetary characterization.

1. Habitable Zone (HZ) Calculation:

Research Reference: Probing the Capability of Future Direct-Imaging Missions to Spectrally Constrain the Frequency of Earth-like Planets

The Habitable Zone (HZ) refers to the range of distances from a star where conditions may be right for liquid water to exist on a planet's surface. The HZ is critical for determining whether a planet could potentially support life.

The HZ is calculated using the host star's stellar luminosity (L*). A more luminous star will have a broader and more distant habitable zone.

In our code, we utilize this formula to define the boundaries where an exoplanet could maintain surface conditions conducive to life. If the semi-major axis (planet-star distance, a) falls within this zone, the planet is considered to be potentially habitable.

2. Equilibrium Temperature (T_eq) Calculation:

Research Reference: Thermal Radiative Equilibrium Models in Exoplanet Atmospheres

A planet's equilibrium temperature (T_eq) is a key factor in determining its habitability. It represents the temperature a planet would have if it were only heated by its star and radiated energy back into space in balance.

The equilibrium temperature depends on the star’s effective temperature (T_eff), stellar radius (R*), the planet-star distance (a), and the planet's albedo (reflectivity). A higher albedo indicates that the planet reflects more radiation, resulting in a lower surface temperature

In our algorithm, we use this formula to calculate T_eq. Planets with T_eq values between 200 K and 330 K are considered potentially suitable for hosting liquid water, a key indicator of habitability.

3. Angular Separation and Contrast Calculation:

Research Reference: Exoplanet Direct Imaging: Separability and Detection Thresholds

For an exoplanet to be detected through direct imaging, it must be resolved separately from its host star. This is determined by its angular separation (θ) and the contrast ratio between the planet and the star.

For a planet to be detectable, its contrast ratio must exceed the telescope’s contrast limit (e.g., 1e-10 for the HWO). The algorithm computes this ratio and filters out planets with insufficient contrast for detection.

4. 3D Visualize (Three JS):
We extract the useful values from the data given by NASA. We have a data.json file (converted table.csv to data.json) and extract the result.json (an algorithm that detects the Habitable Exo Planets from the above-mentioned steps).

Once we get useful values like Habitable's Hoststar Radius, Planet Radius, Distance between Hoststar and Planet, Distance between Habitable Table and our Earth, etc. We get our rough estimation of how our 3D world will look like.

Then with the help of these values, we can map them to a 3D world using React Fiber (THREE JS). You can view it in the source code. Then we convert the real-world values to 3D world values by using Ratio and also zoom distance to get clear view of the Universe of Habitable Exo Planets.

You can see more details in the GitHub source code, and also our demo video/images in PPT.

Conclusion:
The project can be made in real-time, by just having a CRON Jobs in the server (that calls the NASA Exo Planets data API and performs the algorithm to give us the result.json file) and the client requesting the server for results.json (Habitable Exo Planets Data)

2024 NASA Space Apps Challenge

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