Exoplaneteer

High-Level Summary

We developed Exoplaneteer, an interactive 3D visualization app that simulates the potential of the Habitable Worlds Observatory (HWO) to characterize known exoplanets. The app visualizes the exoplanet population and allows users to adjust telescope and instrument parameters, such as aperture and sensor size, to see how these changes affect the number of detectable exoplanets. By offering real-time updates on the observability of exoplanets, Exoplaneteer helps NASA stakeholders explore HWO's performance, providing valuable insights into which exoplanets are most promising for further study and how to optimize the observatory’s capabilities. This tool supports informed decision-making in the ongoing search for habitable worlds.

Project Demo and Product

YT Demo: https://youtu.be/PPG6z5W9HdM

Product: https://soft-alpaca-79d6db.netlify.app/

Presentation Slides

Project Details

Overview

The Exoplaneteer project provides a 3D visualization designed to simulate and analyze the performance and capabilities of the Habitable Worlds Observatory (HWO) in characterizing known exoplanets. The app allows users to view exoplanets mapped in 3D space, look at details about them and their host stars, and adjust telescope parameters in order see how these changes impact the number of observable and characterizable exoplanets. Furthermore, it provides analytics to determine promising habitable exoplanet candidates, such as habitability scores, habitability zones, and others.

Process

The app processes exoplanet data from the NASA Exoplanet Archive, which is used to map them in 3D space. Their positions are determined by galactic coordinates. We then use a cone to represent the line of sight of the HWO, which can be adjusted by tweaking the focal length and sensor size. The user is also able to adjust the aperture size, which affects the characterizability of exoplanets, which is updated in real time. The app uses signal-to-noise ratio (SNR) and distance from earth to calculate if an exoplanet is characterizable.

Analytics

The app provides many analytics to access the capabilities of the exoplanet. The app shows how useful a set of telescope parameters and orientations will be by showing the following data:

Total exoplanets in field of view Total characterizable exoplanets Earth Similarity Index (ESI) graph Distance from habitable zone

By looking at the graphs and values of the above, we can access how useful this mission will be, and its potential to find something valuable

Exoplanet Specifics and Filtering

Users can search for specific exoplanets, or filter by specific parameters, such as ESI, host star, distance from habitable zone, characterizability. This feature will also color code the planets in the 3D visual, allowing for a visual representation of the distribution of exoplanetary parameters around us.

Allowing users to look for and sort by different properties allows for a broader understanding of exoplanets in relation to each other, and the effect they have on the HWO.

A neat, color coded visual allows the user to see such relations and benefits on the go.

We allow users to look into specific exoplanet systems in relation to their host stars and habitable zone. They can find many more specifics about the exoplanet and its star, such as the discoverer, mass, radius, ESI, stellar class, and much more.

Tools and Technology

We utilized the following tools and technologies to help us create Exoplaneteer

• Languages; JavaScript, HTML, Python, and CSS

• Frameworks and Libraries: ReactJS, Three.js, React Three Fiber, D3.js, TailwindCSS, Chart.js

• Data: NASA Exoplanet Archive

Equations

SNR and ESmax

The SNR and max distance are given by:

$SNR = SNR_0 \cdot \left( \frac{Rstar \cdot R_P \cdot \left( \frac{D}{6} \right)}{\left( \frac{ES}{10} \right) \cdot PS} \right) \cdot 2$

$ES_{max} = 15 \cdot \frac{\left( \frac{D}{6} \right)}{PS}$

Var	Description	Units
SNR	Signal-To-Noise Ratio	—
SNR0	Base Signal-To-Noise Ratio	—
ESmax	Maximum Distance from Earth	pc
Rstar	Host Star Radius	Rsun
RP	Exoplanet Radius	REarth
D	Diameter of Telescope	m
ES	Distance from Earth	pc
PS	Planet-Star Distance	AU

The exoplanet is considered characterizable if $SNR > 5 \quad \text{and} \quad ES \leq ES_{max}$

Line of Sight Cone

The cone of line of sight is computed using the following equations:

$\text{HFOV} = \tan^{-1}\left(\frac{\text{sensorSize}}{2 \times \text{focalLength} \times 1000}\right)$

$\text{radius} = h \cdot \tan(\text{HFOV})$

Name	Description	Units
HFOV	Horizontal Field of View	radians
sensorSize	Sensor size	mm
focalLength	Focal length of the lens	m
h	Distance from point to base of LOS	m

ESI

The ESI is calculated by:

$\text{ESI}(S, R) = 1 - \sqrt{\frac{1}{2} \left[ \left( \frac{S - S_\oplus}{S + S_\oplus} \right)^2 + \left( \frac{R - R_\oplus}{R + R_\oplus} \right)^2 \right]}$

Name	Description	Units
ESI	Earth Similarity Index	—
S	Stellar Flux of Exoplanet	Earth Solar Flux
$S \oplus$	Stellar Flux of Earth	Earth Solar Flux
R	Radius of Exoplanet	REarth
$R \oplus$	Radius of Earth	REarth

Exoplanet to params

To scale a 3D point $\text{point} = (x, y, z)$ to a specified orbital radius $\text{orbitRad}$, the scaling factor $a$ is calculated as follows:

$a = \frac{\text{orbitRad}}{\sqrt{x^2 + y^2 + z^2}}$

The scaled point is then obtained by multiplying the original point by this scaling factor:

${scaledPoint} = \text{point} \times a$

Next, to find the pitch, yaw, and roll angles between two 3D vectors $\text{v1}$ and $\text{v2}$:

$\text{unitV1} = \frac{\text{v1}}{||\text{v1}||}, \quad \text{unitV2} = \frac{\text{v2}}{||\text{v2}||}$

$\text{direction} = \text{unitV2} - \text{unitV1}$

$\text{quaternion} = \text{Quaternion}(\text{unitV1}, \text{unitV2})$

$\text{Euler} = \text{QuaternionToEuler}(\text{quaternion})$

$\text{pitch} = \text{radToDeg}(euler.x), \quad \text{yaw} = \text{radToDeg}(euler.y), \quad \text{roll} = \text{radToDeg}(euler.z)$

The resulting angles can be represented as:

${ \text{pitch}, \text{yaw}, \text{roll} }$

Habitable Zone

To calculate the radii of the habitability zone around a star based on its apparent magnitude, distance, and spectral type, the following steps are performed:

$M = m - 5 \cdot \log_{10}\left(\frac{d}{10}\right)$

$M_{bol} = M + BC$

$L = 10^{\frac{M_{bol} - M_{bol_{Sun}}}{-2.5}}$

$R_{inner} = \sqrt{\frac{L}{1.1}}$

$R_{outer} = \sqrt{\frac{L}{0.54}}$

The habitability zone radii can then be represented as:

${ R_{inner}, R_{outer} }$

Var	Description	Units
$m$	Apparent Magnitude of the star	Magnitude
$d$	Distance from Earth to the star	Parsecs (pc)
$M$	Absolute Magnitude of the star	Magnitude
$M_{bol}$	Bolometric Magnitude of the star	Magnitude
$L$	Absolute Luminosity of the star	Solar Luminosity (L☉)
$R_{inner}$	Inner radius of the habitability zone	AU (Astronomical Units)
$R_{outer}$	Outer radius of the habitability zone	AU (Astronomical Units)
$specType$	Spectral Type correction factor	Magnitude
$M_{bol_{Sun}}$	Bolometric Magnitude of the Sun	Magnitude

Benefits

This app provides a visualization that can teach users about exoplanets, the HWO telescope and its configurations and impact on exoplanets The app can help explore habitability and see distributions of exoplanets based on certain parameters It can give stakeholders insight on the usefulness and the impact of the HWO, and how changes to its different aspects may change the capability and potential of the HWO.

The Goal

The goal of the Exoplaneteer is to help NASA stakeholders understand and optimize the observational capabilities of the HWO. By allowing users to interact with the telescope parameters and see their effects on the exoplanets detected, the app aims to allow for strategic decisions about instrument parameters, and accessing the usefulness of the HWO, contributing to the search for habitable worlds.

The Future

We plan on furthur developing this website into somehting robust and useful, instead of it being a simple one-off project for the hackathon. We have the following planned for the future in order of importance:

• Coronagraph Implementation
  • A coronagraph will allow the telescope to see many more exoplanets than without, for this reason, it is very important to have this considered in the calculations for the most accurate results
• Cost Calculations
  • The HWO is still in development, so estimating its cost based on its parameters will prove to be useful and impactful in understanding the project's magnitude in terms of resources
• Image Generator
  • We may not be able tosee teh images from the HWO for years, so we might as well have fun predicting them in a smart way
• Time-Specific Data:
  • Currently, the calculatisn are done for the lifetime of the telescope and under optimal conditions, not considering the blockading of stars and exoplanets by each other. This is important to tackle in order to get accurate data for a timefram
• Life Simulations:
  • Simulating life on different exoplanets will give us more idea on the usefullness of the HWO
• Real-Time Updates:
  • The only reason this si last is because the launch of HWO is still far, but as soon as it is launched, this will be the highest priority.

Refereces

• Habitable Zone Calculation
• FOV Calculations
• ESI Calculations
• ESI Calculations
• NASA Exoplanet Archive

Contact

Contact me at [email protected] for any questions or query