Strengthening Planetary Defense: Developing Algorithms to Determine Asteroid’s Physical Properties and Success of Deflection Missions
June 14, 2023
September Update: The 34th European Union Contest for Young Scientists (EUCYS) was held in Brussels, Belgium from 11-17 September 2023. It brought together 136 promising young scientists aged 14 to 20, from 36 countries across the EU and beyond for a five-day competition. I was honored to represent Canada as Winner of 2023 Top Award at the 2023 Canada-Wide Science Fair.
My project "Developing Algorithms to Determine Asteroid's Physical Properties and Success of Deflection Missions" won the second prize. I was the youngest contestant and the prize winner.
My project "Developing Algorithms to Determine Asteroid's Physical Properties and Success of Deflection Missions" won the second prize. I was the youngest contestant and the prize winner.
The 2023 Canada-Wide Science Fair (CWSF) organised by Youth Science Canada took place in Edmonton, Alberta, from May 14 to May 19, 2023. It brought together some 396 regional science fair finalists from 7th to 12th grade from across Canada.
My project "Developing algorithms to determine asteroid’s physical properties and success of deflection missions" won the 2023 Best Project Award of the Canada-Wide Science Fair (Innovation). I will now represent Canada at the European Union Contest for Young Scientists (EUCYS) in Brussels in September 2023. (See Press Release)
My project "Developing algorithms to determine asteroid’s physical properties and success of deflection missions" won the 2023 Best Project Award of the Canada-Wide Science Fair (Innovation). I will now represent Canada at the European Union Contest for Young Scientists (EUCYS) in Brussels in September 2023. (See Press Release)
In addition to the Best Project Award, I won 5 more awards:
- Gold Medal
- The Actuarial Foundation of Canada Award
- Excellence in Astronomy Award from the Royal Astronomical Society of Canada
- Top of the Category Award in Curiosity and Ingenuity
- Youth Can Innovate Award
I also won the 2022 Best Project Award last year, becoming the first back-to-back best project award winner since 1989-1990 and the youngest ever to do so.
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Project Overview:
The pace of discovery of near-earth asteroids outpaces current abilities to analyze them. Knowledge of an asteroid's physical properties is essential to deflect them. I developed open-source algorithms that combine images from robotic telescopes and open data to determine asteroids' size, rotation, and strength. I took observations of the Didymos binary asteroid, and my algorithm determined it to be 850m wide, with a 2.26-hour rotation period and rubble pile strength. I measured a 35-minute decrease in the mutual orbital period after impact by the 2022 NASA DART Mission. External sources validated the findings. Every citizen scientist is now a planetary defender.
Challenge: Asteroid Collision Risks Are Real
As of April 2023, there are 31,750 known Near-Earth Asteroids (NEAs). Hundreds of near-earth asteroids are discovered monthly, outpacing the current ability to analyze them. If an asteroid were on a collision course with Earth, we must know its physical properties to design an effective deflection mission.
Motivation:
In September 2022, NASA's Double Asteroid Redirection Test (DART) Mission crashed a fridge-sized spacecraft on asteroid Dimorphos - the moonlet of binary asteroid Didymos to change its path and needed support from citizen scientists. I was motivated to combine my passion for math and astronomy with programming to strengthen planetary defense.
Goal:
My project had two goals
- Develop algorithms to determine the physical properties of near-earth asteroids by combining images from robotic telescopes, open-data and school-level math.
- Apply the algorithm to a real-world planetary defense test by determining the physical properties of the Didymos binary asteroid and measuring changes after the DART impact to validate the success of the asteroid deflection mission.
Approach:
I used robotic ground-based telescopes in Australia, Canada, Chile, the USA, and the NEOSSat Space telescope to observe Didymos. I created algorithms that perform photometric analysis of images from robotic telescopes and generate lightcurves to determine an asteroid's physical properties (absolute magnitude, size, strength, rotation period, mutual orbital period).
Application:
My algorithms accurately determined the asteroid's physical properties and confirmed the DART mission's success in changing the orbit of Dimorphos. I published my code open-source so that citizen scientists can become planetary defenders.
Background Research:
To learn about asteroid photometry (brightness measurement), I researched online, participated in astronomy-related Zoom conferences, and corresponded with astronomers.
Data:
I wrote research proposals to get observing time on robotic telescopes. I used open datasets:
- GAIA Catalog: To select comparison stars
- Horizons Database: To get positions of asteroids based on date and time
Methodology:
a. Imaging the Asteroid and Data Pre-processing
I imaged Didymos binary asteroid for 55 hours before, during and after the DART spacecraft impact. Using open-data, weighted mean, and area of a circle formula, I centroided known stars and asteroids in the images.
I imaged Didymos binary asteroid for 55 hours before, during and after the DART spacecraft impact. Using open-data, weighted mean, and area of a circle formula, I centroided known stars and asteroids in the images.
b. Undertaking Photometry to Measure the Absolute Magnitude and Size of Didymos
I determined the correct aperture size to measure the pixel brightness of Didymos across all images using the slope and median functions. I eliminated variations in the asteroid's brightness because of changes in weather and seeing conditions using comparison stars of known brightness.
As asteroids orbit the Sun, their brightness varies because their distance from Sun and Earth changes. I eliminated these changes by calculating unity and phase angle offsets, resulting in the asteroid's absolute magnitude and size.
I determined the correct aperture size to measure the pixel brightness of Didymos across all images using the slope and median functions. I eliminated variations in the asteroid's brightness because of changes in weather and seeing conditions using comparison stars of known brightness.
As asteroids orbit the Sun, their brightness varies because their distance from Sun and Earth changes. I eliminated these changes by calculating unity and phase angle offsets, resulting in the asteroid's absolute magnitude and size.
c. Creating Composite Asteroid Light Curves to Determine Rotation Period
When asteroids rotate, different sides reflect different amounts of light, allowing measurement of their rotation period. My algorithm fitted the asteroid's individual time-series computed magnitude to composite lightcurves of different periodicities. The periodicity of the composite lightcurve corresponding to the smallest root-mean-square error was the asteroid’s rotation period.
When asteroids rotate, different sides reflect different amounts of light, allowing measurement of their rotation period. My algorithm fitted the asteroid's individual time-series computed magnitude to composite lightcurves of different periodicities. The periodicity of the composite lightcurve corresponding to the smallest root-mean-square error was the asteroid’s rotation period.
d. Determining Changes in Orbital Period to Validate Success of NASA DART Mission
Subtracting the rotation period from the composite lightcurve yielded the mutual orbital period. Measuring changes in the orbital period of Dimorphos around Didymos post-impact yielded the changes in Dimorphos's orbital radius - validating the success of the asteroid deflection mission.
Subtracting the rotation period from the composite lightcurve yielded the mutual orbital period. Measuring changes in the orbital period of Dimorphos around Didymos post-impact yielded the changes in Dimorphos's orbital radius - validating the success of the asteroid deflection mission.
Results
Algorithms were successfully developed to combine observations from robotic telescopes with open-data and math to determine the physical properties of asteroids.
The algorithms were applied to a real-world planetary defense test to measure the physical properties of the Didymos binary asteroid before, during and after the DART impact. It yielded the following results:
1. Absolute Magnitude and Size of Didymos
The absolute magnitude was determined to be 18.03, and its size 820 metres.
The absolute magnitude was determined to be 18.03, and its size 820 metres.
2. Rotation Period of Didymos
Didymos' rotation period was calculated to be 2.26 hours and did not change post-impact.
Didymos' rotation period was calculated to be 2.26 hours and did not change post-impact.
3. Mutual Orbital Period of Dimorphos
Pre-impact mutual orbital period of Dimorphos around Didymos was measured to be 11.91 hours. Post-impact, it reduced by 35 minutes and became 11.34 hours.
Pre-impact mutual orbital period of Dimorphos around Didymos was measured to be 11.91 hours. Post-impact, it reduced by 35 minutes and became 11.34 hours.
4. Increase in Peak Brightness of Didymos Binary Asteroid
Post-impact, the brightness of the Didymos binary asteroid increased by 1.2 magnitude because of the expansion of the ejected material (dust particles) from Dimorphos that reflected sunlight.
Post-impact, the brightness of the Didymos binary asteroid increased by 1.2 magnitude because of the expansion of the ejected material (dust particles) from Dimorphos that reflected sunlight.
5. Length of the Ejecta Tail of Dimorphos
Ejecta tail was calculated to be over 20,000 km long a week after the impact.
Ejecta tail was calculated to be over 20,000 km long a week after the impact.
Validation of Results
The results from my algorithms matched those obtained by the NASA DART Mission. There was a perfect match in the rotation period, pre-impact mutual orbital period, peak brightness of the ejecta, ejecta tail length, and asteroid strength calculations.
There was less than a 5% discrepancy in the size measurement of Didymos. My algorithm determined the size using ground-based telescopes from the absolute magnitude and surface reflectivity of Didymos. NASA measurements were from space using the DRACO camera onboard the DART spacecraft on its approach towards Didymos.
Mathematics and Statistics Used
Robotic telescopes image the night sky digitally using charged coupled devices (CCD) cameras. This means that the images are in the form of rectangular arrays of different pixel values. Photometry analysis applies mathematical and statistical tools to these pixel values.
Centroiding of Celestial Objects:
As the stars and asteroids are brighter in the center and become dimmer towards the edges, the weighted mean of pixel brightness values was calculated to find the photometric centers of the object.
As the stars and asteroids are brighter in the center and become dimmer towards the edges, the weighted mean of pixel brightness values was calculated to find the photometric centers of the object.
Determining Correct Aperture Size:
Slope analysis was performed to find the aperture size that included all bright pixels constituting the asteroid while keeping the CCD pixel noise minimal. As the aperture size should be constant across all images, the median of the aperture size of individual images was used.
Slope analysis was performed to find the aperture size that included all bright pixels constituting the asteroid while keeping the CCD pixel noise minimal. As the aperture size should be constant across all images, the median of the aperture size of individual images was used.
Converting Observed Brightness to Magnitude Scale:
The "magnitude" scale used to specify the brightness of celestial objects is a logarithmic scale of base 2.5. It meant converting all pixel brightness values into "magnitude" scale using log transformation.
The "magnitude" scale used to specify the brightness of celestial objects is a logarithmic scale of base 2.5. It meant converting all pixel brightness values into "magnitude" scale using log transformation.
Determining Rotation Period:
To fit time-series computed data to lightcurves with different periods, the time modulus of individual lightcurves was calculated by determining the remainder of the time elapsed after dividing it by the lightcurve period. The curve with the smallest Root Mean Square Error (RMSE)/Standard Deviation was the composite light curve.
To fit time-series computed data to lightcurves with different periods, the time modulus of individual lightcurves was calculated by determining the remainder of the time elapsed after dividing it by the lightcurve period. The curve with the smallest Root Mean Square Error (RMSE)/Standard Deviation was the composite light curve.
Discussions:
Determining Strength of the Asteroid
Asteroids with faster rotation periods (below 2.2 hours) are strength-bound (monolithic). Else they would fly apart. Asteroids with slower rotation periods (over 2.2 hours) and sizes over 150 meters (like Didymos) are likely to be "rubble piles" as bigger asteroids are impacted by other asteroids causing them to fragment.
Asteroids with faster rotation periods (below 2.2 hours) are strength-bound (monolithic). Else they would fly apart. Asteroids with slower rotation periods (over 2.2 hours) and sizes over 150 meters (like Didymos) are likely to be "rubble piles" as bigger asteroids are impacted by other asteroids causing them to fragment.
Determining Changes in the Orbital Path and Success of Deflection Misson
Kepler's third law relates the orbital period of a celestial object with its orbital radius. A 35-minute post-impact decrease in the orbital period of Dimorphos translates to 40 metres reduction in its orbital radius, showing spacecraft's kinetic impact successfully changed the asteroid’s path.
Kepler's third law relates the orbital period of a celestial object with its orbital radius. A 35-minute post-impact decrease in the orbital period of Dimorphos translates to 40 metres reduction in its orbital radius, showing spacecraft's kinetic impact successfully changed the asteroid’s path.
Errors and Limitations
- My remote telescope observation plans had a Signal-to-Noise Ratio (SNR) > 100, meaning the brightness measurement uncertainty was 0.01 magnitude. This was acceptable to measure Didymos's rotation period, which has an amplitude of 0.1 magnitude.
- Limited processing capability of my home computer restricted the iterations I could perform to find the best fit for rotation and mutual orbital periods, limiting the preciseness of results to 2 significant digits.
Conclusions
The project goals were met:
- Algorithms were developed to determine the physical properties of near-earth asteroids by combining images from robotic telescopes, open-data and math.
- Algorithms successfully determined the physical properties of the Didymos binary asteroid, and the results matched those obtained by NASA.
- Citizen scientists can become planetary defenders by analyzing the physical properties of asteroids and measuring the success of asteroid deflection missions.
Future:
- My algorithms will support the upcoming Chinese and Japanese Planetary Defense Test Missions to 30-metre-sized asteroids.
- I will expand my algorithm to combine data from radar observations (from radio telescopes) to allow for 3D shape modelling for additional characterization of asteroids.
- My algorithm can perform precise photometry measurements of asteroids. I plan to adapt it to study exoplanetary atmospheres for biosignatures using the James Webb Space Telescope data.
- Planetary defense is one of the many intergenerational problems our generation faces. I will undertake more science communication and publishing to influence policy and bridge the gap between research and practice.
