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.
2. Rotation Period of Didymos
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.
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.
5. Length of the Ejecta Tail of Dimorphos
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.
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.
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.
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.