Glowing Darkness

https://docs.google.com/presentation/d/1yDzmwUMBFQGPYo_CNSF9zc9uF887yoUa/edit?usp=sharing&ouid=110494428302813353266&rtpof=true&sd=true

https://github.com/jalalirs/asteroid_lightcurve

What is a light curve?

One may think that gazing through the gloomy rocks that live in the asteroid belt and the surrounding Trojans will only send back dark images as they do not produce light. However, these rocks shine back to us their reflection from the sunlight. As we observe this reflected light through time, we notice that the brightness magnitude varies periodically. The reason brightness varies with time is that the asteroid has an irregular shape that produces different reflections as it rotates. Plotting this magnitude against time is called a light curve and it can give very useful information about the asteroid and thus the evolution of the solar system. The light curve period in the below image tells us the rotational period of the asteroid, which is around 7 hours for this case.

figure (1).

The challenge:

The challenge is to develop a tool that allows users to investigate how an asteroid's shape affects the light curve. There are many difficulties in this challenge. For one, how can we make sure the light curve that we are getting is correct? Can you map the pixel brightness to real values, if needed? And how can we know that the axis of rotation of an asteroid reflects reality?

Our solution:

We have developed a tool that can produce light curves for any 3D models that are given by the user or chosen from the mesh gallery. The simulation runs from given initial conditions such as light settings, camera settings, and the asteroid’s angular velocity. The user can choose real light curve plots retrieved from ALCDEF(Asteroid Light Curve Data Exchange format) database and compare them with their simulated light curve match (after normalizing the brightnesses). The simulation also calculates the normalized inertia tensor of the asteroid and predicts whether the direction of rotation that the user gave is a stable rotation. This is crucial because asteroids in the long-term rotate about the stable maximum inertia axis, which is also the lowest energy state. Now the user can get more accurate readings if he/she is patient enough to discover the stable axis of rotation for the downloaded 3D model. Probabilistically, real light curve measurements have more chance to represent stable rotation asteroids than an unstable ones, unless the taken data is of an asteroid that has ‘just’ collided with other objects. The user can also test unstable or tumbling rotation to observe the multiple periodicities that underlie the complex rotation. This is the first tool that integrates 3D model rendering, light curve measurements through image processing, real light curve database, orbital parameters, and stability calculation to produce a light curve study case.

figure(2)

To develop the tool we mainly used:

• Python as the programming language .
• Trimesh that provided some of the rendering functions
• Astropy that has common tools needed for astronomy.
• Poliastro to simulate Astrodynamics and Orbital Mechanic.
• Matplotlib plotting library.

Equations that we relied on:

1. Rotation matrices
2. Translation matrices
3. Inertia tensor equations
4. Pixel brightness equation

One issue we have found is in mapping the brightness magnitude in the simulation with a real meaningful value. Astronomers compare their brightness with a known star brightness, but doing so in computer rendering is difficult. We summed all the pixel brightness to get the magnitude value. Nevertheless, we only care about relative magnitude since the rotation period is the important result and the tool still holds its predictive power.

This video demonstrates how the tool is being implemented. https://www.youtube.com/watch?v=LkDYK82yCeo

figure(3)

There was in the past a debate about the shape of the asteroid Kleopatra. One scientist argued that the light curve that they were getting would indicate an unusual asteroid shape, a bi-lobed. Many scientists disagreed with her but today there is more evidence to suggest that Kleopatra is indeed a bi-lobed or more like a dog-bone. Try out Kleopatra in the simulation and see if it is indeed getting the same light curve with real measurements?

This year, the Lucy mission will be launched with the goal of visiting seven asteroids for the first time. This will be an important event since it will be the first time that researchers gather data of both the light curve and shape estimation of an asteroid. This simulation can help the public and scientists fit 3D model shapes to expected light curves so that they have a prediction tool at their hand.

Future work:

• Generative adversarial network: In the future, we hope to take this project to the next level and integrate a neural network algorithm that can generate thousands of random 3D models with their corresponding light curves. Using this pool of data the AI algorithm will create a model that can predict the light curve of any shape or even be able to inverse model the 3D shape from the light curve.
• Measuring brightness: We will also try to tackle the complicated problem of measuring brightness that can correspond to real-life asteroid values using digital image analysis
• Asteroid shape and noise generator: in order to help the users to explore different shapes and their effects directly by changing scaling and shading the object and rendering the new shape instantly and examine its light curve.
• Add the brightness effects of the asteroids orbital movement as a function of phase angle
• Improve inertia calculation for complex objects
• Incorporate more sophisticated asteroid dynamics based on physical models

We are planning to improve on the tool and make it open-source so that people can learn more about asteroids and have fun! We also showed this tool to two physics professors and they believe it has great potential in the asteroid scientific community.

"During the presentation, the participants were enthusiastic, energetic, and exceptionally well-organized. I have been especially impressed by their determination and sparkle. They have an extremely large responsibility to achieve their aims. I have enjoyed getting to find them quite capable of working entirely on their own in a self-directed manner. I have no doubt that they have the skills, focus, and determination to successfully upgrade their program to be helpful in international researches related to Astronomy. 

 I recommend their program very highly and without reservation."

- Nasreen AlShami , A professor in the physics department at Taibah University.

Our tools relied on NASA's 3D model database [1]. These models are important because they can verify that our simulation produces the correct light curve when comparing it with the measured value. We also used Astropy and Poliastro libraries in Python, which is based on NASA's observations, to plot the orbital shape and take the asteroid distance from the sun as a function of input date. Finally, to make a match between the simulated light curve and observed light curve shapes, we took the light curve real measurements from the ALCDEF database[2] which is funded by NASA and the NSF.

Our journey started with a shared interest in the field of astronomy and space, even though our backgrounds vary from computer science, physics, to aerospace engineering. We wanted to make a change that can help researchers in Lucy's mission and the public who are space enthusiasts be able to use a tool that tests their ideas and expectations, within the limitation of the software. This was a truly challenging problem and we faced many setbacks that made us appreciate the complexity of this topic. We started out using Blender software to render our 3D models but we discovered that we will be limited by a small number of 3D models and also would not be able to verify it using a lightcurve database. So we switched to Python to render our models and eventually we created a whole interface for our tool. The whole process of writing the code and testing the results gave us valuable lessons in coding for members who were not exposed to Python, and also in the scientific method for those with a broad scientific background. The hard work and the all-nighters that we did in the past couple of days in writing and debugging the code have paid off to produce this prototype.

We would like to thank the Saudi Space Commission and the organizers for giving us this opportunity to represent the country globally in this hackathon. We also appreciate the hard work that NASA gave for creating this amazing challenge that we enjoyed every second of. The topic was so intriguing that one of us started thinking about studying asteroids as a master's degree.

We also thank professor Paul Sánchez of physics at the University of Colorado Boulder for testing our tool at the last minute, and professor Al Shamsi for giving us the quoted feedback. Their feedback is important so that we can improve this tool more in the future and have it hopefully spread to universities, scientific institutions, students, and researchers to get a better experience.

[1]. Asteroid shapes models provided by JPL and NASA 3D Resources: 3D models of asteroids.

[2.]Asteroid Lightcurve Data Exchange Format (ALCDEF): Real asteroid data and their observed lightcurves were used to fit the simulated lightcurve.

[3] https://www.scratchapixel.com/lessons/mathematics-physics-for-computer-graphics/lookat-function

Papers:

1. Bezryadin, S., Bourov, P., & Ilinih, D. (2007). Brightness calculation in digital image processing. International Symposium on Technologies for Digital Photo Fulfillment, 2007(1), 10–15. https://doi.org/10.2352/issn.2169-4672.2007.1.0.10.
2. Mottola, Stefano, et al. “Convex Shape and Rotation Model of Lucy Target (11351) Leucus from Lightcurves and Occultations.” The Planetary Science Journal, vol. 1, no. 3, 2020, p. 73., https://doi.org/10.3847/psj/abb942. 
3. https://www.issfd.org/ISSFD_2014/ISSFD24_Paper_S10-3_Bradley.pdf

#Asteroids, #lightcurve, #lucymission, #simulation, #rendering, #Software, #tool, #database, #Jupiter, #Trojans, #astronomy, #3D, #Modeling, #science, #space, #solarsystem, #universe

This project has been submitted for consideration during the Judging process.