MSc Thesis

Projects | 2022 | Links: Thesis .pdf | GitLab Repo

You can find the full thesis here.

1. Introduction
2. Abstract
3. Main results
   1. Simulated images
   2. Orbit determination
   3. Minimum set of images required
   4. Measuring the mass of Dimorphos
   5. Code and performance
4. Full thesis and references

Introduction

Dinosaurs did not have a space agency, but fortunately as humans do. The first ever planetary defense mission (AIDA), which will visit the Didymos-Dimorphos binary asteroid system to test the kinetic impact asteroid deflection technique, is composed of two main spacecraft (and some CubeSats!):

1. DART, the main spacecraft by NASA which will crash into the surface of Dimorphos.
2. Hera, ESA’s spacecraft which will visit the system a few years later to assess DART’s impact.

I wrote my master thesis inspired by the second spacecraft, in which I attempt to perform orbit determination of the binary asteroid system using simulated images by the Hera spacecraft.

Abstract

Asteroids in the solar system arguably pose one of the greatest threats to planet Earth. An impact between a sufficiently large asteroid and planet Earth will lead to catastrophic consequences for the Earth and its inhabitants. To avoid such a scenario, several planetary defense missions and techniques have been proposed over the years in literature. One solution which shows sufficient maturity to be implemented is the kinetic impact technique, which utilizes a spacecraft crashing into an asteroid at high speeds. Based on the law of conservation of momentum, the velocity of the asteroid is then changed just a little due to the impact which -if planned correctly- will be sufficient to ensure that the asteroid will miss the Earth entirely and nullify the probability of collision.

The Asteroid Impact and Deflection Assessment (AIDA) mission is humanity’s first experimental attempt in planetary defense and will attempt to investigate the kinetic impact approach for the binary asteroid system of Didymos-Dimorphos. It consists of two spacecraft: a) DART, which will crash into Dimorphos (the secondary body of the binary asteroid system) and b) Hera, which will arrive at the system after DART’s impact with Dimorphos to investigate the collision further, determine the composition of the two asteroids and accurately characterize the dynamical behavior of the two bodies by performing orbit determination using its instruments.

Inspired by Hera’s mission objectives, the possibility of performing image-based orbit determination using solely photographs captured on-board Hera is examined. Considering the lack of actual images due to the fact that Hera is expected to arrive at the binary asteroid system in late 2026, simulated sets of images containing Didymos and Dimorphos are used instead. The orbit determination problem is then transformed into an optimization problem, where the global minimum of a cost function is searched using a metaheuristic algorithm called the Evolutionary Centers Algorithm (ECA). Results of this approach are extremely promising, demonstrating that the algorithm can accurately determine the orbit of Dimorphos with a mean absolute percentage error below 1% for each osculating orbital element. Finally, using Didymos’ wobble, the mass of Dimorphos can also be determined with this process with an accuracy lower than 0.1%.

Main results

Simulated images

Using data from ESA’s SPICE service for the trajectory of Hera and an in-house J2 propagator, a simulated set of images is obtained as reference. By defining a cost function which creates another set of simulated images, the algorithm tries to obtain the initial state vector which minimizes the residual values between the observed and the predicted images in the pixel grid.

Orbit determination

For the predicted orbit of Dimorphos around Didymos, my code can predict the original orbital elements with a mean absolute percentage error below 1% and the gravitational parameter with a percentage error below 1%, despite the algorithm underperforming in nearly equatorial orbits.

Minimum set of images required

In order to obtain an accurate result for all orbital elements, a minimum of 200 images taken by Hera has to be used.

Measuring the mass of Dimorphos

Expanding the analysis into the detailed characterization phase of Hera, it is possible to adapt the code to estimate the mass of Dimorphos using the wobble of Didymos. The mass of Dimorphos can thus be determined with an accuracy greater than 0.1%!

Code and performance

This thesis was my first major project in the Julia programming language (which is great for scientific computing). I used the Evolutionary Centers Algorithm, and although convergence is not guaranteed for this problem, adequate results are produced within 100 iterations, which take a few minutes to run on a personal computer.

Full thesis and references

If you want to find the full thesis text, check out the code used or simply want to check the sources, be sure to find the full thesis here.