This project involves mathematically modelling the charge distribution on the surface of a spacecraft in outer space orbits.
Understanding the interaction of a spacecraft with the outer space environment forms a crucial part of its functioning. Various phenomena including solar radiation, plasma interaction, dielectric charging, etc, cause a spacecraft to acquire a net charge, which is non-uniformly distributed. This charge distribution poses a risk to the functioning of the spacecraft. Unevenly distributed charge on a spacecraft’s surface can potentially be harmful for several reasons including:
• Electrostatic forces: The uneven charge can cause electrostatic forces to act which can attract or repel nearby charged particles in space. This can affect the spacecraft’s orientation and trajectory, making it unstable.
• Surface charging: Charged particles in outer space can lead to localized regions of surface charging. These can create electrical discharges such as Corona discharge or arcing, which can damage sensitive spacecraft components.
• Radio frequency interference: Uneven charge distribution can also result in radio frequency interference. This interference can harm spacecraft communication systems.
• Thermal effects: Unevenly charged surfaces may heat or cool down unevenly, affecting the temperature distribution. This can impact efficiency and lead to overheating or freezing of critical components.
It is therefore necessary to study and quantify the charge distribution on the surface of the spacecraft in a mathematical way.
The goal of this project is to mathematically model the charge distribution on the surface of the spacecraft in outer space orbits. For the sake of simplicity as well as relevance to current applications, we have chosen a spacecraft modeled on CUBESAT to study the charge distribution profile of its body. We are considering the body of the spacecraft to be a symmetric metallic cube, with a specified edge length. This helps us to focus more on the methodology of arriving at our result by simplifying the object under consideration.
The electric potential on the spacecraft body has only small local variations, so it is generally considered constant. This potential is considered as 1V (this value does not matter as we want to find the relative charge density at different points). Since the body of the spacecraft is equipotential at all times, and we need to devise equations for finding the potential at every point in terms of the unknown charge density ρ. Equations for finding the charge density are made using the method of moments. Following this, we will get ‘N’ equations in ‘N’ distinct variables, which can then be solved using numerical methods like Gaussian elimination, Gauss-Jordan algorithm, TDMA or others of this kind, depending on the equations obtained after performing the above-mentioned steps.
We (the group involved in making of this project) extend our heartfelt gratitude to Dr. Soumyabrata Chakrabarty (scientist - ISRO SAC, professor - IITGN) for providing the problem statement and invaluable guidance that shaped our group project. His expertise and continuous support were instrumental in defining the project’s direction and scope.