Week 1: One small step for Kira…
Kira A -
Welcome back, everyone! This week was full of emotion as I finished my last full day of school and started working on my senior research project full-time. As per my last post, this week was all about learning the basics of orbital maneuvers and implementing them into my code in MATLAB. However, before I could begin, as an aspiring astrodynamicist, I first needed to explore the restricted two-body problem (R2BP). In celestial mechanics, the two-body problem describes the motion of 2 objects orbiting each other in space. R2BP allows for a simplified analysis of the more complicated three-body problem by limiting a three-body system to two masses, with the third object reduced to negligible mass relative to the other masses. This is ideal for situations involving satellites orbiting planets. My research on exploring navigational pathways within the cislunar region begins by understanding and modeling the Restricted Two-Body Problem. Below are graphical representations generated in MATLAB of two objects orbiting one another with respect to different objects or points in the system.
Delving into the Hohmann Transfer, I learned that it is the most efficient two-impulse (or thrust) maneuver for increasing the altitude (or distance from the orbiting body) of a spacecraft’s orbit. This will be integral when I work my way up to the orbit-raising maneuver as it implements a similar technique. Below is a picture of notes I took while studying the Hohmann transfer that include the equations I later implemented into my code.
After fully comprehending and completing the derivations of the equations needed to perform a Hohmann Transfer, I then moved into the Bi-elliptic Hohmann transfer. While very similar to the Hohmann Transfer, I was fascinated to discover that it takes advantage of two coaxial semi-ellipses, as seen below, to increase the altitude of an orbit. Consequently, this makes it a more efficient altitude-altering maneuver than the simple Hohmann transfer when the radius of the final orbit is at least 11.94 times the radius of the inner orbit.
Finally, familiar with the theory behind each maneuver, it was time to apply the knowledge I had gained to MATLAB and numerically represent these maneuvers. At first, creating a program to calculate the desired values from each maneuver was daunting; however, with my previous coding experience in the Python coding language, I realized that much of the logic needed to create a program was present in both languages. Once I felt more confident in my abilities in MATLAB, it was not long before I was able to complete my code. Throughout the process, I encountered many errors that required debugging, a tedious but necessary process, that not only helped me to create the program to calculate the total change in velocity and change in mass due to fuel used of a Hohmann Transfer, but to become more proficient in the MATLAB language and toolbox for more complicated endeavors in the near future for my project.
In the coming week, I look forward to continuing my research into orbital maneuvers and diving deeper into spacecraft design and instrumentation for primary, secondary, and tertiary mission objectives. With a clear end goal and checkpoints along the way, I anticipate consistent progress. I am also excited to meet again with my offsite mentor, Dr. Farooq, and gather his insight on the progress I’ve made throughout the week and approach my next steps with more confidence and wisdom. Additionally, I would like to thank my on-site mentors, Dr. Goodwin and Mr. Joseph, for their consistent support through the beginning phase of my project. Thank you all for tuning in! See you next time.
Ad Lunam!
Comments:
All viewpoints are welcome but profane, threatening, disrespectful, or harassing comments will not be tolerated and are subject to moderation up to, and including, full deletion.