Week 7: Ground Control to Major Tom, we’re go for launch :)
Kira A -
Hey guys. Welcome back to my space-faring journey! Last week I reported some trouble determining how to implement the orbit-raising maneuver (ORM) in my mission. However, after examining the data the Indian Space Research Organisation (ISRO) released on the ORM used in the Chandrayaan 3 mission, I have figured out a basic version of the ORM.
The ORM used by ISRO uses two burns instead of one, as I had previously thought. In this version, the spacecraft still makes a single burn at perigee, however, using a second burn at apogee, the spacecraft raises its perigee, meaning that the second ORM is done from a different starting point. To determine this, I used the vis-viva equation shown below.
The vis-viva equation is used to determine the speed of a spacecraft at any given point in its orbit using its location and the semi-major axis of the orbit. By using the perigee and apogee values of each orbit of the Chandrayaan 3 mission provided by ISRO, I determined the speed of the spacecraft at its periapsis and apoapsis. With each calculated speed value, I then calculated the magnitude of the delta-v required for each ORM completed, determining that two burns were completed per maneuver. Additionally, I calculated the specific angular momentum of each transfer orbit to ensure that it was indeed increasing with each burn, signifying a higher energy orbit. I found that with perigee burns, the specific angular momentum increased by about 800 km2/s, whereas for apogee burns, it increased by only 200 km2/s. Below is an image of the calculations for this method.
From my analysis, I calculated a total fuel expenditure of about 22%, which includes the ORMs and the Trans Lunar Injection (TLI) orbit. As a reminder, the TLI is a transfer orbit that will put the spacecraft on its trajectory to the moon. What I also noticed is that with the final TLI maneuver, the velocity at perigee (288 km) was about 10.8 km/s, which is also very close to the escape velocity at that point (calculated to be 10.9 km/s). This means that our final TLI orbit will land within the sphere of influence of the Earth and be on the right path toward the moon. My analysis does show that the ORMs in conjunction with the TLI orbit does save fuel, leaving more than 75% of fuel available for lunar insertion and maneuvering.
As per my last blog, I visited the ASU Tempe campus where I was able to access ample whiteboard space and computational tools to derive multiple methods of orbit raising. Fortunately, I was able to determine the ORMs employed by ISRO, as I explained above. However, my initial idea, was to use the orbital energy approach – as seen in the picture below.
This method uses the velocity and radius of an orbit to determine the orbital energy of the spacecraft using the equation shown.
Using the orbital energy, we can determine the radius of apogee after the burn, which is used to determine the orbital energy of the starting orbit of the next ORM. This method yielded slightly different and more accurate results than the rocket equation method I described in a previous blog because it takes into account the total energy of the orbit, not merely the velocity (kinetic energy). While this method is more accurate, after discovering the vis-viva method used by ISRO, I will be using that as it has already been used and tested in a cislunar mission.
After attaining a solid foundation in the theory section of ORM, I moved to the plane change maneuver for the final orbit insertion of my spacecraft. I discussed my plan to insert my spacecraft into a near-rectilinear halo orbit (NRHO) in my last blog because of the NASA Gateway station and its applications. To achieve this orbit, the inclination of my spacecraft must change almost 90 degrees, which requires a plane change maneuver.
The plane change maneuver consumes a lot of fuel due to its high delta-v requirement. For this reason, a plane change maneuver is often carried out in conjunction with another orbital maneuver to justify the large fuel consumption. In the example below, I have calculated the total delta-v required to carry out a plane change maneuver at the same time as a change in the right ascension of the ascending node (RAAN).
In the context of my mission, I will be analyzing whether or not to couple my plane change maneuver with a Hohmann transfer to raise my apogee and align my spacecraft with a near-rectilinear halo orbit. It is always more efficient to complete a plane change maneuver further from the orbited body, however, I still need to analyze whether more fuel is used in a single burn to establish NRHO or if more is used in two separate burns, one for plane change and one for apogee raising (or increasing eccentricity).
Looking towards next week, as I stated previously, I will be looking to implement the ORM used by ISRO in the context of my mission in MATLAB and complete an analysis of the plane change and Hohmann transfer needed to establish NRHO. This will allow me to determine which sequence the spacecraft should complete. Additionally, I am planning to jump into CADing my spacecraft to create a 3d model and better visualize the placement and orientation of each component. Hopefully, I can 3d print this model to have a physical representation of the spacecraft at the end of the project and for the presentation.
Thank you so much to my mentors, Mr. Joseph, Dr. Goodwin, and Dr. Farooq, for offering their insight and time to me and this project as well as my friends over at ASU who graciously offered their study space to work on my project. Lastly, thank you to all of you for reading and interacting with my blogs. I hope you will all join me again next week.
Ad Lunam!
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