Hello everyone, we the mentees of Space the Finance Frontier S&T project would like to brief you with the work which we did during the project. Let us begin with the objective and overview of the project. A lot of us have fascination towards space exploration and travel and to kindle the interest of several other students as well, Astronomic Club had streamed and Apollo 11 documentary even before the project began. This really helped create a good background for the upcoming summer project. Main of the main name of the project was not only the Indepth Analysis and Knowledge of Astrodynamics and Rocket Science but also to implement the concepts learned in some way or the other. Be it simulation, mission report or solving the assignments that are provided to us and towards the end also discuss about futuristic and promising techniques that may prove to be revolutionary for the future of industrial travel. A stepwise methodology was followed by proceeding ahead. Starting off with developing some basic knowledge about space missions then learning about several components and systems of rockets and then applying that knowledge in several ways which we will be discussing soon. Some of the major concepts which we learned during the project include rocket design, rocket equations, aerodynamics, engines, reentry, propulsion, orbital dynamics, communication, etc. While studying trajectory optimization various concepts from maths and physics were used which was followed by analysis via MoMA modeling in MATLAB. Coming to a very important section results. We derived the famous rocket equation from simple momentum conservation. Consequently, we got the delta V equation that relates to the specific impulse. For rocket dynamics, the from simple force balance we obtained the general equations of motion in the R and theta direction. We also obtained the function of variation of mass with respect to time. These three main differential equations were used while studying trajectory optimization. From the initial parameters, the thrust produced by the rocket at five different altitudes, we obtained a spline curve of thrust versus altitude in order to know the thrust at any general altitude. Next up, we need to perform a maneuver known as gravity turn in order to achieve a stable orbit around the earth. For this, we need to turn the rocket from 0 degrees to 90 degrees within some altitude. We starting an ending point of gravity turn maneuver were provided and to calculate the angle the rocket weight with the normal at a general altitude, as you can see we use this function in order to plot the graph. As we can see from graph 1, a change is slow is observed at altitudes of around 100 and 350 kilometers which correspond to the starting and ending altitude of gravity turn. Thus, confirming that the plots obtained agree with each other and are not contradictory. Then we proceeded to obtain the variation of drag force and dm by dt with altitude from various different equations and using MATLAB we brought it to graph as well. The sudden jump in graph 4 represents separation of stage 1 and stage 2 respectively. A change in ISP value was the reason for this. Also, after 360 kilometers of altitude, we observed that the change in mass is tending to 0. This is because stage separation is complete and now very few corrections are needed to achieve a required orbit. Now these trajectory equations are optimized but for maximum efficiency, we need to optimize the rocket model for increasing its payload capacity while simultaneously minimizing its cost. Multi-objective genetic algorithm aka MOGA provides us with a very clear and easy way to do so. We and we get a range of optimum values following which we can design a rocket as close to perfect as possible. To study about MOGA modeling, we analyzed a research paper from MIT. Let me guide you through our understanding of the procedure. First, a lot of random models are generated. From them, we choose the ones that are fit, that is, the models that can comfortably reach are target altitude. This is done by introducing a fitness function that gives out penalties based on the final altitude that the models can achieve. Obviously, higher the altitude, lesser the penalty and consequently, the most chance for the model to be selected. Here, the penalties for the 10th and 50th generation of models have been plotted and as you can see, this is the penalty function that we got for the final altitude that is reached by the model. Then, these fit functions are plotted onto a Pareto front with the X and Y axes corresponding to the payload capacity and price respectively. Then the non-dominated individuals, that is, the ones that are better than the others, are selected from this min-mass Pareto front. The graph on the right is a representation of the same. When this process was repeated for 10 times, the fronts were combined yielding the graph on the left. Now, the non-dominated individuals were chosen and the plot on the right was obtained showing us the best of the best models. As is the case with random point generation, we rarely obtain a smooth curve. So, in order to obtain a smooth curve, the process was repeated more times, that is, for 1,640 iterations instead of just 10 times. As you can see, there is a pretty smooth curve which can get even smoother on increasing the iteration count. Now from this graph, we can easily see the utopian point, that is, the point whose cost to mass ratio is the lowest. This is the optimal model that we were aiming for. In this sample mission report, we have also made a comparison among the results and the actual rocket that was launched. We got an error percentage of 1.69%, which was within an agreeable limit. Learning concepts is always nice, but experimenting and applying those things, I had much more to the fun and experience of the project. Hence, we used the knowledge of topics like specific impulse, engines, propulsion, reentry, orbital maneuvers, etc. to plan one and do you know missions in curveable space program. Here are some images from our mission recordings. Thus, after learning such a diverse set of topics, the project aimed at analyzing real world space missions in depth, in which we covered historically important as well as futuristic missions. Ranging from the legendary Apollo 11 mission, India's fried Mars orbiter mission, SpaceX, SpaceX's crew dragon resilience mission and the promising Artemis program. Even though the project has come to an end, the learning doesn't end here. We will be further exploring new modeling techniques, other than MOGA, such as S-H-C-D to get more accurate results. We also plan on doing in depth analysis of the concept studies as well as about orbital perturbations. Here, we also have listed some of the references that we used during our project. We hope that this presentation can delt the spark in you to explore this domain. Thank you and hoping to see you all in Astronomic Club IIT Kanpur.