# Math Exploration: Trajectory Of A Rocket

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Math Exploration: Trajectory of a Rocket By Mridvika Suresh Word Count : Background and Rationale In TV shows or movies, when they show a rocket being launched, it always seems that the rocket is directly launched upwards and travels in a projectile or curved path until it reaches its destination. At least this is the thought I always seemed to believe in. Last week when I found out the truth about rockets, I had to know more about how they worked. The rocket travels in a straight direction (upwards) till it reaches the outer layer of earth and to leave the planet to travel to another one, it travels in a spiral motion. This is so that the rocket experiences less aerodynamic stress. After reaching the atmosphere, the rocket stops using its fuel and uses the earth’s gravity to change its direction for the trans-lunar injection. Introduction…show more content…
I will be considering different rockets from the Apollo missions and research on the different ways to find the trajectory and the factors affecting the trajectory of the rocket. To do this, I will be calculating the equations of the elliptical orbits, use polar coordinate method to get the different trajectories and will find the equations of the elliptical orbits to look for a comparison between the 2 factors. I will be doing this with the help of differential equations, Tsiolkovsky rocket equation and equation of ellipses. Tsiolkovsky rocket equation is used to determine the speed of a rocket. I will need to find the speed of the rocket as there is a relation between the speeds the rocket is launched at and the elliptical path it travels