# Math AA HL IA – 7/7

본 문서는 May 2021년 세션에서 제출된 Math AA HL IA이며 7/7을 받았습니다.

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## Modeling planet elliptical orbits and finding the equation for the distance between Earth and Mars and the rate of change of the distance between the two planets at a given time

IB Analysis and Approaches HL

1. Introduction

There are two main goals to this exploration.

1. The first objective is to model the orbits of Earth, Mars, and the Hohmann Transfer Orbit.
2. The second objective is to find out the equation for the distance between Earth and Mars and the rate of change of the distance between the two planets at a certain date.

Inspired by the Mars perseverance rover that was launched in July 2020, I wanted to base my IA on the mathematical aspects of the orbits of planets and the trajectories of spacecrafts that were sent to outer space. I was intrigued to choose this topic as I wanted to learn more about the planetary orbits and to find out when Mars would likely be visible from Earth. I thought this would be an opportunity to further my knowledge of the solar system and also to apply the trigonometric and vector knowledge that I learned in my IB math classes. There were a few questions I had in mind: Exactly what kind of shape are the planetary orbits? Is there a way to model spacecraft trajectories? Is it possible to know the distance between two planets at a given time? How can this be used to calculate the dates when Mars and Earth are in opposition or in conjunction? Is the velocity at which Earth and Mars moving towards or away from each other constant?

In this IA, I will be focusing on modelling the orbits of Earth and Mars that resemble the orbits shown in figure 1, using ellipse equations and presenting them in polar, cartesian, and parametric forms. To complete the understanding of creating ellipse equations, I will also be modelling the Hohmann transfer orbit, which are used when spacecraft are sent to Mars. This orbit is used to minimize fuel use and maximize efficiency(“Let’s Go”). Then I will be using the parametric forms of the ellipse equations for Earth and Mars to create an equation describing the distance between Earth and Mars at a given point using the distance formula and basic trigonometric functions. The final aim is to differentiate the distance equation to see when Earth and Mars move away from each other at the fastest and slowest rate…

• 총 페이지수: 19 pages
• 과목명: Mathematics
• 주제: Modeling planet elliptical orbits and finding the equation for the distance between Earth and Mars and the rate of change of the distance between the two planets at a given time
• The file is in Word format.