# Modeling Periodic Phenomen The Orbit Of Mars

Introduction

Billions of years old, Mars is the 4th planet from the sun in our solar system and the last of the terrestrial planets before the asteroid belt. The planet neighbors Earth and has seen a plethora of exploration craft from our planet. Mars orbits around the Sun on an ellipse, as dictated by Kepler’s laws (which state that all orbits are ellipses). Mars’ elliptical shape is a lot less circular than Earth, due to its high orbital eccentricity, which is over 5 Earth’s. Because of the elliptical shape of orbits, the distance between Mars and the Sun changes throughout the Martian year, which is 687 Earth days or 668.5991 Martian days (sols). Once per Martian year, Mars is at its farthest point from the sun (also known as the aphelion), and once per year it is at the closest point to the sun (perihelion). The distance to the sun at these points are 249.23 * 106km and 206.62 * 106km, respectively being the aphelion and perihelion. Mars is about 227.9 * 106km away from the sun on average, representing a middle point between the aphelion and perihelion in Mars’ orbit. This orbit, or more specifically, the distance from the Sun to Mars, can be modeled as a periodic function

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As one might expect, that number is a small fraction, due to the fact that it takes 687 days for Mars to complete an orbit of the Sun and 687 is greater than 2훑. This b value can be more easily understood in relation to the scenario by using the equation b=2훑/p, where p is the period. In this scenario, the period, or length to complete a cycle is 687 days (on Earth). This is because 687 days is the time that Mars takes to complete a single orbit around the Sun. By using the 687 days value as p in our equation, we can see that b=2훑/687. By simplifying this, we can achieve b=훑/343.5, as seen in the equation