The Apparent Diameters of the Planets

\documentclass{article} \usepackage[english]{babel} \usepackage[letterpaper,top=2cm,bottom=2cm,left=3cm,right=3cm,marginparwidth=1.75cm]{geometry} \usepackage{amsmath} \usepackage{graphicx} \usepackage[colorlinks=true, allcolors=blue]{hyperref} \title{The Apparent Diameters of the Planets} \author{Kaitlyn Kosten} \begin{document} \maketitle \begin{abstract} Before the invention of the telescope, astronomers had difficulty determining the apparent sizes of planets visible to the naked eye. While Tycho Brahe, Ptolemy, Al-Farghani, and Al-Battānï measured similar apparent sizes for the five visible planets, Giovanni Magini reported drastically different results. To better understand the difficulty faced by early astronomers, I set out to make my own measurements of the naked eye apparent diameters of Venus, Jupiter, and Saturn. I built an apparatus that mounts on top of a telescope and holds a micrometer. When a planet is viewed through the micrometer, the micrometer setting can be adjusted until its prongs align with the outer edges of the planet’s visible disk. From the micrometer reading and the distance from the observer’s eye to the micrometer, the apparent diameter of the planet (as seen by the naked eye) can be found. Using this apparatus I measured the apparent diamete