\documentclass[10pt,a4paper]{article} % Packages \usepackage{fancyhdr} % For header and footer \usepackage{multicol} % Allows multicols in tables \usepackage{tabularx} % Intelligent column widths \usepackage{tabulary} % Used in header and footer \usepackage{hhline} % Border under tables \usepackage{graphicx} % For images \usepackage{xcolor} % For hex colours %\usepackage[utf8x]{inputenc} % For unicode character support \usepackage[T1]{fontenc} % Without this we get weird character replacements \usepackage{colortbl} % For coloured tables \usepackage{setspace} % For line height \usepackage{lastpage} % Needed for total page number \usepackage{seqsplit} % Splits long words. %\usepackage{opensans} % Can't make this work so far. Shame. Would be lovely. \usepackage[normalem]{ulem} % For underlining links % Most of the following are not required for the majority % of cheat sheets but are needed for some symbol support. \usepackage{amsmath} % Symbols \usepackage{MnSymbol} % Symbols \usepackage{wasysym} % Symbols %\usepackage[english,german,french,spanish,italian]{babel} % Languages % Document Info \author{salometabah} \pdfinfo{ /Title (phys-183.pdf) /Creator (Cheatography) /Author (salometabah) /Subject (PHYS 183 Cheat Sheet) } % Lengths and widths \addtolength{\textwidth}{6cm} \addtolength{\textheight}{-1cm} \addtolength{\hoffset}{-3cm} \addtolength{\voffset}{-2cm} \setlength{\tabcolsep}{0.2cm} % Space between columns \setlength{\headsep}{-12pt} % Reduce space between header and content \setlength{\headheight}{85pt} % If less, LaTeX automatically increases it \renewcommand{\footrulewidth}{0pt} % Remove footer line \renewcommand{\headrulewidth}{0pt} % Remove header line \renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit % This two commands together give roughly % the right line height in the tables \renewcommand{\arraystretch}{1.3} \onehalfspacing % Commands \newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour \newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols \newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns \newcommand{\tn}{\tabularnewline} % Required as custom column type in use % Font and Colours \definecolor{HeadBackground}{HTML}{333333} \definecolor{FootBackground}{HTML}{666666} \definecolor{TextColor}{HTML}{333333} \definecolor{DarkBackground}{HTML}{A3A3A3} \definecolor{LightBackground}{HTML}{F3F3F3} \renewcommand{\familydefault}{\sfdefault} \color{TextColor} % Header and Footer \pagestyle{fancy} \fancyhead{} % Set header to blank \fancyfoot{} % Set footer to blank \fancyhead[L]{ \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{C} \SetRowColor{DarkBackground} \vspace{-7pt} {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}} } \end{tabulary} \columnbreak \begin{tabulary}{11cm}{L} \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{PHYS 183 Cheat Sheet}}}} \\ \normalsize{by \textcolor{DarkBackground}{salometabah} via \textcolor{DarkBackground}{\uline{cheatography.com/202611/cs/43008/}}} \end{tabulary} \end{multicols}} \fancyfoot[L]{ \footnotesize \noindent \begin{multicols}{3} \begin{tabulary}{5.8cm}{LL} \SetRowColor{FootBackground} \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}} \\ \vspace{-2pt}salometabah \\ \uline{cheatography.com/salometabah} \\ \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}} \\ \vspace{-2pt}Not Yet Published.\\ Updated 12th April, 2024.\\ Page {\thepage} of \pageref{LastPage}. \end{tabulary} \vfill \columnbreak \begin{tabulary}{5.8cm}{L} \SetRowColor{FootBackground} \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}} \\ \SetRowColor{white} \vspace{-5pt} %\includegraphics[width=48px,height=48px]{dave.jpeg} Measure your website readability!\\ www.readability-score.com \end{tabulary} \end{multicols}} \begin{document} \raggedright \raggedcolumns % Set font size to small. Switch to any value % from this page to resize cheat sheet text: % www.emerson.emory.edu/services/latex/latex_169.html \footnotesize % Small font. \begin{multicols*}{4} \begin{tabularx}{3.833cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Introduction}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Astronomical unit: distance btwn sun \& earth 149,597,870.7km Speed of light: 300,000km/s} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Light year: 9,5x10\textasciicircum{}12\textasciicircum{} km megaparsec: 3.26 mil ly or 3x10\textasciicircum{}19\textasciicircum{} km} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Local galactic group: our galaxy if part of a small cosmic village - {\emph{local group}} which is part of a larger super galaxy cluster called {\emph{Virgo Supercluster}}} \tn % Row Count 8 (+ 4) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Each gal contains 100bil stars and there are about 100bil observable gals} \tn % Row Count 10 (+ 2) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Obserbable uni is a sphere centered on us (bc of how light reached us) with radius of 14bil years} \tn % Row Count 12 (+ 2) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Bigbang→birth of first stars and gals (400 mil yrs)→recycling of material through stars→formation of other stars\&planets} \tn % Row Count 15 (+ 3) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Speed at equator: 1,670km/hr at lat30: 1,275km/hr at lat90: 0km/hr} \tn % Row Count 17 (+ 2) % Row 7 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Degree of ecliptic plane: 23 1/2 = reason for seasons} \tn % Row Count 19 (+ 2) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{The sun is in motion, circling the center of milkyway tipped at angle of 60° about 2/3 from centre and wobbles up and down} \tn % Row Count 22 (+ 3) % Row 9 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Local galaxies move in random motion and can colllide due to gravitational pulls} \tn % Row Count 24 (+ 2) % Row 10 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Signature of expansion: the farther they are, the faster they are receding} \tn % Row Count 26 (+ 2) % Row 11 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Don't know if uni has edges or centres: raisin bread vs ballon model} \tn % Row Count 28 (+ 2) % Row 12 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Earth rotates (\textasciitilde{}1000km/h)→earth orbits sun (100,000km/hr)→solar system moves relative to nearby stars (70,000km/hr)→milkyway rotates once every 230 mil yrs (800,000km/hr)→galaxy moves relative to others in local group (300,000km/hr)→uni expands at speed of light} \tn % Row Count 34 (+ 6) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Introduction (cont)}} \tn % Row 13 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{On small scale, gravity is stronger, on large scale dark energy is stronger = expansion} \tn % Row Count 2 (+ 2) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Astronomy as Science}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Modern scientific method has its roots in Greece} \tn % Row Count 1 (+ 1) % Row 1 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Used shadows in Alexandria in 240bc to measure circumference of earth: knew distance between two cities and used angle of shadow - angle/360 = distance/circum. of earth} \tn % Row Count 5 (+ 4) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{400 BC: geocentric model of uni- thought space must be mathematically perfect, sun\&stars appeared to be moving around earth, no perceptible motion of earth} \tn % Row Count 9 (+ 4) % Row 3 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Ptolomy's model: planets don't follow same path as stars, can have retrograde motion, cant be explained by geocentric model} \tn % Row Count 12 (+ 3) % Row 4 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{This lead to Hipparchus multiple levels of epicycles (no longer perfect) which lead to copernican rev.} \tn % Row Count 15 (+ 3) % Row 5 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Nicholas Copernicus: 1473-reintroduced helocentricmodel, published book on his deathbed, his calculations were wrong but he was right, rock on dude} \tn % Row Count 18 (+ 3) % Row 6 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Tycho Brahe: 1546- compiled 30 yrs of data improving astronomical data, super accurate observational astronomer} \tn % Row Count 21 (+ 3) % Row 7 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Johannes Kepler (my boy): 1571- fit mathematical models to Tycho's data, reformation of ellipitcal orbits (imperfect)} \tn % Row Count 24 (+ 3) % Row 8 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{3 Laws of planetary motion-1 planets orbit sun (in centre) in ellipitcal path 2- planet covers the same area of space in the same amount of time no matter where it is in its orbit-3 a planet's orbital period is proportional to the size of its orbit P\textasciicircum{}2\textasciicircum{}=a\textasciicircum{}3\textasciicircum{} (p=time a=distance) (semi-major axis)} \tn % Row Count 30 (+ 6) \end{tabularx} \par\addvspace{1.3em} \vfill \columnbreak \begin{tabularx}{3.833cm}{X} \SetRowColor{DarkBackground} \mymulticolumn{1}{x{3.833cm}}{\bf\textcolor{white}{Astronomy as Science (cont)}} \tn % Row 9 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Planets move faster when closer to the sun, close in planets move faster} \tn % Row Count 2 (+ 2) % Row 10 \SetRowColor{white} \mymulticolumn{1}{x{3.833cm}}{Galileo: 1564- first to experimentally show newton's first law of motion (things in motion stay in motion), made observations with telescope, showed milky was made of many stars and very far away (no parallax needed)} \tn % Row Count 7 (+ 5) % Row 11 \SetRowColor{LightBackground} \mymulticolumn{1}{x{3.833cm}}{Stellar parallax: apparent shift of position (parallax) of any nearby star against the background of distant stars} \tn % Row Count 10 (+ 3) \hhline{>{\arrayrulecolor{DarkBackground}}-} \end{tabularx} \par\addvspace{1.3em} \begin{tabularx}{3.833cm}{p{0.3033 cm} p{0.3033 cm} p{0.3033 cm} } \SetRowColor{DarkBackground} \mymulticolumn{3}{x{3.833cm}}{\bf\textcolor{white}{Light}} \tn % Row 0 \SetRowColor{LightBackground} \mymulticolumn{3}{x{3.833cm}}{Info from uni comes from light through emission, scattering and absorption} \tn % Row Count 2 (+ 2) % Row 1 \SetRowColor{white} \mymulticolumn{3}{x{3.833cm}}{Also receive info in form of grav waves (2015) and neutrinos (1960s)} \tn % Row Count 4 (+ 2) % Row 2 \SetRowColor{LightBackground} \mymulticolumn{3}{x{3.833cm}}{Imagine} \tn % Row Count 5 (+ 1) \hhline{>{\arrayrulecolor{DarkBackground}}---} \end{tabularx} \par\addvspace{1.3em} % That's all folks \end{multicols*} \end{document}