[Tex/LaTex] Drawing of Sun–Earth–Moon system

pstrickstikz-pgf

Is there a package (or packages) for drawing the Sun–Earth–Moon system with either PSTricks, TikZ, or some other vector graphics language to illustrate Lunar and Solar eclipses, the phases of the Moon, and the seasons on the Earth?

I know of pst-solarsystem but it is not what I'm looking for; here, it is 'only' possible to draw the planets moving in circular orbits around the Sun.

Best Answer

A couple of months ago, I produced a beamer/tikz animation (available on texample.net) of the Earth's orbit around the Sun to illustrate the counterintuitive fact that Earth is farther from the Sun in Summer than it is in Winter. I used that example to demonstrate the power of inducing (and then resolving) cognitive dissonance in the classroom.

I've modified it to also show the Moon following an elliptical orbit around the Earth. (Of course, the Moon's orbit around the Earth is really only approximately elliptical, and does not lie in the Ecliptic Plane.) You can change the positions visited by the Earth and the Moon along their respective orbits (simply change how \Earthangle and \Moonangle are defined in the body of the \foreach, and/or modify the value of \N).

enter image description here

\documentclass{beamer}

\usepackage{lmodern}
\usepackage{tikz}

\setbeamertemplate{navigation symbols}{}

\begin{document}
\begin{frame}[fragile]
\frametitle{}
\begin{center}
    \begin{tikzpicture}[scale=2.5]
        \def\rS{0.3}                                % Sun radius

        \def\rE{0.1}                                % Earth radius
                                                    % Major radius of Earth's elliptical orbit = 1
        \def\eE{0.25}                               % Excentricity of Earth's elliptical orbit       
        \pgfmathsetmacro\bE{sqrt(1-\eE*\eE)}        % Minor radius of Earth's elliptical orbit    

        \pgfmathsetmacro\rM{.7*\rE}                 % Moon radius
        \pgfmathsetmacro\aM{2.5*\rE}                % Major radius of the Moon's elliptical orbit
        \def\eM{0.4}                                % Excentricity of Earth's elliptical orbit
        \pgfmathsetmacro\bM{\aM*sqrt(1-\eM*\eM)}    % Minor radius of the Moon's elliptical orbit 
        \def\offsetM{30}                            % angle offset between the major axes of Earth's and the Moon's orbits


        % This function computes the direction in which light hits the Earth.
        \pgfmathdeclarefunction{f}{1}{%
            \pgfmathparse{
                ((-\eE+cos(#1))<0) * ( 180 + atan( \bE*sin(#1)/(-\eE+cos(#1)) ) ) 
                +
                ((-\eE+cos(#1))>=0) * ( atan( \bE*sin(#1)/(-\eE+cos(#1)) ) ) 
            }
        }

        % This function computes the distance between Earth and the Sun,
        % which is used to calculate the varying radiation intensity on Earth.
        \pgfmathdeclarefunction{d}{1}{%
            \pgfmathparse{ sqrt((-\eE+cos(#1))*(-\eE+cos(#1))+\bE*sin(#1)*\bE*sin(#1)) }
        }

        % Draw the elliptical path of the Earth.
        \draw[thin,color=gray] (0,0) ellipse (1 and \bE);

        % Draw the Sun at the right-hand-side focus
        \shade[
            top color=yellow!70,
            bottom color=red!70,
            shading angle={45},
            ] ({sqrt(1-\bE*\bE)},0) circle (\rS);
         %\draw ({sqrt(1-\b*\b)},-\rS) node[below] {Sun};

        % Produces a series of frames showing one revolution
        % (the total number of frames is controlled by macro \N)
        \pgfmathtruncatemacro{\N}{12}
        \foreach \k in {0,1,...,\N}{
            \pgfmathsetmacro{\Earthangle}{360*\k/\N}
            \pgfmathsetmacro{\Moonangle}{3*360*\k/\N} % <--- change the multiplying factor to suit your needs
            % Draw the Earth at \Earthangle
            \pgfmathsetmacro{\radiation}{100*(1-\eE)/(d(\Earthangle)*d(\Earthangle))}
            \colorlet{Earthlight}{yellow!\radiation!blue}
            \pgfmathparse{int(\k+1)}
            \onslide<\pgfmathresult>{
                \shade[
                    top color=Earthlight,
                    bottom color=blue,
                    shading angle={90+f(\Earthangle)},
                    ] ({cos(\Earthangle)},{\bE*sin(\Earthangle)}) circle (\rE);
                 %\draw ({cos(\Earthangle)},{\bE*sin(\Earthangle)-\rE}) node[below] {Earth};  

                 % Draw the Moon's (circular) orbit and the Moon at \Moonangle
                 \draw[thin,color=gray,rotate around={{\offsetM}:({cos(\Earthangle)},{\bE*sin(\Earthangle)})}]
                    ({cos(\Earthangle)},{\bE*sin(\Earthangle)}) ellipse ({\aM} and {\bM});
                 \shade[
                    top color=black!70,
                    bottom color=black!30,
                    shading angle={45},
                    ]   ({cos(\Earthangle)+\aM*cos(\Moonangle)*cos(\offsetM)-\bM*sin(\Moonangle)*sin(\offsetM)},%
                         {\bE*sin(\Earthangle)+\aM*cos(\Moonangle)*sin(\offsetM)+\bM*sin(\Moonangle)*cos(\offsetM)}) circle (\rM);   
            }
        }
    \end{tikzpicture}
\end{center}
\end{frame}
\end{document}

Here is non-animated version in the article class.

enter image description here

\documentclass{article}

\usepackage{lmodern}
\usepackage{tikz}
\usepackage{kantlipsum}

\begin{document}
\section{Eclipses}
\kant[1]
\begin{figure}
\centering
    \begin{tikzpicture}[scale=2.5]
        \def\rS{0.3}                                % Sun radius

        \def\Earthangle{30}                         % angle wrt to horizontal        
        \def\rE{0.1}                                % Earth radius
                                                    % Major radius of Earth's elliptical orbit = 1
        \def\eE{0.25}                               % Excentricity of Earth's elliptical orbit       
        \pgfmathsetmacro\bE{sqrt(1-\eE*\eE)}        % Minor radius of Earth's elliptical orbit

        \def\Moonangle{-45}                         % angle wrt to horizontal           
        \pgfmathsetmacro\rM{.7*\rE}                 % Moon radius
        \pgfmathsetmacro\aM{2.5*\rE}                % Major radius of the Moon's elliptical orbit
        \def\eM{0.4}                                % Excentricity of Earth's elliptical orbit
        \pgfmathsetmacro\bM{\aM*sqrt(1-\eM*\eM)}    % Minor radius of the Moon's elliptical orbit 
        \def\offsetM{30}                            % angle offset between the major axes of Earth's and the Moon's orbits



        % This function computes the direction in which light hits the Earth.
        \pgfmathdeclarefunction{f}{1}{%
            \pgfmathparse{
                ((-\eE+cos(#1))<0) * ( 180 + atan( \bE*sin(#1)/(-\eE+cos(#1)) ) ) 
                +
                ((-\eE+cos(#1))>=0) * ( atan( \bE*sin(#1)/(-\eE+cos(#1)) ) ) 
            }
        }

        % This function computes the distance between Earth and the Sun,
        % which is used to calculate the varying radiation intensity on Earth.
        \pgfmathdeclarefunction{d}{1}{%
            \pgfmathparse{ sqrt((-\eE+cos(#1))*(-\eE+cos(#1))+\bE*sin(#1)*\bE*sin(#1)) }
        }

        % Draw the elliptical path of the Earth.
        \draw[thin,color=gray] (0,0) ellipse (1 and \bE);

        % Draw the Sun at the right-hand-side focus
        \shade[
            top color=yellow!70,
            bottom color=red!70,
            shading angle={45},
            ] ({sqrt(1-\bE*\bE)},0) circle (\rS);
         %\draw ({sqrt(1-\b*\b)},-\rS) node[below] {Sun};


        % Draw the Earth at \Earthangle
        \pgfmathsetmacro{\radiation}{100*(1-\eE)/(d(\Earthangle)*d(\Earthangle))}
        \colorlet{Earthlight}{yellow!\radiation!blue}
        \shade[%
            top color=Earthlight,%
            bottom color=blue,%
            shading angle={90+f(\Earthangle)},%
        ] ({cos(\Earthangle)},{\bE*sin(\Earthangle)}) circle (\rE);
        %\draw ({cos(\Earthangle)},{\bE*sin(\Earthangle)-\rE}) node[below] {Earth};  

        % Draw the Moon's (circular) orbit and the Moon at \Moonangle
        \draw[thin,color=gray,rotate around={{\offsetM}:({cos(\Earthangle)},{\bE*sin(\Earthangle)})}]
            ({cos(\Earthangle)},{\bE*sin(\Earthangle)}) ellipse ({\aM} and {\bM});
        \shade[
            top color=black!70,
            bottom color=black!30,
            shading angle={45},
        ]   ({cos(\Earthangle)+\aM*cos(\Moonangle)*cos(\offsetM)-\bM*sin(\Moonangle)*sin(\offsetM)},%
            {\bE*sin(\Earthangle)+\aM*cos(\Moonangle)*sin(\offsetM)+\bM*sin(\Moonangle)*cos(\offsetM)}) circle (\rM);   
    \end{tikzpicture}
    \caption{Sun, Earth and Moon}
\end{figure}
\end{document}

Related Solutions

[Tex/LaTex] Drawing system architecture in Latex

Maybe something along these lines with TikZ:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{matrix,shapes.multipart,shapes.geometric,fit,scopes}
\tikzset{
  >= latex,
  el/.style={ellipse, draw, text width=8em, align=center},
  rs/.style={rectangle split, draw, rectangle split parts=#1},
  ou/.style={draw, inner xsep=1em, inner ysep=1ex, fit=#1}
}
\begin{document}
\begin{tikzpicture}
  \matrix[matrix of nodes, row sep=5ex, column sep=1em] (mx) {
    INPUT:& |[el]| newspaper text \\
    ANALYSER& |[rs=3]|
    lexical tagger\nodepart{two}morphological analyser\nodepart{three}parser \\
    & |[el]| {analysed newspaper text} \\
    SIMPLIFIER& |[rs=2]| syntactic simplifier\nodepart{two}lexical simplifier \\
    OUTPUT:& |[el]| simplified newspaper text \\
  };
  \node[ou=(mx-2-2)] (ana) {};
  \node[ou=(mx-4-2)] (sim) {};
  {[->]
  \draw(mx-1-2)edge(ana) (ana)edge(mx-3-2) (mx-3-2)edge(sim) (sim)edge(mx-5-2);
  }
\end{tikzpicture}
\end{document}

enter image description here

Or, with MetaPost (compile with lualatex):

\documentclass{article}
\usepackage{luamplib}
\begin{document}
\begin{mplibcode}
input boxes;

nodesep := 15; % space between nodes
ellipdy := 15; % the dy of ellipses

vardef cuta(suffix a, b) = % from Peter Grogono's MetaPost reference manual
  drawarrow a.c -- b.c cutbefore bpath.a cutafter bpath.b;
enddef;

beginfig(1);
  % define contents
  circleit.txt("newspaper text");
  boxjoin(a.sw = b.nw; a.se = b.ne);
  boxit.lext("lexical tagger");
  boxit.mora("morphological analyser");
  boxit.prsr("parser");
  boxjoin();
  circleit.atxt("analysed text");
  boxjoin(a.sw = b.nw; a.se = b.ne);
  boxit.syns("syntactic simplifier");
  boxit.lexs("lexical simplifier");
  boxjoin();
  circleit.stxt("simplified text");

  % position and tweak
  txt.dy  = ellipdy;
  atxt.dy = ellipdy;
  stxt.dy = ellipdy;
  lext.ne - lext.nw = (110,0);
  txt.s  - lext.n = (0,nodesep);
  prsr.s - atxt.n = (0,nodesep);
  atxt.s - syns.n = (0,nodesep);
  lexs.s - stxt.n = (0,nodesep);

  % draw everything
  picture pic; pic := image(drawboxed(lext, mora, prsr););
  draw pic; draw bbox pic;
  drawboxed(txt, atxt);
  pic := image(drawboxed(syns, lexs));
  draw pic; draw bbox pic;
  drawboxed(stxt);
  cuta(txt, lext);
  cuta(prsr, atxt);
  cuta(atxt, syns);
  cuta(lexs, stxt);
endfig;
end;
\end{mplibcode}
\end{document}

enter image description here

[Tex/LaTex] Move Moon on its orbit around the Earth

Run with --shell-escape and needs imagemagick installed.

\documentclass[preview,border={10pt 0pt 10pt 10pt}]{standalone}

\usepackage{filecontents}
\begin{filecontents*}{moon.tex}
\documentclass[tikz,preview,border=15mm]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{3d,calc}

\begin{document}
 \foreach \x in {5,10,...,355}{
\begin{tikzpicture}
    % Earth
    \path[use as bounding box] (-3,-3) rectangle (3,3);
    \shade[ball color=blue!10!white,opacity=0.20] (0,0) circle (1.5);
    \node[align=center](earth) at (0,0) {Earth};

    % Orbitz
    \draw[circle] (0,0) circle (3);

    %Moon
    \shade[ball color=blue!10!white,opacity=0.20] (\x:3) circle (0.5);
    \node[align=center](moon) at (\x:3) {Moon};
\end{tikzpicture}
}
\end{document}

\end{filecontents*}
%
\immediate\write18{pdflatex moon}

% convert to GIF animation
%\immediate\write18{convert -delay 10 -loop 0 -density 400 -alpha remove moon.pdf moon.gif}
%
% convert to PNG
\makeatletter
\immediate\write18{convert -density 200 -alpha on moon.pdf moon-\@percentchar02d.png}
\makeatother

\usepackage{animate}
\begin{document}
\begin{preview}
%\animategraphics[controls,autoplay,loop,scale=<integer>]{<frame rate>}{<PDF filename without extension>}{<left blank>}{<left blank>}
\animategraphics[controls,autoplay,loop,scale=1]{10}{moon}{}{}
\end{preview}
\end{document}

enter image description here

Elliptical orbits:

\documentclass[preview,border={10pt 0pt 10pt 10pt}]{standalone}

\usepackage{filecontents}
\begin{filecontents*}{moon.tex}
\documentclass[tikz,preview,border=-2mm]{standalone}
\usetikzlibrary{calc}
\usetikzlibrary{3d,calc}

\begin{document}
 \foreach \x in {5,10,...,355}{
\begin{tikzpicture}[rotate=-52]
    % Earth
    \clip[use as bounding box,yslant=0.5,xslant=0.5,circle] (0,0) circle (5);
    %\draw[use as bounding box] (-4,-4) rectangle (4,4);
    \shade[ball color=blue!10!white,opacity=0.20] (0,0) circle (1.5);
    \node[align=center](earth) at (0,0) {Earth};

    % Orbitz
    \begin{scope}[yslant=0.5,xslant=0.5]
    \draw (0,0) circle (4);

    %Moon
    \node (\x) at (\x:4) {};
    \node[align=center](moon) at (\x:4) {Moon};
    \end{scope}
    \shade[ball color=blue!10!white,opacity=0.20] (\x) circle (0.5);
\end{tikzpicture}
}
\end{document}


\end{filecontents*}
%
\immediate\write18{pdflatex moon}

% convert to GIF animation
%\immediate\write18{convert -delay 10 -loop 0 -density 400 -alpha remove moon.pdf moon.gif}
%
% convert to PNG
\makeatletter
\immediate\write18{convert -density 200 -alpha on moon.pdf moon-\@percentchar02d.png}
\makeatother

\usepackage{animate}
\begin{document}
\begin{preview}
%\animategraphics[controls,autoplay,loop,scale=<integer>]{<frame rate>}{<PDF filename without extension>}{<left blank>}{<left blank>}
\animategraphics[controls,autoplay,loop,scale=1]{10}{moon}{}{}
\end{preview}
\end{document}

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Drawing system architecture in Latex

[Tex/LaTex] Move Moon on its orbit around the Earth

Related Question