# How to draw a diagram for "Rope Around the Earth" problem?

I would like to produce an image to help students to better understand the celebrated Rope Around the Earth'' problem, which asks---how much slack must be added to a tightly fitting rope around the earth's equator in order to uniformly elevate the rope 1 foot uniformly above the equator.

I would be grateful if someone suggest how to do this with the image of a circular cord (rope image, if possible) circumscribing a 2 (or three)-dimensional earth at the equator with the two radii labeled.

• I added the photo from the old question so it's clearer for future visitors. Oct 19 '20 at 18:36
• I've never used it but with metapost there is this mp-geo and with pstrick there is that ctan pst-geo Oct 19 '20 at 19:07
• @Alenanno Thank you for the edit, as well as for your excellent answer! Oct 19 '20 at 19:49

So I tried to reproduce the graphics you posted but removing the circle around the Earth and using it to make the equator. Yes, it's a shaded sphere but its position is accurate, trust me.

You can replace the shaded sphere in the code with an actual image of Earth, but here I'm using this one as en example because I was not sure about matters of copyright. Download here

## Code

\documentclass[tikz, margin=10pt]{standalone}

\usetikzlibrary{calc, arrows.meta}

\newcommand\earth{5cm} % the image's width/height
\newcommand\myclip{\earth/2-1.2pt} % clips the black borders from the sphere

\tikzset{%
lbl/.style={text=black,anchor=west, at end}
}

\begin{document}
\begin{tikzpicture}

\begin{scope}
\clip (0,0) circle (\myclip);
\node[inner sep=0, circle,opacity=.8] (earth) at (0,0) {\includegraphics[width=\earth, keepaspectratio]{earth.jpg}}; % save the image in the same folder as this .tex file
\draw[line width=1.5pt, yellow!40!orange]
($(0,0)+(-\myclip-1pt,0)$) arc (180:360:2.5cm+1pt and 8mm);
\end{scope}
\draw[line width=2pt] (0,0) circle (\myclip+1cm);

\draw[line width=1pt,
red, {Stealth[scale=1.5]}-{Stealth[scale=1.5]}]
(80:\myclip+1.5mm) arc (80:25:\myclip+1.5mm) node[lbl] {$C_E$};
\draw[line width=1pt,
violet,{Stealth[scale=1.5]}-{Stealth[scale=1.5]}]
(80:\myclip+1.2cm) arc (80:25:\myclip+1.2cm) node[lbl] {$L_R$};

\draw[line width=1pt] node[fill,inner sep=1pt, circle] at (earth) {}
edge[red, -{Stealth[scale=1.5]}] node[lbl] {$R_E$} (290:\myclip)
edge[violet, -{Stealth[scale=1.5]}] node[lbl] {$R_R$} (320:\myclip+1cm)
;

\end{tikzpicture}
\end{document}

Compile with Asymptote.

Step 1: Find an image in svg of earth on the internet! Example: an image

Step 2: Convert it (from svg to eps), save as for example Glose.eps. Online tool like https://convertio.co/vn/svg-eps/.

Step 3: Create asy code and put Glose.eps in the same folder.

unitsize(1cm);

label(graphic("Globe.eps","width=5cm"),(0,0));
clip(scale(2.5)*unitcircle);
layer();

pair center=(0,0);

draw(scale(2.5)*unitcircle,linewidth(0.7bp));
draw(scale(3)*unitcircle,linewidth(0.7bp));

draw(scale(.7)*Label("$R_E$",EndPoint,black),center--center+2.5*dir(-65),red,Arrow);
draw(scale(.7)*Label("$R_R$",EndPoint,black),center--center+3*dir(-40),blue,Arrow);
draw(scale(.7)*Label("$C_E$",BeginPoint,black),arc(center,2.65,30,80),red,Arrows);
draw(scale(.7)*Label("$L_R$",BeginPoint,black),arc(center,3.15,30,80),blue,Arrows);
dot(center,linewidth(2bp));

shipout(bbox(2mm,invisible));

The result:

• A good Asymptote answer \ _(+_+)_/ too! Oct 22 '20 at 20:06

A PSTricks solution only for either fun or comparison purposes.

\documentclass[pstricks,dvipsnames]{standalone}
\usepackage{pst-geo}
\psset
{
Decran=9.6,
path=C:/texlive/2020/texmf-dist/tex/generic/pst-geo/data,
}

\begin{document}
\begin{pspicture}(-5,-5)(5,5)
\WorldMapThreeD[circles=false,blueEarth=true]
\pscircle{4}
\psset{linewidth=3pt,arrows=->,arrowinset=0}
\psline[linecolor=blue](4;-40)
\psline[linecolor=red](2.5;-70)
\uput[-40](4;-40){$R_R$}
\uput[-70](2.5;-70){$R_E$}
\psset{arrows=<->}
\psarc[linecolor=blue](0,0){4.25}{10}{80}
\psarc[linecolor=red](0,0){2.75}{10}{80}
\uput[-60](4.25;10){$L_R$}
\uput[-45](2.5;10){$C_E$}
\end{pspicture}
\end{document}

RotX=-45,
RotZ=-45,
PHI=45,
THETA=30,

Add them to the first \psset.

• +1 Good PSTricks answer. :-(
– user213378
Oct 22 '20 at 8:31
• You can visit my blog! I will show all my Asymptote knowledge in that blog. :-)))
– user213378
Oct 24 '20 at 16:43
• @TrongVuong1998: You should add Google Adsense to make more money there! Oct 24 '20 at 20:54
• It is a nonprofit blog! :-((
– user213378
Oct 24 '20 at 21:01
• @TrongVuong1998: Make getting a profit as a side effect. :-) Oct 24 '20 at 21:06

Instead of using LaTeX, you can also use Asymptote code to generate a graph. It is compatible with LaTeX, so you can use this code in a LaTeX interpreter.

• Welcome to TeX.SE! This already suggested TrongVuong1998. He also show how to draw this image with asymptote ... Oct 20 '20 at 7:25