How can I make a simple 3D graphic as in the following image? Figure
I know it is simply a sphere and a circle with several joining lines but I dont know how to make such simple one. I can use ParametricPlot3D to draw the sphere $(\cos[u]\cos[v],\cos[u]\sin[v],\sin[u])$ for $-\pi\leq u,v\leq\pi$ and the circular orbit which can be taken as the intersection of the sphere with a twice radius and the plane $y+z=0$ or $x-y+z=0$. But I can not simplify the figure, i.e., making the sphere transparent so that the data can be put inside it and etc.


2 Answers 2


Do a "Satellite" search on Demonstrations Project. You can find things like these:

The Effect of the Spherical Harmonic Gravitational Potential on Satellite Orbits, by Pradipto Ghosh

Also take a look at this post.

enter image description here


This is the simple figure I was looking for.

(* Parametric form of the unit sphere in 3D *)
α[t_, s_] = {Cos[s] Cos[t], Cos[s] Sin[t], Sin[s]};
(* Scale $α$ with $r$ and rotate in such a way that it is perpendicular to the vector $n$ *)
(* This will help in setting the position of the orbit of the satellite *)
β[t_, r_, n_] = r*RotationMatrix[{Cross[α[0, 0], α[π/2, 0]], n}].α[t, 0];
(* Parametric form of the orbit of the satellite *)
orbit[t_] = β[t, Sqrt[2], {1, -2, 1}];
(* The initial and the current position of the satelite*)
ip = orbit[0];
cp = orbit[π/2];
(* The projection of the current position of the satellite onto the plane $z=0$ *)
cpp = {cp[[1]], cp[[2]], 0};
(* The angle between the projection point and the $x$-axis *)
cppa = VectorAngle[cpp, {1, 0, 0}];
(* Plot in 3D*)
    ParametricPlot3D[{α[u, 0], α[π/2, u], orbit[u]}, {u, -π, π}, AxesOrigin -> {0, 0, 0}, Boxed -> False, PlotStyle -> {{Black}, {Black}, {Black}}, Ticks -> None, ViewPoint -> {2, 1, 1}, ImageSize -> 400], 
    Graphics3D[{{PointSize[Large], Gray, Point[ip]}, {PointSize[Large], Point[cp]}, {PointSize[Small], Point[cpp]}}], 
    Graphics3D[{Dashed, Line[{{0, 0, 0}, cp, cpp, {0, 0, 0}}]}], 
    Graphics3D[{Text[Style["x", Italic, 14], {1.5, 0, 0}], Text[Style["y", Italic, 14], {0, 1.2, 0}],  Text[Style["z", Italic, 14], {0, 0, 1.5}], Text[Style["Initial position", 14], ip + {0, 0, -0.25}], Text[Style["Current position", 14], cp + {0, 0, 0.25}], Text[Style["ℓ", 16], cp/2 + {0, 0, 0.1}], Text[Style["θ", 14], {0.4*Cos[cppa/2], 0.4*Sin[cppa/2], 0}], Text[Style["ρ", 14], cpp/2 + {0.1, 0.1, 0}]}], 
    ParametricPlot3D[0.2*α[u, 0], {u, 0, cppa}, PlotStyle -> Directive[Dashed]]
(* See for traditional axes style in 3D - http://math.stackexchange.com/a/16499/53441 *)


  • $\begingroup$ However, I have a little problem with the positioning of the image. How can I make it fit the Image box (which appears in orange color when the image is selected) with everything visible? When I click on the image and select Trim Bounding Box some parts become missing. $\endgroup$
    – bkarpuz
    Commented Dec 21, 2012 at 9:46
  • $\begingroup$ Using Ctrl + Drag works for cropping the output figure but it is the original size when exported. This therefore didn't work for me. $\endgroup$
    – bkarpuz
    Commented Dec 21, 2012 at 11:19
  • $\begingroup$ Crtl + Shift helps in repositioning the output figure manually, and it applies to the exported file too unlike Ctrl + Drag. $\endgroup$
    – bkarpuz
    Commented Dec 22, 2012 at 14:29
  • $\begingroup$ Use the options SphericalRegion -> True for the Show[] function if you want to get rid of the jumping. $\endgroup$
    – B flat
    Commented Dec 27, 2016 at 22:02

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.