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Draw an oscillating circle on a sphere ?

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Hello there, I have a sphere and I want to draw a circle on the surface of the sphere somewhere above the equator. I did this, but I also want to draw an additional circle on the same place which has an oscillatory behavior (oscillating on the z-direction). I tried to do it, but I got a result which doesn't please me. Is there an elegant way of drawing the oscillating circle? (So I can modify the color of the line, the thickness, and all that stuff) Thank you in advance!

Here is my code that I made so far:

j = 1;
t1 = 2;
t2 = 10*t1;
a = 0.1;
th0 = 45*\[Pi]/180;
om1 = (2 \[Pi])/t1;
om2 = (2 \[Pi])/t2;
s1 = SphericalPlot3D[j, {\[Theta], 0, Pi}, {\[Phi], 0, 2 Pi}, 
   PlotStyle -> White];
s2 = ParametricPlot3D[{Cos[u]*Cos[th0], Sin[u]*Cos[th0], 
    Sin[th0]}, {u, 0, 2 \[Pi]}, PlotStyle -> {Red, Thick}];
s3 = ParametricPlot3D[{Cos[om2*t]*Cos[th0], Sin[om2*t]*Cos[th0], 
   Sin[th0] + a*Cos[om1*t]}, {u, 0, 2 \[Pi]}, {t, 0, 20}, 
  PlotStyle -> {Red, Thick}]
Show[s1, s2, s3]
POSTED BY: Robert Poenaru
Answer
12 days ago

This may be similar to what you need:

Show[s1, s2, 
 ParametricPlot3D[
  FromSphericalCoordinates[{j, th0 + .2 Cos[10 t], t}], {t, -Pi, Pi}]]
POSTED BY: Gianluca Gorni
Answer
12 days ago

Hey there,

Thank you for the response :)

The oscillations which are drawn with your command are on the surface of the sphere. What I want is to have them oscillate only in the z-axis direction (so, up and down). Do you know how can I do this?

POSTED BY: Robert Poenaru
Answer
11 days ago

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