3d Orbits um Sphäre mit Koordinaten oder Punkten auf Umlaufbahn

\documentclass{article} 
\usepackage{tikz, tikz-3dplot} 
\usetikzlibrary{calc,fadings,decorations.pathreplacing}

%% helper macros
\newcommand{\pgfmathsinandcos}[3]{% 
  \pgfmathsetmacro#1{sin(#3)}% 
  \pgfmathsetmacro#2{cos(#3)}% 
} 
\newcommand{\LongitudePlane}[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
  \tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand{\LatitudePlane}[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % latitude
  \pgfmathsetmacro\yshift{\cosEl*\sint}
  \tikzset{#1/.style={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} % 
}
\newcommand{\OrbitPlane}[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
  \tikzset{#1/.style={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand{\DrawLongitudeCircle}[2][1]{
  \LongitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1}}
   % angle of "visibility" 
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1); 
  \draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1); 
}
\newcommand{\DrawLatitudeCircle}[2][1]{
  \LatitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1}}
  \pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)} 
  % angle of "visibility"
  \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}  
  \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1); 
  \draw[current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}
\newcommand{\DrawOrbitCircle}[2][1]{
  \OrbitPlane{\angEl-8}{#2} % orbit kippen!!!
  \tikzset{current plane/.prefix style={scale=#1}}
   % angle of "visibility" 
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  % original
    \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1); % sichtbarkeit des vor der kugel befindlichen bereichs
   \draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1); 
   } % achtung unten auch eine winkeländerung !!!???

%% document-wide tikz options and styles
\tikzset{%
  >=latex, % option for nice arrows 
  inner sep=0pt,%
  outer sep=2pt,%
  mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,fill=black,circle}%
}

\begin{document} 
\begin{tikzpicture}

%% some definitions 
\def\R{4} % sphere radius
\def\rr{5} % orbit radius?
\def\angEl{35} % elevation angle 
\def\angAz{-105} % azimuth angle 
\def\angPhi{-40} % longitude of point P 
\def\angBeta{25} % latitude of point P

%######################################################################
%% working planes
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\tikzset{xyplane/.style={cm={cos(\angAz),sin(\angAz)*sin(\angEl),-sin(\angAz),cos(\angAz)*sin(\angEl),(0,-\H)}}}
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhi}
\LongitudePlane[yzplane]{\angEl}{\angAz+90}
\LatitudePlane[equator]{\angEl}{0}
\OrbitPlane[orbplanetwo]{\angEl-8}{\angAz} % dem orbit oben und unten winkel anpassen
\OrbitPlane[orbplane]{\angEl-8}{\angAz+60} % dem orbit oben und unten winkel anpassen

%######################################################################
%% draw xyplane and sphere
\fill[ball color=white!50!gray] (0,0) circle (\R); % 3D lighting effect
\draw[white] (0,0) circle (\R);

%% characteristic points
\path[orbplane] (\angBeta+10:\R/1) coordinate[mark coordinate,color=black] (P1); % works fine
\path[orbplane] (\angBeta+10:\rr/1) coordinate[mark coordinate,color=blue] (P2); % works fine

%#############################-problem-#########################################
\path[orbplanetwo] (\angPhi+50:\R/1) coordinate[mark coordinate,color=orange] (A1); % not at the expected position ???
\path[orbplanetwo] (\angBeta:\rr/1) coordinate[mark coordinate,color=orange] (A2); % not at the expected position ???

%##-wanted position of the orange dots-#####
\node at (-0.93,0) {o};
\node at (-1.15,0.05) {O};

%######################################################################
% Äquator, Orbit, Subspur etc.
%% draw meridians and latitude circles
\DrawLatitudeCircle[\R,yellow]{0} % equator
\DrawOrbitCircle[\rr,cyan]{\angAz+60} % orbit plane drehen !!!
\DrawOrbitCircle[\R,green]{\angAz+60} % orbit subspur !!!
\DrawOrbitCircle[\rr,red]{\angAz} % orbit plane drehen !!!
\DrawOrbitCircle[\R,red]{\angAz} % orbit subspur !!!

\end{tikzpicture} 
\end{document}