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增加双曲线轨迹的复杂性

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增加双曲线轨迹的复杂性

Jubobs 生成了此代码绘制双曲线轨迹。

如果我们画一条与双曲线相交的水平线（我真的不想把它添加到图片中），我们会有一些角度。我想制作这个角度90。我们该怎么做？我知道我们可以使用rotate around，但我们要旋转什么才能保持轨迹的方向相同？ (0,0)不是重点，我们需要旋转多少？

此外，轨迹必须16193.6与地心偏移 千米。因此，如果我们想让轨迹以6878千米的距离在近地点经过地球，我们需要偏移2.3544。

有没有更清洁的方法？

\usepackage{tikz}
\begin{document}

\begin{center}
  \begin{tikzpicture}[scale=2]
    \pgfmathsetmacro{\e}{1.44022}               % eccentricity of the hyperbola
    \pgfmathsetmacro{\a}{1}
    \pgfmathsetmacro{\b}{\a*sqrt((\e)^2 - 1)}
    \pgfmathsetmacro{\c}{sqrt((\a)^2+(\b)^2}    % distance from centre to focus
    \pgfmathsetmacro{\Earthradius}{0.1}        % Earth radius
    \pgfmathsetmacro{\UFOradius}{.03}
    \pgfmathsetmacro{\thetamax}{1.2}

    \draw plot[domain = -\thetamax:\thetamax] ({\a*cosh(\x)}, {\b*sinh(\x)});

    \path (\c,0) node(a) {\includegraphics[width=.5cm]{earth.png}};

  \pgfmathtruncatemacro{\N}{8}  % an even number is best here
  \pgfmathsetmacro{\thetaoffset}{.05*\thetamax}
  \foreach \k in {0,1,...,\N}{
    \pgfmathsetmacro{\theta}{(\thetamax-\thetaoffset)*(2*\k/\N-1)}
        \shade[top color=black,bottom color=gray]
            ({\a*cosh(\theta)}, {\b*sinh(\theta)}) circle (\UFOradius);

    }
    \end{tikzpicture}
\end{center}
\end{document}

以下是一张粗略的图画： 在此处输入图片描述

答案1

我最后只是围绕焦点旋转一切a*e

在此处输入图片描述

 \begin{center}
          \begin{tikzpicture}[line join = round, line cap = round, scale = 4,
            >=triangle 45]
            \draw (2.2,0) -- (.46,0.13);
            \draw (0.57,0) -- (2.2,0);
            \draw[rotate around = {-43.9:(.576088,0)}] (0,0) -- (.65,0);
            \begin{scope}[decoration = {markings,
                mark = at position 0.2 with {\arrow{>}},
                mark = at position 0.7 with {\arrow{>}}, }]
              \pgfmathsetmacro{\e}{1.44022}
              \pgfmathsetmacro{\a}{.4}
              \pgfmathsetmacro{\b}{\a*sqrt((\e)^2 - 1)}
              \pgfmathsetmacro{\c}{sqrt((\a)^2+(\b)^2}
              \pgfmathsetmacro{\Earthradius}{0.1}
              \pgfmathsetmacro{\Sunradius}{0.17}
              \pgfmathsetmacro{\UFOradius}{.02}
              \pgfmathsetmacro{\thetamax}{1.5}

              \shade[%                                                            
              top color=yellow!70,%                                               
              bottom color=red!70,%                                               
              shading angle={45},%                                                
              ] (2.2,0) circle (\Sunradius);

              \draw[postaction = decorate, rotate around = {-43.9:(.576088,0)}]
              plot[domain = -\thetamax:\thetamax]
              ({\a*cosh(\x)}, {\b*sinh(\x)});

              \path (\c,0) node(a) {\includegraphics[width=.5cm]{earth.png}};

              \pgfmathtruncatemacro{\N}{6}  % an even number is best here         
              \pgfmathsetmacro{\thetaoffset}{.05*\thetamax}
              \foreach \k in {0,1,...,\N}{
                \pgfmathsetmacro{\theta}{(\thetamax-\thetaoffset)*(2*\k/\N-1)}
                \shade[top color = black, bottom color = gray, rotate around
                = {-43.9:(.576088,0)}]
                ({\a*cosh(\theta)}, {\b*sinh(\theta)}) circle (\UFOradius);
 }
            \end{scope}
            \begin{scope}[rotate around = {-43.9:(.576088,0)}]
              \draw (0,0) -- (46.0254:1.25cm);
              \draw (0,0) -- (-46.0254:1.25cm);
              \draw (-46.0254:.2cm) arc (-46.0254:46.0254:.2cm);
          \node[scale = .75, fill = white, inner sep = .01cm] at (23:.2cm)
              {$\beta$};
              \node[scale = .75, fill = white, inner sep = .01cm] at (-23:.2cm)
              {$\beta$};
            \end{scope}
          \end{tikzpicture}
        \end{center}

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