Orbital elements or Keplerian elements
作者:
ImJaviPerez@gmail.com
最近上传:
4 年前
许可:
Creative Commons CC BY 4.0
摘要:
Elliptical orbital elements or Keplerian elements
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\begin
Discover why 18 million people worldwide trust Overleaf with their work.
\documentclass[compress,9pt]{beamer} % TALK
\usepackage{pgfpages}
\author{ImJaviPerez}
%\setbeameroption{hide notes} % solo muestra la presentación.
%\setbeameroption{show only notes} % solo muestras las notas.
%\setbeameroption{show notes on second screen=right} % presentación el doble de ancha que contiene las diapositivas y las notas.
\usepackage{tikz} %TikZ is required for this to work. Make sure this exists before the next line
\usepackage{tikz-3dplot} %requires 3dplot.sty to be in same directory, or in your LaTeX installation
%\usetikzlibrary{babel}
\begin{document}
% Orbital elements or Keplerian elements
\begin{frame}[fragile,label={frm:elipse+}]
%
\begin{figure}[H]
\centering
\def\r{3.5}
\pgfmathsetmacro{\inclination}{35}
\pgfmathsetmacro{\nuSatellite}{55}
\pgfmathsetmacro{\gammaAngle}{290}
\tdplotsetmaincoords{70}{165}
\begin{tikzpicture}[tdplot_main_coords]
\onslide<1->{
\fill (0,0) coordinate (O) circle (5pt) node[left =7pt] {$M_\oplus$};
% Draw equatorial ellipse
%\tdplotdrawarc[thin]{(0,0,0)}{\r}{-90}{205}{label={[xshift=-3.7cm, yshift=0.9cm]Equatorial plane}}{}
%\tdplotdrawarc[dotted]{(0,0,0)}{\r}{205}{270}{}{}
% Draw equatorial plane
\draw[] (0,-\r,0) -- (\r,-\r,0) node[below]{Equatorial plane} -- (\r,\r,0) -- (-\r,\r,0) -- (-\r,-0.65*\r,0);
\draw[dotted] (-\r,-0.65*\r,0) -- (-\r,-\r,0) -- (0,-\r,0);
% Draw ellipses intersection. Line of nodes
\draw[dashed] (0,-1.3*\r,0) -- (0,1.3*\r,0) node[right] {Line of nodes};
% Draw gamma direction
}
\onslide<2->{
% Set gamma direction
\tdplotsetcoord{Pg}{1.3*\r}{90}{\gammaAngle}
\draw[->] (0,0,0) -- (Pg) node[anchor=east] {Direcc. de referencia $\boldsymbol{\gamma}$};
}
\onslide<1->{
% Create a new rotated system in the center
\tdplotsetrotatedcoords{0}{\inclination}{90}
% Draw orbital ellipse
\tdplotdrawarc[tdplot_rotated_coords,thin,blue]{(0,0,0)}{\r}{-125}{180}{label={[xshift=-5.7cm, yshift=-2.2cm]Orbital plane}}{}
\tdplotdrawarc[tdplot_rotated_coords,dotted,blue]{(0,0,0)}{\r}{180}{235}{}{}
% Define m position
\pgfmathsetmacro{\omegaSatellite}{90}
\pgfmathsetmacro{\xmRot}{\r*cos(\omegaSatellite+\nuSatellite)}
\pgfmathsetmacro{\ymRot}{\r*sin(\omegaSatellite+\nuSatellite)}
\pgfmathsetmacro{\zmRot}{0}
% Draw a vector to m
\draw[tdplot_rotated_coords,thin,->,blue] (0,0,0) -- (\xmRot,\ymRot,\zmRot);
% Draw a mass
\filldraw[tdplot_rotated_coords, blue] (\xmRot,\ymRot,\zmRot) circle (2pt) node[above left] {$m$};
}
\onslide<5->{
% Draw periapsis line
\draw[dashed,tdplot_rotated_coords,blue] (0,0,0) -- (0,\r,0) node[anchor=south west] {Periapsis};
}
\onslide<5->{
% Draw omega angle
\tdplotdrawarc[tdplot_rotated_coords,thick,-stealth,blue]{(0,0,0)}{0.4*\r}{0}{\omegaSatellite}{anchor=south west}{$\omega$}
% Draw nu angle
\tdplotdrawarc[tdplot_rotated_coords,thick,-stealth,blue]{(0,0,0)}{0.4*\r}{\omegaSatellite}{\omegaSatellite+\nuSatellite}{anchor=south west}{$\nu$}
}
\onslide<3->{
% Create rotated shifted system at (0,\r,0)
\tdplotresetrotatedcoordsorigin
\tdplotsetrotatedcoords{0}{0}{180}
% Draw \Omega
% Hidden part of the arc
%% \tdplotdrawarc[tdplot_rotated_coords,dashed,thick,brown]{(0,0,0)}{0.4*\r}{0}{90}{anchor=south}{}%{$\Omega$}
% Visible part of the arc
\tdplotdrawarc[tdplot_rotated_coords,thick,-stealth,brown]{(0,0,0)}{0.4*\r}{\gammaAngle-180}{270}{anchor=north east}{$\Omega$}
% Shift the rotated coordinates
\coordinate (Shift) at (0,\r,0);
\tdplotsetrotatedcoordsorigin{(Shift)}
% \draw[thick,tdplot_rotated_coords,->,blue] (0,0,0) -- (.5,0,0) node[anchor=north west]{$x_2$};
% \draw[thick,tdplot_rotated_coords,->,blue] (0,0,0) -- (0,.5,0) node[anchor=north]{$y_2$};
% \draw[thick,tdplot_rotated_coords,->,blue] (0,0,0) -- (0,0,.5) node[anchor=south west]{$z_2$};
}
\onslide<4->{
% Draw inclination angle
\tdplotsetrotatedthetaplanecoords{0}
\tdplotdrawarc[tdplot_rotated_coords,thick,-stealth,brown]{(Shift)}{0.3*\r}{90}{90-\inclination}{anchor=west}{$i$}
}
\end{tikzpicture}
\caption{Orbital elements or Keplerian elements}\label{fig:elipseNodos2}
\end{figure}
\end{frame}
\end{document}