From e47c4d3deb95a6003869194655a5a1de0922eb7b Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?=D0=90=D0=BB=D0=B5=D0=BA=D1=81=D0=B5=D0=B9=20=D0=A8=D0=B5?= =?UTF-8?q?=D0=BF=D0=B5=D0=BB=D0=B5=D0=B2?= Date: Thu, 6 Jun 2024 22:34:45 +0200 Subject: [PATCH] semi shadow lunar eclipse scheme --- sections/geometrical-astronomy/eclipses.tex | 152 +++++++++++++++++++- 1 file changed, 147 insertions(+), 5 deletions(-) diff --git a/sections/geometrical-astronomy/eclipses.tex b/sections/geometrical-astronomy/eclipses.tex index c512614..6d39453 100644 --- a/sections/geometrical-astronomy/eclipses.tex +++ b/sections/geometrical-astronomy/eclipses.tex @@ -18,7 +18,7 @@ \subsection{Затмения} \tkzDefLine[tangent from = X](C1,R1) \tkzGetPoints{A1}{B1} \tkzDefLine[tangent from = X](C2,R2) \tkzGetPoints{A2}{B2} - \tkzDrawPolygon[fill=gray!40,draw=none](X,A1,B1) + \tkzDrawPolygon[fill=gray!70,draw=none](X,A1,B1) \tkzDrawCircles[fill=white, thick, draw=black](C1,R1 C2,R2) \tkzDrawSegments(X,A2 X,B2 X,C2 C2,A2 C2,B2 C1,A1 C1,B1) @@ -72,7 +72,7 @@ \subsection{Затмения} %%% draw - \tkzDrawPolygon[fill=gray!40,draw=none](X,A1,B1) + \tkzDrawPolygon[fill=gray!70,draw=none](X,A1,B1) \tkzDrawPolygon[fill=white,draw=none](X,H1,H2) \tkzDrawCircles[fill=white, thick, draw=black](C1,R1 C2,R2 C3,R3) @@ -192,7 +192,7 @@ \subsection{Затмения} \tkzInterLL(S',M')(S'',M'') \tkzGetPoint{I''} - \tkzDrawPolygon[fill=gray!40,draw=none](M',I'',M'') + \tkzDrawPolygon[fill=gray!70,draw=none](M',I'',M'') \tkzDrawCircles[black, thick, fill=white](E,e S,s M,m) @@ -768,13 +768,20 @@ \subsection{Затмения} \tkzInterLL(E,x)(I,E'') \tkzGetPoint{I''} % Draw shadow - \tkzDrawPolygon[fill=gray!40,draw=none](E',I,E'') + \tkzDrawPolygon[fill=gray!70,draw=none](E',I,E'') % Draw objects \tkzDrawCircles[black, thick, fill=white](E,e) \tkzDrawCircles[black, thick, fill=white](S,s) \tkzDrawCircles[black, thick, fill=white](M,m) + \begin{scope}[ + dim style/.style={black, latex-latex, opacity=1}, + dim fence style/.style={black, opacity=1} + ] + \tkzDrawSegment[opacity=0, dim={$D$, -1.6cm, below=2pt}](S,E) + \end{scope} + \tkzDrawSegments(S,I E,M S,S' S,S'' E,E' E,E'' M,M' E,I'') \tkzDrawSegments[semithick](S',I S'',I) \tkzDrawSegments[dashed](M,I') @@ -791,7 +798,7 @@ \subsection{Затмения} \tkzMarkAngle[arc=lll, size=1.5](I,E,M) \tkzLabelAngle[pos=1.7](I,E,M){\footnotesize$\gamma$} - \tkzDrawPoints(S, S') + \tkzDrawPoints(S, S', S'') \tkzDrawPoints(E, E', E'') \tkzDrawPoints(M, M') \tkzDrawPoints(I, I', I'') @@ -799,11 +806,146 @@ \subsection{Затмения} \tkzLabelSegment[right](S,S'){$R_0$} \tkzLabelSegment[right](E,E'){$R$} \tkzLabelSegment[right=-1pt,pos=0.4](M,M'){$r$} + \tkzLabelSegment[above=-1pt,pos=0.45](E,M){$d$} \end{tikzpicture} \caption{} \label{pic:eclipses-full-lunar-eslipse} \end{figure} +\begin{figure}[h!] + \centering + \tikzsetnextfilename{eclipses-semi-shadow-lunar-eclipse} + \begin{tikzpicture} + \footnotesize + + % Radius of the Sun + \def\RS{1.4} + + % Radius of the Earth + \def\RE{0.9} + + % Radius of the Moon + \def\RM{0.4} + + % Earth orbit radius + \def\AE{5} + + % Moon orbit radius + \def\AM{2} + + \tkzInit[ + xmax=3.0, + xmin=-6.5, + ymin=-2.2, + ymax=2.2 + ] + + \tkzClip + + % ALPHA + \pgfmathsetmacro\ALPHA{asin((\RS + \RE) / \AE)} + + % BETA + \pgfmathsetmacro\BETA{acos((\RE - \RM) / \AM)} + + % GAMMA + \pgfmathsetmacro\GAMMA{90 + \ALPHA - \BETA} + + % Earth + \tkzDefPoint(0,0){E} + \tkzDefCircle[R](E,\RE) \tkzGetPoint{e} + + % Sun + \tkzDefShiftPoint[E](-\AE,0){S} + \tkzDefCircle[R](S,\RS) \tkzGetPoint{s} + + % Moon + \tkzDefShiftPoint[E](\AM,0){m} + \tkzDefPointBy[rotation=center E angle \GAMMA](m) \tkzGetPoint{M} + \tkzDefCircle[R](M,\RM) \tkzGetPoint{m} + + % Intersections of Sun-Earth and common tangent to Sun and Earth + \tkzDefPointBy[homothety=center S ratio (\RS / (\RS - \RE))](E) + \tkzGetPoint{I} + \tkzDefPointBy[homothety=center S ratio (\RS / (\RS + \RE))](E) + \tkzGetPoint{I'} + + % Full shadow tangent points of the Sun + \tkzDefLine[tangent from = I](S,s) \tkzGetPoints{S'}{x} + \tkzDefPointBy[reflection = over S--E](S') \tkzGetPoint{S''} + + % Semi-shadow tangent points of the Sun + \tkzDefLine[tangent from = I'](S,s) \tkzGetPoints{SsS'}{x} + \tkzDefPointBy[reflection = over S--E](SsS') \tkzGetPoint{SsS''} + + % Full shadow tangent points of the Earth + \tkzDefLine[tangent from = I](E,e) \tkzGetPoints{E'}{x} + \tkzDefPointBy[reflection = over S--E](E') \tkzGetPoint{E''} + + % Semi-shadow tangent points of the Earth + \tkzDefLine[tangent from = I'](E,e) \tkzGetPoints{SsE'}{x} + \tkzDefPointBy[reflection = over S--E](SsE') \tkzGetPoint{SsE''} + + % Tangent point of the Moon + \tkzDefLine[tangent from = I'](M,m) \tkzGetPoints{M'}{x} + + % Projection of the center of the Moon to the radius of the Earth + \tkzDefPointBy[projection=onto E--SsE'](M) \tkzGetPoint{I''} + + % Semishadow + \tkzDefPointBy[homothety=center SsE'' ratio -1.7](I') \tkzGetPoint{Ss1} + \tkzDefPointBy[homothety=center SsE' ratio -1.7](I') \tkzGetPoint{Ss2} + + % Draw semishadow + \tkzFillSector[gray!30](I',Ss1)(Ss2) + \tkzFillSector[white](I',SsE'')(SsE') + \tkzDrawSegments[semithick](SsS',Ss2 SsS'',Ss1) + + % Draw shadow + \tkzDrawPolygon[fill=gray!70,draw=none](E',I,E'') + + % Draw objects + \tkzDrawCircles[black, thick, fill=white](E,e) + \tkzDrawCircles[black, thick, fill=white](S,s) + \tkzDrawCircles[black, thick, fill=white](M,m) + + \begin{scope}[ + dim style/.style={black, latex-latex, opacity=1}, + dim fence style/.style={black, opacity=1} + ] + \tkzDrawSegment[opacity=0, dim={$D$, -1.6cm, below=2pt}](S,E) + \tkzDrawSegment[opacity=0, dim={$d$, 1.1cm, below right=1pt, pos=0.46, fill=none}](M,E) + \end{scope} + + \tkzDrawSegments(S,I E,M S,S' S,S'' E,E' M,M' E,SsE' E,SsE'' S,SsS' S,SsS'') + \tkzDrawSegments[semithick](S',I S'',I) + \tkzDrawSegments[dashed](M,I'') + + \tkzMarkRightAngles[size=0.15](I,E',E I,S',S S,S'',I SsE',M',M E,SsE',Ss2 S,SsS',I' I',SsS'',S Ss1,SsE'',E M,I'',SsE') + + \tkzMarkAngle[arc=l, size=0.5](E,I',SsE') + \tkzLabelAngle[pos=0.7](E,I',SsE'){\footnotesize$\alpha$} + + \tkzMarkAngle[arc=ll, size=0.2](M,E,SsE') + \tkzLabelAngle[pos=0.4](M,E,SsE'){\footnotesize$\beta$} + + \tkzMarkAngle[arc=lll, size=0.4](I,E,M) + \tkzLabelAngle[pos=0.6](I,E,M){\footnotesize$\gamma$} + + \tkzDrawPoints(S, S', S'', SsS', SsS'') + \tkzDrawPoints(E, E', E'', SsE', SsE'') + \tkzDrawPoints(M, M') + \tkzDrawPoints(I, I') + + \tkzLabelSegment[left](S,S''){$R_0$} + \tkzLabelSegment[left](E,SsE'){$R$} + \tkzLabelSegment[right=-1pt,pos=0.4](M,M'){$r$} + \end{tikzpicture} + \caption{} + \label{pic:eclipses-semi-shadow-lunar-eclipse} +\end{figure} + + \term{Синодический месяц}~--- промежуток времени между одинаковыми фазами Луны, равен 29.53 суток. \term{Драконический месяц}~--- промежуток времени между двумя последовательными прохождениями Луны через один и тот же узел орбиты,~--- 27.21 суток.