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StarMaps101.tex
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\documentclass[a4paper,12pt]{extarticle}
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\fancyhead[L]{Star Charts 101}
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\title{{\fontsize{30}{30}\selectfont\textbf{\textsc{Star Charts 101 and Practices}}}}
\author{Fahim Rajit Hossain Shwadhin}
\date{\today}
\begin{document}
\begin{titlepage}
\maketitle
\begin{figure}[H]
\centering
\includegraphics[width=0.35 \linewidth]{ori_1.eps}
\end{figure}
\vspace{1cm}
This practice book is dedicated to all Astronomy enthusiasts and those aiming for cracking Star Charts part of Astronomy and Earth Science Olympiads. It is not a full star atlas but it will fulfill its duty as a practice book. I'll recommend students to \textbf{Print} it then solve problems. Keep it during your exam days as \textbf{only printed materials} are allowed in IOAA. \\
\textit{Written from my experience of both being a participant of two international Olympiads as well as team leader for IOAA since 2018. I've also tried to mix my added experience as a stargazer/amateur astronomer into it!}\\
New versions can be found -- \url{https://github.com/Rajit13/Star-Maps-101-and-Practices}
\vfill{\LaTeX \; compiled and \copyright \; 2025 by \textsf{Fahim Rajit Hossain Shwadhin} is licensed under CC BY-NC-SA 4.0. To view a copy of this license, visit \url{http://creativecommons.org/licenses/by-nc-sa/4.0/} }\\
\hfill \url{[email protected]}
\end{titlepage}
\tableofcontents
\clearpage
\begin{abstract}
{\color{blue} This book delves into the fundamental knowledge necessary for computations associated with studying the sky and the positions of celestial objects, specifically in observational astronomy—focusing on naked-eye observation. It elucidates practical examples that progressively increase in complexity. Initially, memorizing all the constellations might seem daunting for enhanced observational skills. However, contrary to this belief, memorization isn't required. Instead, this book systematically guides you in understanding the sky, allowing you to approach challenges as if solving a puzzle.}
\end{abstract}
\section{Stars, Constellations, and Olympiads}
If you are aiming for Astronomy and Astrophysics Olympiad\footnote{IOAA/IAO} or even Earth Science Olympiad\footnote{IESO} you may find a section where problems contains a star map. So what is a star chart i.e. Sky Map?\\
But before that, you should know some basic concepts i.e. what are Constellations? How stars move across the sky or it affects our observation? \\
\textbf{Constellations} represent apparent patterns formed by stars in the sky, often resembling figures or shapes perceived by humans. For instance, constellations might create recognizable figures like a Man (You may already guess the specific constellation I'm referring to!). They aid in identifying and recalling specific portions of the sky. However, it's important to note that creating random figures or personalized constellations is not officially recognized in Olympiads or by the International Astronomical Union (IAU). The IAU has officially acknowledged 88 constellations, while other popular patterns that are not part of these recognized constellations are referred to as Asterisms (e.g., Summer Triangle, Heavenly G, Big Dipper).\\
In a sky map, constellations are organized as their apparent orientation (projections) in the sky with respect to other celestial objects. In Olympiads question setters provides a sky map of a certain region (latitude $\phi$) and ask students to determine some things or identify objects or constellation. Basics of Celestial Coordinate system is needed to understand the maps as well as solve the problems.
\subsection{Constellation Names}
Each Latin constellation name has two forms: the nominative, for use when talking about the constellation itself, and the genitive, or possessive, which is used in star names. For instance, Hamal, the brightest star in the constellation Aries (nominative form), is also called Alpha Arietis (genitive form), meaning literally, ``the alpha of Aries".\\
All modern constellations were codified in the European scientific subculture prior to the 19th century. As Latin was the international language of science up to that time, Latin governs the pronunciation of constellation names.\footnote{Source: \url{https://www.handprint.com/ASTRO/connames.html}} The Latin names of all the constellations, their abbreviated names and boundaries can be found in the table below. They are a mix of the ancient Greek patterns recorded by Ptolemy as well as some more ``modern" patterns observed later by more modern astronomers.\\
The IAU\footnote{Source: \url{https://www.iau.org/public/themes/constellations/}} adopted three-letter abbreviations of the constellation names at its inaugural General Assembly in Rome in 1922. The abbreviations devised by the IAU each have three letters which in the majority of cases are the first three letters of the constellation name, such as AND for Andromeda, EQU for Equuleus, HER for Hercules, ORI for Orion and so on. This trend is not strictly adhered to in cases where confusion may arise. This happens with the two constellations Leo (abbreviated LEO) and Leo Minor (abbreviated LMI). Similarly, because Triangulum (TRI) may be mistaken for Triangulum Australe, the latter is abbreviated TRA. Other instances occur with Sagitta (SGE) and Sagittarius (SGR) and with Canis Major (CMA) and Canis Minor (CMI) where the first two letters from the second names of the constellations are used. This is also the case with Corona Australis (CRA) and Corona Borealis (CRB) where the first letter of the second name of each constellation is incorporated. Finally, mention must be made of Crater (CRT) which has been abbreviated in such a way as to avoid confusion with the aforementioned CRA (Corona Australis).\\
In Olympiads, students are allowed to use star or constellation names based on their system, yet obtaining permission is necessary for IOAA/IAO/APAO/OWAO competitions. Typically, team leaders should inquire about this with the host jury. Therefore, students from countries like Bangladesh are advised to consistently utilize names designated by the IAU. However, for a comprehensive understanding of the Bangla names of stars and constellations, along with their background stories, students are encouraged to read the book {\color{blue}``\textbf{Tara Porichity} by Abdul Jobbar''}.\\
\textbf{Learning how to recognize constellations}
\begin{enumerate}[1.]
\itemsep0em
\item Write down the list of all the constellations you want to remember (let's call this to be ``C-List")
\item Open the Stellarium app\footnote{Download from: \url{https://stellarium.org/}},
\item Turn the constellation lines on, and the constellation names on.
\item Find all the constellation from the ``C-list," try to remember where they are situated and how they look
\item Turn the constellation names off (leave only the constellation lines on).
\item Try to find all the constellations from the ``C-List" without the ``Search" function. If you can find the constellation, you strike it out of the ``C-list." If not, find it with the ``Search" function, try to remember where it is situated and how it looks.
\item Then, repeat all the previous steps with all the constellations left after the first striking-out. If you can find the constellation you strike it out of the ``C-list". If not, find it with the "Search" function, try to remember where it is situated and how it looks
\item Repeat the striking-out rounds until you have no constellations left in your ``C-list."
\item If you every day repeat steps 1-8 (each day you start with blank ``C-list" with no constellations struck out), just in 4-5 days you will be able to recognize the constellations lines and will have the basic knowledge about how they are situated on the night sky.
\item When you can strike all the constellations from the ``C-list" in one striking out round, you can start repeating all the previous steps, but now with constellation lines turned off. If you repeat these steps every day, just in some days you will get good skills of determining the position of the constellation, and recognizing it by its picture or stars around.
\end{enumerate}
\subsection{Star Names}
Most of the brighter stars were assigned their first systematic names by the German astronomer Johann Bayer in 1603, in his star atlas \textit{Uranometria}. Bayer assigned a lowercase Greek letter, such as alpha ($\alpha$), beta ($\beta$), gamma ($\gamma$), etc., to each star he catalogued, combined with the Latin name of the star’s parent constellation in genitive (possessive) form. (See 88 modern constellations for the genitive forms later on the table.) For example, Aldebaran is designated $\alpha$ Tauri (pronounced Alpha Tauri), which means ``Alpha of the constellation Taurus".\\
A constellation’s most brilliant star is often called Alpha, the first letter in the Greek alphabet. The letters are used with the Latin genitive form of the constellation name, so the Alpha star of Centaurus is called “Alpha Centauri.” But there are few exceptions. For example, Gemini’s brightest star is $\beta$ and that of octans is $\nu$. Here is the lowercase Greek alphabet as used by astronomers:
\begin{table}[H]
\centering
\begin{tabular}{lll}
\begin{tabular}[c]{@{}l@{}}$\alpha$ Alpha\\ $\beta$ Beta\\ $\gamma$ Gamma\\ $\delta$ Delta\\ $\varepsilon$ Epsilon\\ $\zeta$ Zeta\\ $\eta$ Eta\\ $\theta$ Theta\end{tabular} & \begin{tabular}[c]{@{}l@{}}$\iota$ Iota\\ $\kappa$ Kappa\\ $\lambda$ Lambda\\ $\mu$ Mu\\ $\nu$ Nu\\ $\xi$ Xi\\ o Omicron\\ $\pi$ Pi\end{tabular} & \begin{tabular}[c]{@{}l@{}}$\rho$ Rho\\ $\sigma$ Sigma\\ $\tau$ Tau\\ $\upsilon$ Upsilon\\ $\phi$ Phi\\ $\chi$ Chi\\ $\Psi$ Psi\\ $\omega$ Omega\end{tabular}
\end{tabular}
\end{table}
In Olympiad questions, when asked about a star’s name examiners and Jury prefer these Greek letter titles (Flamsteed or Bayer Designation) rather than actual popular name. So it is a wise decision to remember star names by Greek letters.\\
A student should always know which star is the $\alpha$, $\beta$ star for a certain constellation. Specially exceptions. Sometimes you may have to remember special stars designated $\gamma$ or $\zeta$ etc.\\
\textbf{Knowing where the brightest constellation stars are situated}\\
For learning where they are on the night sky, you can use the plan similar to the one for learning the constellations:
You can learn their position with the same plan
\begin{enumerate}[1.]
\item Write down the list of all the stars you want to remember (let's call this to be ``S-List")
\item Open the Stellarium app, try to find a star without turning the names and lines of the constellations on. If you managed to strike it out of the ``S-List."
\item If not, turn on the constellation lines and try to find the star again. If you managed to find it, leave the star in the list without striking it out.
\item If not, find the star with the ``Search" function, try to remember where it is situated and how it looks. Don't strike it out.
\item Repeat the striking-out rounds until you have no stars left in your ``S-list."
\end{enumerate}
If you every day repeat steps 1-5 (each day you start with blank ``S-list" with no stars struck), just in a week, you will be able to recognize the stars on the night sky. You will also have a good knowledge of the relative positions of the constellations.
\clearpage
\begin{table}[H]
\caption{\textbf{Constellation Table}
}
\begin{tabular}{llclll}
\rowcolor[HTML]{EFEFEF}
\multicolumn{1}{c}{\cellcolor[HTML]{EFEFEF}{\color[HTML]{000000} \textbf{No.}}} & {\color[HTML]{000000} \textbf{Constellation}} & {\color[HTML]{000000} \textbf{Location}} & {\color[HTML]{000000} \textbf{Supposed Figure}} & \multicolumn{1}{c}{\cellcolor[HTML]{EFEFEF}{\color[HTML]{000000} \textbf{Code}}} & {\color[HTML]{000000} \textbf{Brightest Star}} \\
1 & Andromeda & N & Andromeda & And & Alpheratz ($\alpha$) \\
2 & Antlia & S & The Air Pump & Ant & {\color[HTML]{000000} $\alpha$ Antliae} \\
3 & Apus & S & The Bird of Paradise & Aps & $\alpha$ Apodis \\
4 & Aquarius & S/Eq & The Water Carrier & Aqr & Sadal Melik ($\alpha$) \\
5 & Aquila & Eq & The Eagle & Aql & Altair ($\alpha$) \\
6 & Ara & S & The Altar & Ara & $\beta$ Arae \\
7 & Aries & N & The Ram & Ari & Hamal ($\alpha$) \\
8 & Auriga & N & The Charioteer & Aur & Capella ($\alpha \ast$) \\
9 & Boötes & N & The Herdsman & Boo & Arcturus ($\alpha$) \\
10 & Caelum & S & The Graving Tool & Cae & $\alpha$ Caeli \\
11 & Camelopardalis & N & The Giraffe & Cam & $\beta$ Camelopardalis \\
12 & Cancer & N & The Crab & Cnc & Al Tarf ($\beta$) \\
13 & Canes Venatici & N & The Hunting Dogs & CVn & Cor Caroli ($\alpha$) \\
14 & Canis Major & S & The Great Dog & CMa & Sirius ($\alpha \ast$) \\
15 & Canis Minor & N/Eq & The Little Dog & CMi & Procyon ($\alpha \ast$) \\
16 & Capricornus & S & The Goat & Cap & Al Giedi ($\alpha$) \\
17 & Carina & S & The Keel & Car & Canopus ($\alpha\ast$) \\
18 & Cassiopeia & N & Cassiopeia & Cas & Schedar ($\alpha$) \\
19 & Centaurus & S & The Centaur & Cen & Rigil Kentaurus ($\alpha \ast$) \\
20 & Cepheus & S & Cepheus & Cep & Alderamin ($\alpha$) \\
21 & Cetus & Eq & The Whale & Cet & Diphda ($\beta$) \\
22 & Chamaeleon & S & The Chameleon & Cha & $\alpha$ Chamaeleontis \\
23 & Circinus & S & The Pair of Compasses & Cir & $\alpha$ Circini \\
24 & Columba & S & The Dove & Col & Phact ($\alpha$) \\
25 & Coma Berenices & N & Berenice’s Hair & Com & $\beta$ Comae Berenices \\
26 & Corona Australis & S & The Southern Crown & CrA & $\alpha$ Coronae Australis \\
27 & Corona Borealis & N & The Northern Crown & CrB & Gemma or Alphecca ($\alpha$) \\
28 & Corvus & S & The Crow & Crv & Gienah ($\gamma$) \\
29 & Crater & S & The Cup & Crt & $\delta$ Crateris \\
30 & Crux & S & The Cross & Cru & Acrux ($\alpha \ast$) \\
31 & Cygnus & N & The Swan & Cyg & Deneb ($\alpha \ast$) \\
32 & Delphinus & N & The Dolphin & Del & Rotanev ($\beta$) \\
33 & Dorado & S & The Goldfish & Dor & $\alpha$ Doradus \\
34 & Draco & N & The Dragon & Dra & Eltanin ($\gamma$) \\
35 & Equuleus & N & The Foal & Equ & Kitalpha ($\alpha$) \\
36 & Eridanus & S/Eq & The River & Eri & Achernar ($\alpha \ast$) \\
37 & Fornax & S & The Furnace & For & $\alpha$ Fornacis \\
38 & Gemini & N & The Twins & Gem & Pollux ($\beta \ast$) \\
39 & Grus & S & The Crane & Gru & Alnair ($\alpha$) \\
40 & Hercules & N & Hercules & Her & Ras Algethi ($\alpha$) \\
41 & Horologium & S & The Pendulum Clock & Hor & $\alpha$ Horologii \\
42 & Hydra & S/Eq & The Water Snake & Hya & Alphard ($\alpha$) \\
43 & Hydrus & S & The Lesser Water Snake & Hyi & $\beta$ Hydri \\
44 & Indus & S & The Indian & Ind & $\alpha$ Indi
\end{tabular}
\end{table}
\clearpage
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\begin{tabular}{llclll}
\rowcolor[HTML]{EFEFEF}
{\color[HTML]{000000} \textbf{No.}} & {\color[HTML]{000000} \textbf{Constellation}} & {\color[HTML]{000000} \textbf{Location}} & {\color[HTML]{000000} \textbf{Supposed Figure}} & {\color[HTML]{000000} \textbf{Code}} & {\color[HTML]{000000} \textbf{Brightest Star}} \\
45 & Lacerta & N & The Lizard & Lac & $\alpha$ Lacertae \\
46 & Leo & N/Eq & The Lion & Leo & Regulus ($\alpha \ast$) \\
47 & Leo Minor & N & Lion Cub & LMi & Praecipua \\
48 & Lepus & S & The Hare & Lep & Arneb ($\alpha$) \\
49 & Libra & S & The Scales & Lib & Zubeneschamali ($\beta$) \\
50 & Lupus & S & The Wolf & Lup & $\alpha$ Lupus \\
51 & Lynx & N & The Lynx & Lyn & $\alpha$ Lyncis \\
52 & Lyra & N & The Lyre & Lyr & Vega ($\alpha \ast$) \\
53 & Mensa & S & The Table Mountain & Men & $\alpha$ Mensae \\
54 & Microscopium & S & The Microscope & Mic & $\gamma$ Microscopii \\
55 & Monoceros & Eq & The Unicorn & Mon & $\beta$ Monocerotis \\
56 & Musca & S & The Fly & Mus & $\alpha$ Muscae \\
57 & Norma & S & The Level & Nor & $\gamma$ Normae \\
58 & Octans & S & The Octant & Oct & $\nu$ Octanis \\
59 & Ophiuchus & Eq & The Serpent Bearer & Oph & Ras Alhague ($\alpha$) \\
60 & Orion & Eq & The Hunter & Ori & Rigel ($\beta \ast$) \\
61 & Pavo & S & The Peacock & Pav & $\alpha$ Pavonis \\
62 & Pegasus & N & Pegasus & Peg & Enif ($\varepsilon$) \\
63 & Perseus & N & Perseus- Demi God & Per & Mirfak ($\alpha$) \\
64 & Phoenix & S & The Phoenix & Phe & Ankaa ($\alpha$) \\
65 & Pictor & S & The Painter’s Easel & Pic & $\alpha$ Pictoris \\
66 & Pisces & N/Eq & The Fish & Psc & Alpherg $(\eta$) \\
67 & Pisces Australis & S & The Southern Fish & PsA & Fomalhaut ($\alpha\ast$) \\
68 & Puppis & S & The Stern & Pup & Naos ($\zeta$) \\
69 & Pyxis & S & The Mariner’s Compass & Pyx & $\alpha$ Pyxidis \\
70 & Reticulum & S & The Net & Ret & $\alpha$ Reticuli \\
71 & Sagitta & S & The Arrow & Sge & $\gamma$ Sagittae \\
72 & Sagittarius & S & The Archer & Sgr & Kaus Australis ($\varepsilon$) \\
73 & Scorpius & S & The Scorpion & Sco & Antares ($\alpha \ast$) \\
74 & Sculptor & S & The Sculptor & Scl & $\alpha$ Sculptoris \\
75 & Scutum & S & The Shield & Sct & Ionnina \\
76 & Serpens & Eq & The Serpent & Ser & Unukalhai ($\alpha$) \\
77 & Sextans & Eq & The Sextant & Sex & $\alpha$ Sextantis \\
78 & Taurus & N/Eq & The Bull & Tau & Aldebaran ($\alpha \ast$) \\
79 & Telescopium & S & The Telescope & Tel & $\alpha$ Telescopii \\
80 & Triangulum & N & The Triangle & Tri & $\beta$ Trianguli \\
81 & Triangulum Australe & S & The Southern Triangle & TrA & Atria ($\alpha$) \\
82 & Tucana & S & The Toucan & Tuc & $\alpha$ Tucanae \\
83 & Ursa Major & N & The Great Bear & UMa & Alioth ($\varepsilon$) \\
84 & Ursa Minor & N & The Little Bear & Umi & Polaris ($\alpha$) \\
85 & Vela & S & The Sail & Vel & Suhail ($\alpha$) \\
86 & Virgo & Eq & The Virgin & Vir & Spica ($\alpha \ast$) \\
87 & Volans & S & The Flying Fish & Vol & $\beta$ Volantis \\
88 & Vulpecula & N & The Fox & Vul & Anser
\end{tabular}
\end{table}
\textbf{$\ast$ Indicates brightest stars in the sky}
\begin{table}[H]
\centering
\begin{tabular}{lllllll}
$\alpha$ And & $\beta$ Aur & $\alpha$ CMa & $\alpha$ Gem & $\alpha$ Ori & $\alpha$ Psc & $\beta$ UMa \\
$\beta$ And & $\alpha$ Boo & $\beta$ CMa & $\beta$ Gem & $\beta$ Ori & $\alpha$ Sco & $\alpha$ UMi \\
$\alpha$ Ari & $\beta$ Boo & $\alpha$ CMi & $\alpha$ Leo & $\alpha$ Oph & $\beta$ Sco & $\beta$ UMi \\
$\beta$ Ari & $\alpha$ Cap & $\beta$ CMi & $\beta$ Leo & $\beta$ Oph & $\alpha$ Ser & $\beta$ Cyg \\
$\alpha$ Aql & $\alpha$ Cas & $\alpha$ CrB & $\alpha$ Lep & $\alpha$ Per & $\varepsilon$ Sgr & \\
$\beta$ Aql & $\beta$ Cas & $\beta$ CrB & $\alpha$ Lib & $\beta$ Per & $\alpha$ Tau & \\
$\alpha$ Aqr & $\alpha$ Cep & $\gamma$ Dra & $\alpha$ Lyr & $\alpha$ Peg & $\beta$ Tau & \\
$\alpha$ Aur & $\alpha$ Cet & $\alpha$ Cyg & $\beta$ Lyr & $\beta$ Peg & $\alpha$ UMa &
\end{tabular}
\caption{Suggested Bright Stars of interest}
\end{table}
\textbf{List of brightest natural objects in the sky}- \url{https://en.wikipedia.org/wiki/List_of_brightest_natural_objects_in_the_sky}
\subsection{Constellation Figures}
In star maps it is common to mark line “patterns” that represent the shapes that give the name to the constellations. However, the IAU defines a constellation by its boundary (indicated by sky coordinates) and not by its pattern and the same constellation may have several variants in its representation.\\
The constellations should be differentiated from asterisms. Asterisms are patterns or shapes of stars that are not related to the known constellations, but nonetheless are widely recognized by laypeople or in the amateur astronomy community. Examples of asterisms include the seven bright stars in Ursa Major known as “the Plough” in Europe or “the Big Dipper” in America, as well as “the Summer Triangle”, a large triangle, seen in the summer night sky in the northern hemisphere and composed of the bright stars Altair, Deneb and Vega. Whilst a grouping of stars may be officially designated a constellation by the IAU, this does not mean that the stars in that constellation are necessarily grouped together in space. Sometimes stars will be physically close to each other, like the Pleiades, but constellations are generally really a matter of perspective. They are simply our Earth-based interpretation of two dimensional star patterns on the sky made up of stars of many differing brightnesses and distances from Earth.\\
In the next page you'll find the official figures from IAU. Notice that you should \textbf{only} remember constellation figures from IAU. You'll find many shapes of same constellation on the internet which might differ due to distortion or variable conditions on their observations.
\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{chart_legend.pdf}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C1.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C2.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C3.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C4.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C5.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C6.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C7.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C8.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C9.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C10.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C11.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C12.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C13.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C14.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C15.eps}
\end{figure}
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C16.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C17.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C18.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C19.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C20.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C21.eps}
\end{figure}
\clearpage
\begin{figure}
\centering
\includegraphics[width=\linewidth]{C22.eps}
\end{figure}
\clearpage
\begin{figure}[H]
\centering
\includegraphics[width=0.5\linewidth]{C23.eps}
\end{figure}
\vspace{1.5cm}
After printing use these constellation images to practice DSOs, planet positions, and angular sizes of a particular projection. Trust me it'll be helpful! A cartoon may describe it like--
\begin{figure}[H]
\centering
\includegraphics[width=0.5\linewidth]{statusb.png}
\end{figure}
\clearpage
\section{Exploring the Moon}
The Moon is by far the most rewarding celestial object for a small telescope. Even a very small instrument will reveal its bleak, blasted landscape of mountain ranges, plains, hills, valleys, and craters. Even binoculars show many features, and there are enough interesting sites on the Moon to keep a telescopic explorer busy forever.
\begin{figure}[H]
\centering
\includegraphics[width=0.9\linewidth]{moon1.png}
\end{figure}
You'll notice right away that except when the Moon is full, it is divided by the terminator, the line separating lunar day and night. Here is where detail shows best. When the Moon is a waxing (growing) crescent, we see the parts on the right edge of the map. At first-quarter phase we see the entire right half, and so on. To use this lunar map, turn the chart until it matches your view. Note: Some telescopes give a mirror image, which will not match this map no matter how you turn it.\\
Refractors and Cassegrain reflectors give mirror images when used with a star diagonal; so does any other instrument containing an odd number of mirrors. If you find this to be a problem, take out the star diagonal and view ``straight through." A correct image is much easier to compare with any map.\\
Once the map is oriented, it will be simple to identify the major craters, mountains, and other features. In time, the geography of this alien world will become as familiar to you as that of our own.
\subsection{Moon's motion}
The Moon's orbital plane has an inclination of $5^\circ9'$ in relation to the ecliptic. Although this angle remains approximately constant, the orbital plane is not fixed, moving such that its axis describes a complete circle around of the ecliptic axis in a period of 18.6 years.\\
Therefore, in relation to the Celestial Equator, the Moon's orbit has an inclination that varies from $18.4^\circ(23.5^\circ - 5.15^\circ$) to $28.7^\circ(23.5^\circ + 5.15^\circ$).\\
Per day, the Moon moves $\dfrac{360^\circ}{27.3 \;\rm days} \approx 13^\circ$ east in relation to the stars. This movement is a reflection of the Moon's revolution around the Earth, which completes every 27.3 days (sidereal month). The Sun moves $\approx 1^\circ$ east per day, therefore the Moon is $\approx 12^\circ$ east of the Sun per day. Because of this, the Moon crosses the local meridian $12^\circ$ . $\dfrac{4 \;\rm min}{1^\circ} \approx 50$ min later than the previous day.
\subsection{Moon's Phase}
\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{mphase1.eps}
\caption{Lunar Phase Geometry}
\end{figure}
From the diagram, $\angle SME= \Psi$ and $MN= CM \cos \measuredangle CMN=r\cos (90^\circ- \measuredangle CME)=r\cos [90^\circ-(90^\circ-\measuredangle SME)]= r \cos \Psi$. So here $\phi$ is phase of the moon, which is the ratio between illuminated part of lunar disk and total visible disk.।
\[\boxed{0 \leq \phi \leq 1}\]
\begin{align}
\phi &=\frac{BN}{AB}=\frac{r+MN}{2r}=\frac{r+r\cos\Psi}{2r} \nonumber \\
\phi&= \frac{1+\cos\Psi}{2}\\
&=\frac{\sin^2\frac{\Psi}{2}+\cos^2\frac{\Psi}{2}+ \cos^2\frac{\Psi}{2}-\sin^2\frac{\Psi}{2}}{2}\nonumber\\
\phi&=\cos^2 \frac{\Psi}{2} \label{lunareqq}
\end{align}
\begin{figure}[H]
\centering
\includegraphics[width=0.7\linewidth]{moon_phase.png}
\caption*{\textsf{\textbf{Question}} Name the Lunar Phase for Northern hemisphere!\\
(Image inverted for printing purposes)}
\end{figure}
\textsf{\textbf{\large Problem: Moon features}}
\begin{enumerate}
\item Match the selenographic objects numbered in the photo and their names and complete the table. Some of the designations of selenographic objects in the list superfluous.
\item Estimate the angular and linear size of the lunar sea No 4, as well as its area (in km$^2$).
\item Mark the Moon's poles with signs • and label them with N (North) and S (South).
\item Mark the landing site for the Apollo 17 mission with an $\times$. Selenographic coordinates this point: $20.2^\circ$ N. lat., $30.8^\circ$ E.
\end{enumerate}
\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{moon2.png}
\end{figure}
\begin{table}[H]
\centering
\begin{tabular}{|l|l|l|l|l|l|lll}
\cline{1-6}
Sea (mare) & No\quad & Sea & No\quad & Crater & No & & & \\ \cline{1-6} \cline{8-9}
Vaporum & & Nectaris & & Aristotle & & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Size} & \multicolumn{1}{l|}{Answer} \\ \cline{1-6} \cline{8-9}
Tranquility & & Homorum & & Kepler & & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Angular} & \multicolumn{1}{l|}{} \\ \cline{1-6} \cline{8-9}
Clarity & & Fecunditatis & & Copernicus & & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Linear} & \multicolumn{1}{l|}{} \\ \cline{1-6} \cline{8-9}
Frigoris & & Imbrium & & Tycho & & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{Area} & \multicolumn{1}{l|}{} \\ \cline{1-6} \cline{8-9}
Crisium & & Nubium & & Eratosthenes & & & & \\ \cline{1-6}
\end{tabular}
\end{table}
\textbf{Word Meaning} Vaporum = Vapour (Steam), Frigoris = Cold, Crisium = Crises, Nectaris = Nectar, Homorum = Moisture, Fecunditatis = Ferticility, Imbrium = Rain, Nubium = Clouds.
\clearpage
\section{Deep Sky Objects}
\textbf{Deep Sky Objects} shortly DSOs are another interesting element of night sky observation as well as Observation round. Deep sky objects can galaxies, star clusters both open and globular or nebula. It is important to know which what and their perspective position in sky. So it is no wonder that someone has already classified these objects in night sky. The one classification now Astronomers widely follow is done by the French astronomer Charles Messier in his Catalogue des Nébuleuses et des Amas d'Étoiles (Catalogue of Nebulae and Star Clusters). Because Messier was only interested in finding comets, he created a list of those non-comet objects that frustrated his hunt for them. The compilation of this list, in collaboration with his assistant Pierre Méchain, is known as the Messier catalogue. This catalogue of objects is one of the most famous lists of astronomical objects, and many Messier objects are still referenced by their Messier number. You can find 3 kinds of catalogue on the star map-- Messier Catalogue (M), New General Catalogue (NGC), Index Catalogue (IC)\\
For Olympiad a student must know the position and type of some DSOs. Here are some of these that I recommend---\\
\textbf{Most Important}: {\color{red} 1, 8, 13, 15, 20, 27, 31, 33, 41, 42, 44, 45, 51, 57, 63, 64, 81, 82, 101, 102, 104.}\\
\textbf{Important}: 6, 7, 11, 16, 17, 18, 22, 40, 43, 67, 74, 76, 78, 83, 94, 97.\\
It is not customary to also remember how a particular DSO looks. But for the fascination of these and to know the structure, some examples should be remembered which are very popular. For instance, Andromeda galaxy, Pleiades or Ring Nebula. In the \nth{12}, 2018 and nth{15}, 2022 IOAA recognizing DSOs by their image was a controversial question. So I'll suggest, \textit{Be safe than sorry}!
\begin{figure}[H]
\centering
\includegraphics[width=0.8\linewidth]{m_o.jpg}
\end{figure}
In the next page the complete list Messier Objects is given.
\clearpage
\begin{table}[H]
\tiny
\centering
\caption{\large Messier Object List}
\label{Messier_list}
\begin{tabular}{cccccccc}
\rowcolor[HTML]{EFEFEF}
{\color[HTML]{000000} \textbf{Messier}} & {\color[HTML]{000000} \textbf{English Name}} & {\color[HTML]{000000} \textbf{Constellation}} & {\color[HTML]{000000} \textbf{Status}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Apparent \\ Magnitude\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Arc Size \\ (In Minute)\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Minimum \\ Aperture\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Coordinates\\ Dec/RA\end{tabular}}} \\
\rowcolor[HTML]{FFFFFF}
\textbf{M1} & Crab Nebula & Taurus & Supernova Remnant & 8.4 & $6\times4$ & 50 mm & $+22^\circ 00'/ 05^h 34^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M2} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Aquarius & Globular Cluster & 6.3 & 13 & Naked Eye & $-00^\circ 49'/ 21^h 33^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M3} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Canes Venatici & Globular Cluster & 6.2 & 16 & Naked Eye & $+28^\circ 22'/ 13^h 42^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M4} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Scorpius & Globular Cluster & 5.9 & 26 & 15 mm & $-26^\circ 31'/ 16^h 23^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M5} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Serpens & Globular Cluster & 6.7 & 17 & Naked Eye & $+02^ 04'/ 15^h 18^m $ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M6} & Butterfly Cluster & Scorpius & Open Cluster & 4.2 & 15 & Naked Eye & $-32^\circ 13'/ 17^h 40.1^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M7} & Ptolemy Cluster & Scorpius & Open Cluster & 3.3 & 80 & Naked Eye & $-34^\circ 47'/ 7^h 53^m$ \\
\rowcolor[HTML]{E6B8AF}
\textbf{M8} & Lagoon Nebula & Sagittarius & Diffuse Nebula & 6 & $90 \times 40$ & Naked Eye & $-24^\circ 23'/ 18^h 03^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M9} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Ophiuchus & Globular Cluster & 8.4 & 9 & 30 mm & $-18^\circ 30'/ 17^h 19^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M10} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Ophiuchus & Globular Cluster & 6.4 & 15 & Naked Eye & $-04^\circ 05'/ 16^h 57^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M11} & Wild Duck Cluster & Scutum & Open Cluster & 6.3 & 14 & Naked Eye & $-06^\circ 16'/ 18^h 51.1^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M12} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Ophiuchus & Globular Cluster & 7.7 & 15 & 15 mm & $-01^\circ 56'/ 16^h 47^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M13} & \begin{tabular}[c]{@{}c@{}}Great Hercules \\ Cluster\end{tabular} & Hercules & Globular Cluster & 5.8 & 17 & Naked Eye & $+36^\circ 27'/ 16^h 41^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M14} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Ophiuchus & Globular Cluster & 8.3 & 12 & 30 mm & $-03^\circ 14'/ 17^h 37^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M15} & \begin{tabular}[c]{@{}c@{}}Great Pegasus \\ Cluster\end{tabular} & Pegasus & Globular Cluster & 6.2 & 12 & Naked Eye & $+12^\circ 10'/ 21^h 29^m$ \\
\rowcolor[HTML]{D9D2E9}
\textbf{M16} & Eagle Nebula & Serpens & Stellar Nebula & 7 & 7 & Naked Eye & $-13^\circ 49'/ 18^h 18^m$ \\
\rowcolor[HTML]{D9D2E9}
\textbf{M17} & Omega Nebula & Sagittarius & Stellar Nebula & 6 & $46\times37$ & 30 mm & $-16^\circ 10'/ 18^h 20^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M18} & Swan & Sagittarius & Open Cluster & 7.5 & 9 & 15 mm & $-17^\circ 08'/ 18^h 19.9^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M19} & \multicolumn{1}{l}{\cellcolor[HTML]{FFF2CC}} & Ophiuchus & Globular Cluster & 7.5 & 14 & 30 mm & $-26^\circ 16'/ 17^h 02^m$ \\
\rowcolor[HTML]{E6B8AF}
\textbf{M20} & Trifid Nebula & Sagittarius & Diffuse Nebula & 6.3 & $28\times 28$ & 30 mm & $-23^\circ 01'/ 18^h 02^m $ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M21} & & Sagittarius & Open Cluster & 6.5 & 13 & 15 mm & $-22^\circ 30' / 18^h 04.6^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M22} & \multicolumn{1}{c}{\cellcolor[HTML]{FFF2CC}Sagittarius Cluster} & Sagittarius & Globular Cluster & 5.1 & 24 & Naked Eye & $-23^\circ 54'/ 18^h 36^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M23} & & Sagittarius & Open Cluster & 6.9 & 27 & Naked Eye & $-19^\circ 01'/ 17^h 56.8^m$ \\
\rowcolor[HTML]{FFFFFF}
\textbf{M24} & \multicolumn{1}{c}{\cellcolor[HTML]{FFFFFF}Sagittarius Star Cloud} & Sagittarius & Star Cloud & 2.5 & $90\times 60$ & Naked Eye & $-18^\circ 29' / 18^h 17^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M25} & & Sagittarius & Open Cluster & 4.6 & 32 & Naked Eye & $-19^\circ 15'/ 18^h 31.6^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M26} & & Scutum & Open Cluster & 8 & 15 & 50 mm & $-09^\circ 24' / 18^h 45.2^m$ \\
\rowcolor[HTML]{D0E0E3}
\textbf{M27} & \multicolumn{1}{c}{\cellcolor[HTML]{D0E0E3}Dumbbell Nebula} & Vulpecula & Planetary Nebula & 7.5 & $8\times6$ & 30 mm & $+22^\circ 43'/ 19^h 59^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M28} & & Sagittarius & Globular Cluster & 7.7 & 11 & 30 mm & $-24^\circ 52'/ 18^h 24^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M29} & Cooling Tower & Cygnus & Open Cluster & 7.1 & 7 & Naked Eye & $+38^\circ 31'/ 20^h 23^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M30} & & Capricornus & Globular Cluster & 7.7 & 11 & 30 mm & $-23^\circ 10'/ 21^h 40^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M31} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Andromeda Galaxy} & Andromeda & Spiral Galaxy & 3.4 & $190.2\times 60$ & Naked Eye & $+41^\circ 16'9''/ 00^h 42^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M32} & & Andromeda & Elliptical Galaxy & 8.1 & $8\times6$ & 30 mm & $+40^\circ51'/ 00^h 42^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M33} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Triangulum Galaxy} & Triangulum & Spiral Galaxy & 5.7 & $70.8\times 41.7$ & Naked Eye & $+30^\circ 39'/ 01^h 33^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M34} & & Perseus & Open Cluster & 5.2 & 35 & Naked Eye & $+42^\circ 46'/ 02^h 42.1^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M35} & & Gemini & Open Cluster & 5.5 & 28 & Naked Eye & $+24^\circ 21'/ 06^h 09.1^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M36} & & Auriga & Open Cluster & 6.3 & 12 & Naked Eye & $+34^\circ 08'/ 05^h 36^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M37} & & Auriga & Open Cluster & 6.2 & 24 & Naked Eye & $+32^\circ 33'/ 05^h 52^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M38} & Starfish Cluster & Auriga & Open Cluster & 7..4 & 21 & Naked Eye & $+35^\circ 51'/ 05^h 28^m $ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M39} & & Cygnus & Open Cluster & 5.5 & 32 & Naked Eye & $+48^\circ 26'/ 21^h 31^m$ \\
\textbf{M40} & \multicolumn{1}{c}{Winnecke 4} & Ursa Major & Double Star & 9.7 & 1 & 50 mm & $+58^\circ 4'/ 12^h 22^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M41} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}Little Beehive} & Canis Major & Open Cluster & 4.5 & 38 & Naked Eye & $-20^\circ 46'/ 06^h 46.0^m$ \\
\rowcolor[HTML]{E6B8AF}
\textbf{M42} & \multicolumn{1}{c}{\cellcolor[HTML]{E6B8AF}Orion Nebula} & Orion & Diffuse Nebula & 4 & $65\times 60$ & Naked Eye & $-05^\circ 23'/ 05^h 35^m$ \\
\rowcolor[HTML]{E6B8AF}
\textbf{M43} & \multicolumn{1}{c}{\cellcolor[HTML]{E6B8AF}De Mairan’s Nebula} & Orion & Diffuse Nebula & 9 & $20\times 15$ & 50 mm & $-05^\circ 16'/ 05^h 35^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M44} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}Praesepe /Beehive} & Cancer & Open Cluster & 3.7 & 95 & Naked Eye & $+19^\circ 59'/ 08^h 40.4^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M45} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}Pleiades} & Taurus & Open Cluster & 1.6 & 110 & Naked Eye & $+24^\circ 07'/ 03^h 47^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M46} & & Puppis & Open Cluster & 6.1 & 27 & Naked Eye & $-14^\circ 49'/ 07^h 41.8^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M47} & & Puppis & Open Cluster & 4.2 & 30 & Naked Eye & $-14^\circ 30'/ 07^h 36.6^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M48} & & Hydra & Open Cluster & 5.5 & 54 & Naked Eye & $-05^\circ 45'/ 08^h 13.7^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M49} & & Virgo & Elliptical Galaxy & 9.4 & 97 & 50 mm & $+08^\circ 00'/ 12^h 29^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M50} & & Monoceros & Open Cluster & 5.9 & 16 & Naked Eye & $-08^\circ 20'/ 07^h 03.2^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M51} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Whirlpool Galaxy} & Canes Venatici & Spiral Galaxy & 8.4 & $11\times8$ & 50 mm & $+47^\circ 11'/ 13^h 29^m $ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M52} & & Cassiopeia & Open Cluster & 5 & 13 & 30 mm & $+61^\circ 35'/ 23^h 24.2^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M53} & & Coma Berenices & Globular Cluster & 8.3 & 13 & 30 mm & $+18^\circ 10'/ 13^h 12^m $ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M54} & & Sagittarius & Globular Cluster & 8.4 & 9 & 50 mm & $-30^\circ 28'/ 18^h 55^m $ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M55} & & Sagittarius & Globular Cluster & 7.4 & 19 & Naked Eye & $30^\circ 57'/ 19^h 39^m $ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M56} & & Lyra & Globular Cluster & 8.3 & 7 & 50 mm & $+30^\circ 11'/ 19^h 16^m$ \\
\rowcolor[HTML]{D0E0E3}
\textbf{M57} & \multicolumn{1}{c}{\cellcolor[HTML]{D0E0E3}Ring Nebula} & Lyra & Planetary Nebula & 8.8 & 1.3 & 50 mm & $+33^\circ 01'/ 18^h 53^m $ \\
\rowcolor[HTML]{00FFFF}
\textbf{M58} & & Virgo & Spiral Galaxy & 10.5 & $5\times4$ & 50 mm & $+11^\circ 49'/ 12^h 37^m $ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M59} & & Virgo & Elliptical Galaxy & 10.6 & $5\times3$ & 50 mm & $+11^\circ 38' 49''/ 12^h 42^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M60} & & Virgo & Elliptical Galaxy & 9.8 & $7\times6$ & 50 mm & $+11^\circ 33'/ 12^h 43^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M61} & & Virgo & Spiral Galaxy & 10.2 & $6\times5$ & 50 mm & $+04^\circ 28'/ 12^h 21^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M62} & & Ophiuchus & Globular Cluster & 7.4 & 14 & 15 mm & $-30^\circ 06'/ 17^h 01^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M63} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Sunflower Galaxy} & Canes Venatici & Spiral Galaxy & 9.3 & $12\times 8$ & 30 mm & $+42^\circ 01'/ 13^h 15^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M64} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Black Eye Galaxy} & Coma Berenices & Spiral Galaxy & 9.4 & $9\times5$ & 50 mm & $+21^\circ 40'/ 12^h 56^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M65} & Leo Triplet & Leo & Spiral Galaxy & 10.3 & $10\times3$ & 30 mm & $+13^\circ 05'/ 11^h 18^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M66} & Leo Triplet & Leo & Spiral Galaxy & 8.9 & $9\times4$ & 30 mm & $+12^\circ 59'/ 11^h 20^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M67} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}King Cobra} & Cancer & Open Cluster & 6.1 & 30 & \multicolumn{1}{l}{\cellcolor[HTML]{D9EAD3}} & $+11^\circ 49'/ 08^h 51.3^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M68} & & Hydra & Globular Cluster & 9.7 & 12 & 50 mm & $-26^\circ 44'/ 12^h 39^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M69} & & Sagittarius & Globular Cluster & 8.3 & 7 & 50 mm & $-32^\circ 20'/ 18^h 31^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M70} & & Sagittarius & Globular Cluster & 9.1 & 8 & 50 mm & $-32^\circ 17'/ 18^h 43^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M71} & & Sagitta & Globular Cluster & 6.1 & 7 & 50 mm & $+18^\circ 46'/ 19^h 53^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M72} & & Aquarius & Globular Cluster & 9.4 & 6 & 50 mm & $-12^\circ 32'/ 20^h 53^m$ \\
\textbf{M73} & & Aquarius & Asterism & 9 & 1 & 50 mm & $-12^\circ 38'/ 20^h 58^m 54^s$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M74} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}The Phantom} & Pisces & Spiral Galaxy & 10 & $10\times9$ & 50 mm & $+15^\circ 47'/ 01^h 36^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M75} & & Sagittarius & Globular Cluster & 9.2 & 6 & 50 mm & $-21^\circ 55'/ 20^h 06^m$ \\
\rowcolor[HTML]{D0E0E3}
\textbf{M76} & \multicolumn{1}{c}{\cellcolor[HTML]{D0E0E3}\begin{tabular}[c]{@{}c@{}}Little Dumbbell \\ Nebula\end{tabular}} & Perseus & Planetary Nebula & 10.1 & $2\times1$ & 50 mm & $+51^\circ 34'/ 01^h 42.4^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M77} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Cetus A} & Cetus & Spiral Galaxy & 9.6 & $7\times6$ & 50 mm & $-00^\circ 00'/ 02^h 42^m$
\end{tabular}
\end{table}
\clearpage
\begin{table}[H]
\centering
\tiny
\begin{tabular}{clcccccc}
\rowcolor[HTML]{EFEFEF}
{\color[HTML]{000000} \textbf{Messier}} & \multicolumn{1}{c}{\cellcolor[HTML]{EFEFEF}{\color[HTML]{000000} \textbf{English Name}}} & {\color[HTML]{000000} \textbf{Constellation}} & {\color[HTML]{000000} \textbf{Status}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Apparent \\ Magnitude\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Arc Size \\ (In Minute)\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Minimum \\ Aperture\end{tabular}}} & {\color[HTML]{000000} \textbf{\begin{tabular}[c]{@{}c@{}}Coordinates\\ Dec/RA\end{tabular}}} \\
\rowcolor[HTML]{E6B8AF}
\textbf{M78} & & Orion & Diffuse Nebula & 8.3 & $8\times6$ & 50 mm & $+00^\circ 00'/ 05^h 46^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M79} & & Lepus & Globular Cluster & 8.6 & 9 & 50 mm & $-24^\circ 31'/ 05^h 24^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M80} & & Scorpius & Globular Cluster & 7.9 & 9 & 50 mm & $-22^\circ 58'/ 16^h 17^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M81} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Bode’s Galaxy} & Ursa Major & Spiral Galaxy & 6.9 & $26\times14$ & Naked Eye & $+69^\circ 3'/ 09^h 55^m$ \\
\textbf{M82} & \multicolumn{1}{c}{Cigar Galaxy} & Ursa Major & Irregular Galaxy & 8.4 & $11\times5$ & 30 mm & $+69^\circ 40'/ 09^h 55^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M83} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Southern Pinwheel} & Hydra & Spiral Galaxy & 7.5 & $11\times10$ & 30 mm & $29^\circ 51'/ 13^h 37^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M84} & & Virgo & Elliptical Galaxy & 10.1 & $5\times4$ & 50 mm & $+12^\circ 53'/ 12^h 25^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M85} & & Coma Berenices & Elliptical Galaxy & 10 & $7\times5$ & 50 mm & $+18^\circ 11'/ 12^h 25^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M86} & & Virgo & Elliptical Galaxy & 9.8 & $7\times5$ & 50 mm & $+12^\circ 56'/ 12^h 26^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M87} & Virgo A & Virgo & Elliptical Galaxy & 9.6 & 7 & 50 mm & $+12^\circ 23'/ 12^h 30^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M88} & & Coma Berenices & Spiral Galaxy & 10.4 & $7\times4$ & 50 mm & $+14^\circ 25'/ 12^h 31^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M89} & & Virgo & Elliptical Galaxy & 10.7 & 4 & 50 mm & $+12°^\circ 33'/ 12^h 35^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M90} & & Virgo & Spiral Galaxy & 10.3 & $10\times5$ & 50 mm & $+13^\circ 09'/ 12^h 36^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M91} & & Coma Berenices & Spiral Galaxy & 11 & $5\times4$ & 60 mm & $+14^\circ 29'/ 12^h 35^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M92} & & Hercules & Globular Cluster & 6.4 & 11 & Naked Eye & $+43^\circ 08'/ 17^h 17^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M93} & & Puppis & Open Cluster & 6 & 22 & 30 mm & $-23^\circ 52'/ 07^h 44.6^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M94} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Cat’s Eye Galaxy} & Canes Venatici & Spiral galaxy & 9 & $11\times9$ & 30 mm & $+41^\circ 07'/ 12^h 50^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M95} & & Leo & Spiral Galaxy & 11.4 & $7\times5$ & 50 mm & $+11^\circ 42'/ 10^h 43^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M96} & & Leo & Spiral Galaxy & 10.1 & $7\times5$ & 50 mm & $+11^\circ 49'/ 10^h 46^m$ \\
\rowcolor[HTML]{D0E0E3}
\textbf{M97} & \multicolumn{1}{c}{\cellcolor[HTML]{D0E0E3}Owl Nebula} & Ursa Major & Planetary Nebula & 9.9 & 3 & 50 mm & $+55^\circ 01'/ 11^h 14^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M98} & & Coma Berenices & Spiral Galaxy & 11 & $10\times3$ & 50 mm & $+14^\circ 54'/ 12^h 13^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M99} & & Coma Berenices & Spiral Galaxy & 10.4 & 5 & 50 mm & $14^\circ 24'/ 12^h 18^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M100} & & Coma Berenices & Spiral Galaxy & 10.1 & $7\times6$ & 50 mm & $+15^\circ 49'/ 12^h 22^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M101} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Pinwheel Galaxy} & Ursa Major & Spiral Galaxy & 7.9 & $27\times26$ & 50 mm & $+54^\circ 20'/ 14^h 03^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M102} & \multicolumn{1}{c}{\cellcolor[HTML]{F3F3F3}Spindle Galaxy} & Draco & Elliptical Galaxy & 10.7 & $6\times 3$ & 50 mm & $+55^\circ 45'/ 15^h 06^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M103} & & Cassiopeia & Open Cluster & 7.4 & 6 & 30 mm & $+60^\circ 42'/ 01^h 33.2^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M104} & \multicolumn{1}{c}{\cellcolor[HTML]{00FFFF}Sombrero Galaxy} & Virgo & Spiral Galaxy & 9 & 94 & 50 mm & $-11^\circ 37'/ 12^h 39^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M105} & & Leo & Elliptical Galaxy & 10.2 & $5\times4$ & 50 mm & $+12^\circ 34'/ 10^h 47^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M106} & & Canes Venatici & Spiral Galaxy & 9.1 & $18\times8$ & 30 mm & $+47^\circ 18'/ 12^h 18^m$ \\
\rowcolor[HTML]{FFF2CC}
\textbf{M107} & & Ophiuchus & Globular Cluster & 8.9 & 10 & 30 mm & $-13^\circ 03'/ 16^h 32^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M108} & & Ursa Major & Spiral Galaxy & 10.7 & $8\times2$ & 50 mm & $+55^\circ 40'/ 11^h 11^m$ \\
\rowcolor[HTML]{00FFFF}
\textbf{M109} & & Ursa Major & Spiral Galaxy & 10.6 & $8\times5$ & 50 mm & $+53°^\circ 22'/ 11^h 57^m$ \\
\rowcolor[HTML]{F3F3F3}
\textbf{M110} & & Andromeda & Elliptical Galaxy & 9 & $7\times10$ & 50 mm & $+41^\circ 41'/ 00^h 40^m$ \\
\rowcolor[HTML]{D9EAD3}
\textbf{M111} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}\begin{tabular}[c]{@{}c@{}}Western Part of \\ Double Cluster\end{tabular}} & Perseus & Open Cluster & 4.5 & 30 & Naked Eye & - \\
\rowcolor[HTML]{D9EAD3}
\textbf{M112} & \multicolumn{1}{c}{\cellcolor[HTML]{D9EAD3}\begin{tabular}[c]{@{}c@{}}Western Part of \\ Double Cluster\end{tabular}} & Perseus & Open Cluster & 4.5 & 30 & Naked Eye & -
\end{tabular}
\end{table}
For Table (\ref{Messier_list}), In the next table here is the color code meaning--
\begin{table}[H]
\centering
\begin{tabular}{|c|}
\hline
\rowcolor[HTML]{FFF2CC}
\textbf{Globular Cluster} \\
\rowcolor[HTML]{D0E0E3}
\textbf{Planetary Nebula} \\
\rowcolor[HTML]{D9D2E9}
\textbf{Stellar Nebula} \\
\rowcolor[HTML]{E6B8AF}
\textbf{Diffuse Nebula} \\
\rowcolor[HTML]{D9EAD3}
\textbf{Open Cluster} \\
\rowcolor[HTML]{00FFFF}
\textbf{Spiral Galaxy} \\
\rowcolor[HTML]{F3F3F3}
\textbf{Elliptical Galaxy} \\
\rowcolor[HTML]{FFFFFF}
\textbf{Other} \\
\hline
\end{tabular}
\caption{Messier Object Color Code}
\end{table}
\textbf{Some key facts about Messier Objects}
\begin{itemize}
\item Only 34 out of 88 constellations contain Messier Objects
\item Sagittarius contains the most about 35 where Virgo have 11, Coma Berenices have 8, Ursa Major and Ophiachus with 7 each, Canes Venatici and Leo contains 5 each, and Scorpius contains 4.
\item The list of 109 objects compiled by C. Messier contains many of the fines deep sky objects however observed from Paris. So far southern sky was lost to him. That's why 62 of his objects lie in these 8 constellations, famously known as Messier Northern Bias.
\end{itemize}
\clearpage
\subsection{Short Problems and Solutions on DSOs}
\fbox{\begin{minipage}{43em}
For data related to the problems below refer to the Messier Object List table.
\end{minipage}}\\
\textsf{\textbf{Question 1}} The latitude of the location is $60^\circ$ N. Questions 1.1 to 1.4 refer to the same location, but may not refer to the sky on the same day/night. \\
\textbf{Object of consideration:} Butterfly Cluster (M6), Trifid Nebula (M20), Wild Duck Cluster (M11), Ring Nebula (M57), Albireo, Arcturus, Rasalhague, M3.\\
1.1 \textbf{Which object/star cannot be seen at this location at any time of the year?}
\begin{sol}
-- M6 as You cannot see any object below $-30^\circ$ declination.
\end{sol}
1.2 \textbf{Which object below cannot be seen on the night of the vernal equinox at midnight?}
\begin{sol}
-- Wild Duck Cluster (M11), At midnight of the Vernal Equinox, the meridian is 12h. As such, any object within 6h to 18h will not be able to be seen. That is apart from those that are circumpolar.
\end{sol}
1.3 \textbf{If M3 is currently at the local meridian, in how many hours will Albireo set?}
\begin{sol}
-- If M3 is at the local Meridian, then Albeiro would be just rising. As such, it will set in 12 hours.
\end{sol}
1.4 \textbf{Which object will be closest to the zenith when it culminates on the local meridian?}
\begin{sol}
-- Ring Nebula (M57), We look for the item with the declination is the closest to +60◦, which is local zenith at that location.
\end{sol}
\textsf{\textbf{Question 2}} A deep-sky object located directly at the celestial equator with an angular diameter of $10'$ is viewed from the eyepiece of a telescope with a true field of view of $0.8^\circ$. Object tracking on the telescope is disabled and the object is aligned at the edge of the field of view. Assuming the object moves along the diameter of the eyepiece before disappearing, calculate the time it takes for the object to drift out of view of the eyepiece.
\begin{sol}
-- Objects on the Celestial Equator in the sky rotate once every sidereal day, that is, $360^\circ$ in $23^h56^m4.1^s$. This gives $0.251^\circ$/min. The time it takes to drift out of the eyepiece is thus--
\[\frac{0.8^\circ}{0.251^\circ/\rm min}=3.19\; \rm min\]
\end{sol}
\textsf{\textbf{Question 3}} Imagine that you are in a post-COVID world without travel restrictions and are currently on a stargazing trip in a remote location at a latitude of $35^\circ$ N. Capella (RA/DE: 5h 18m / +46 deg 01min) is currently 3 degrees above the western horizon. The following table shows a list of DSOs you have decided to try to observe for tonight. \\
\textbf{Object of consideration:} Heart Nebula, Omega Centauri, Black-Eye Galaxy, Dumbbell Nebula. \\
\textbf{In what order, from highest to lowest priority, should you arrange your observations so as to maximise your chances of seeing every one of the DSOs on your list?}
\begin{sol}
-- Omega Centauri, Black Eye Galaxy, Dumbbell Nebula, Heart Nebula\\
A quick calculation ($90^\circ-61^\circ= 29^\circ$) shows us that the Heart Nebula is circumpolar and thus has lower priority. Ideally, one would want to view it when it is near the meridian, and judging by the RA (which is earlier than Capella), it is around its lower culmination. The Dumbbell Nebula has a RA of 20h, indicating that it is on the eastern side of the sky and thus would have lower priority. Between Omega Centauri and the Black Eye Galaxy, the latter has a slightly earlier RA and thus is normally prioritized if we are near the equator. However, at northern latitudes, objects with more southern declinations spend less time above the horizon and thus set faster. While we normally need spherical trigonometry to ascertain which objects set earlier, there is a very small difference in RA between Omega Centauri and Black Eye Galaxy (31 minutes). Omega Centauri will set earlier and thus should be prioritized. (Note: Omega Centauri is very barely visible.)
\end{sol}
\textsf{\textbf{Question 4}} \textbf{Object of consideration:} Triangulum Galaxy, Andromeda Galaxy, Orion Nebula, Dumbbell Nebula and Eskimo Nebula where it has apparent magnitude of 10.1 and apparent size of $0.8\times 0.8$. \\
\textbf{Calculate the surface brightness of each DSO in $\rm mag/arcsec^2$, and hence arrange them in order of increasing surface brightness.}
\begin{sol}
-- Triangulum Galaxy, Andromeda Galaxy, Orion Nebula, Dumbbell nebula, Eskimo
Nebula.\\
The calculated surface brightness of the objects are\\
• Triangulum: 23.3\\
• Andromeda: 22.5\\
• Orion: 21.87\\
• Dumbbell: 20.6\\
• Eskimo: 18.5
\end{sol}
\fbox{\begin{minipage}{42em}
$^{\color{red} \ast}$\textbf{Surface Brightness:} The total luminosity emitted by a column of linear area $dA =\Omega r^2$. Generally presented as,
$$\Sigma \approx \frac{F}{\Omega} \approx \frac{L}{4\pi d^2 \, \pi (R/d)^2} \approx \frac{L}{4\pi^2 R^2}; \quad \;\rm Unit: Wm^{-2}ster^{-1}$$
Surface Magnitude: Logarithmic form of Surface brightness, generally presented as,
$$\mu = -2.5\, \log\, \Sigma +C$$
Just like any other magnitude term you can't easily multiply, add or subtract $\mu$. The unit of $\mu$ is $\rm mag/arcsec^2$. To understand this suppose a star has a surface magnitude of $13\, \rm mag/arcsec^2$, it is actually comparable to a star with angular area of $1\, \rm arcsec^2$ to seem to have an apparent magnitude of $13^m$.
\end{minipage}}
\vspace{0.5 cm}
\textsf{\textbf{Question 5}} You are given a list of the following planetary nebulae for an upcoming observation session near the Equator. \\
\textbf{Object of consideration:} M27 (Dumbbell Nebula), M57 (Ring Nebula), M76 (Little Dumbbell Nebula), M97 (Owl Nebula), C39 (Eskimo Nebula), C63 (Helix Nebula).\\
\textbf{What are planetary nebulae? Briefly describe how they are formed.}
\begin{sol}
-- They are emission nebulae surrounding the cores of old red giants. As these stars exhaust their fuel, the core contracts under its own gravity, increasing its temperature and
increasing the luminosity. These conditions cause the red giant star to lose most of its outer layers to space, which are subsequently ionised by the hot remnant core/white dwarf to form these planetary nebulae.
\end{sol}
\textbf{A proper observation plan should be sorted by the time objects rise. Sort the objects in this list by the order in which they rise, with the earliest object first.}
\begin{sol}
-- M76 $\rightarrow$ C39 $\rightarrow$ M97 $\rightarrow$ M57 $\rightarrow$ M27 $\rightarrow$ C63
\end{sol}
\textbf{Suppose that during one night, you notice that the Owl Nebula is
setting. Other than the Owl Nebula, what objects are above the
horizon right now?}
\begin{sol}
-- M57, M27, C63.
\end{sol}
\textsf{\textbf{Question 6}} \textbf{In a mildly light-polluted night sky with a surface brightness of $19.4\; \rm mag/arcsec^2$, which of the above objects are visible with the naked eye}.
\begin{sol}
-- Orion Nebula and Andromeda Galaxy,\\
Dumbbell Nebula and Eskimo Nebula are too small to be seen with the naked eye. Triangulum Galaxy requires very dark skies (around Bortle 2 and below, which is around a surface brightness of 21 and above). Surface brightness is not a completely reliable predictor of visibility. Other factor like the actual luminosity distribution of the object are more important in affecting visibility. For instance, both the Orion Nebula and Andromeda Galaxy have extremely bright central cores.\\
\underline{Note:} This question would benefit those who have actually burnt midnight oil to go stargazing.
\end{sol}
\textsf{\textbf{Question 7}} \textbf{Observe the Andromeda Galaxy (M31) then draw the approximate shape and size of the galaxy that you see through the binoculars in the frame below with correct orientation.}
\begin{figure}[H]
\centering
\includegraphics[width=0.4\linewidth]{andromedasize.eps}
\end{figure}
\textbf{Caution:}\\
{\color{red} Correct shape and size (between 0.5 to 1 degrees)-- \textbf{3 points}\\
Correct orientation (within $23^\circ$ of the picture) -- \textbf{ 2 points}}
\clearpage
\section{Star Charts}
A star chart or star map is a map of the night sky. Astronomers divide these into grids to use them more easily. They are used to identify and locate astronomical objects such as stars, constellations and galaxies. They have been used for human navigation since time immemorial. Note that a star chart differs from an astronomical catalog, which is a listing or tabulation of astronomical objects for a particular purpose.
\subsection{Coordinate Lines}
To help with navigation, some star maps include coordinate lines that allow you to more accurately track down a faint fuzzy or an interesting object. The coordinates right ascension (RA) and declination (dec) – roughly equivalent to longitude and latitude on Earth – are sometimes marked on a star map. RA and dec (also represented by the Greek letter $\delta$) are coordinates marking a star’s (or galaxy’s) position with respect to two points in the sky:
\begin{itemize}
\item The celestial equator (a line in the sky directly above the Earth’s equator). This can be represented by a straight line or a curve depending on viewing position but one key point to remember is that this line always goes from East, \textit{E} to West\textit{ W}.
\item RA is measured as the angular distance along the celestial equator from the First Point of Aries, a position on the celestial equator in the constellation of Pisces. Rather than measure this angle in degrees, RA is measured in hours, minutes and seconds, so that the whole circle around the Earth is 24 hours.\footnote{I'll cover very little of Celestial Coordinate system here so knowledge of the different coordinate system--their conversion and how to draw a celestial sphere is presumed here. We'll need some hardcore knowledge of the time keeping systems also. I would suggest you read ``Astronomy Principles and Practice" by Roy and Clarke: Subchapters 8.1 – 8.5, 8.8 – 8.9, and 8.11}
\begin{figure}[H]
\centering
\includegraphics[width=\linewidth]{cel.png}
\caption{Celestial Sphere for EQS and ECS}
\end{figure}
Therefore, when someone says that Canopus has an RA of $06^h 24^m$, it means that it's RA coordinate is just over one quarter of the way around the sky ($6^h$ is one-quarter of $24^h$) from the First Point of Aries. RA is always measured eastward from the First Point of Aries.
\end{itemize}
\begin{table}[H]
\centering
\begin{tabular}{|c|l|c|}
\hline
System & \multicolumn{1}{c|}{Coordinates} & Interval \\ \hline \hline
Equatorial & \begin{tabular}[c]{@{}l@{}}$\delta$: declination\\ $\alpha$: right Ascension\end{tabular} & \begin{tabular}[c]{@{}c@{}}$-90^\circ \leq \delta \leq +90^\circ$\\ 0h $\leq \alpha \leq$ 24h\end{tabular} \\ \hline
Horizontal & \begin{tabular}[c]{@{}l@{}}$a$: altitude\\ $A$: azimuth\end{tabular} & \begin{tabular}[c]{@{}c@{}}$-90^\circ \leq a \leq +90^\circ$\\ $0^\circ \leq A \leq 360^\circ$\end{tabular} \\ \hline
\begin{tabular}[c]{@{}c@{}}Equatorial\\ Time\end{tabular} & \begin{tabular}[c]{@{}l@{}}$\delta$: declination\\ $H$: hour angle\end{tabular} & \begin{tabular}[c]{@{}c@{}}$-90^\circ \leq \delta \leq +90^\circ$\\ 0h $\leq H \leq$ 24h\end{tabular} \\ \hline
Ecliptic & \begin{tabular}[c]{@{}l@{}}$b$: ecliptic latitude\\ $l$: ecliptic longitude\end{tabular} & \begin{tabular}[c]{@{}c@{}}$-90^\circ \leq b \leq +90^\circ$\\ $0^\circ \leq l \leq 360^\circ$\end{tabular} \\ \hline
Galactic & \begin{tabular}[c]{@{}l@{}}$B$: galactic latitude\\ $L$: galactic longitude\end{tabular} & \begin{tabular}[c]{@{}c@{}}$-90^\circ \leq B \leq +90^\circ$\\ $0^\circ \leq L \leq 360^\circ$\end{tabular} \\ \hline
\end{tabular}
\caption{Summery of Celestial Coordinate Systems}
\end{table}
\clearpage
\subsection{Projections}
A stereographic projection is mostly used, as is the convention for printed star maps. A planisphere is this type of star chart. But you might encounter different projects or a map of Horizon Views, showing the stars above the horizon as seen from a specified observing site at a given date and time. Another famous projection style which we also use for geographical position is Mercator projections. You'll encounter basically these 3 types of map projections. Now we will discuss each type of these maps and their pros and cons.
\subsubsection{Horizon Views}
Horizon views shows the portion of the sky that is viewed by a Telescope Field of View (FOV) or Human eye. In astronomy, the field of view is the amount of sky you can see, whether with your unaided vision, binoculars, or a telescope. The FOV of a telescope varies due to usage of different telescope eyepieces whereas human eye spans approximately $120^\circ$ of arc. So FOV is an important part of these maps as they also provide us with a crucial information--the Range of the Sky! Also, a telescope which has a much smaller field of view will have significant advantages, such as greater magnification and light-gathering power.
\begin{figure}[H]
\centering
\includegraphics[width=0.6\linewidth]{Hor_1.png}
\caption{View toward horizon from $23^\circ$ N $89^\circ$ E, azimuth $0^\circ$ (N) Wed 2022 Jan 26 0:27 UTC. Here the FOV is $75^\circ$}.
\end{figure}
To measure other information about the location of the observing place the chart should contain the \textit{Pole star} or the Azimuth of the sky portion should be close $0^\circ$. As we know the altitude of the Pole star is equal to the latitude of the Observing place, this makes the whole procedure easy. \\
One might ask how can we know the scale of the image? Your scale is the Ursa Major/Minor constellation itself! But with this particular viewing the longitude of the observing place can not be determined easily. But using the Dipper clock orientation you can determine the current month of the observation provided that you know the time when it was observed. This is important as same sky viewing constellation will be present at night once a year. But another thing to remember is that if you've seen this portion of the sky at midnight today, you can find the same orientation after 6 months at midday [If there was no atmosphere which we can do using Stellarium].\\
You'll get the same result for 06-26-2022 at 12:27 UTC. Don't just believe me try it yourself! A clever use of these type of maps are done in IOAA-18 O3 (See Figure \ref{A2018_O3}).
\begin{figure}[H]
\centering
\includegraphics[width=0.9\linewidth]{skyhorizon.png}
\caption{a) $55^\circ$ N, b) $45^\circ$ N, c) $35^\circ$ N.}
\end{figure}
The effect of changing latitude on Horizon views. Travelling south causes constellations in the north to sink towards the horizon.