# Physics Tutorial: Orientation in the Sky and Constellations

In this Physics tutorial, you will learn:

• What is celestial sphere?
• What is the configuration of celestial sphere?
• What are equatorial coordinates? How to calculate them?
• What is horizon?
• What are horizontal coordinates? How to calculate them?
• What are vernal points? When do they occur?
• What are constellations? Which are the most visible constellations in the sky?
• Where do constellations differ from galaxies?
• What are the Zodiac constellations? Do they have any connection to the fate of people?

## Introduction

Do you know how to find the north direction during the night? Can you find the other directions if you know the direction of north?

Do we always see the same celestial bodies at the same position in the sky?

Do we always see the same celestial bodies at the same position in the sky in different periods of year?

How do we take the position of Earth when observing the sky? Does it make any difference if you take another celestial body as a frame of reference? Why?

Like all the other phenomena, the study of the sky requires some reference points as orientation. Recall that all planets of the solar system including Earth revolve around the Sun in elliptic orbits. Stars and planets rotate around their own axis as well. An observer on Earth (if taking Earth as fixed reference system) considers the Sun, Moon and stars as revolving in periodic orbits around it, in very regular periods. This approach puts us in the the same position as our ancestors who believed that the Earth is stationary and all celestial bodies revolve around it. Although we now know that this is not true, this approach is very comfortable in our goal of gaining acquaintance with the sky and all "actors" participating in the nighlty show it offers to our sight.

## Orientation in the Sky

When we study the movement of celestial bodies in the sky for orientation purpose, we are not interested in their distance from Earth but only for their position at a certain period of year. This is because the sky offers a 2 dimensional view to us; our eyes are unable to perceive the dimension of depth when looking at it. Therefore, knowing the distance of a celestial body from Earth would be a useless information when looking at the sky for orientation purposes. Hence, for convenience we can show the position of celestial bodies in 2 coordinates, just like the position of any point on the surface of a sphere. We consider the sky as a very large sphere where all stars lie on its surfaces and Earth is located at centre of this sphere, as shown in the figure below.

From the classical astronomy viewpoint, the figure shows a big sphere known as a celestial sphere, a line PP' collinear to Earth axis, the equator of celestial sphere (shown with dashed line) and the Earth located at centre of sphere. All celestial bodies lie on the surface of celestial sphere. In other words, celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, which may be centered on Earth or the observer. The concept of celestial sphere is mainly used in astronomy and navigation,

There are two questions derived from this approach. First, can we neglect the dimension of Earth when taking it at centre of celestial sphere and second, can we neglect the dimensions of Earth's orbit when using this approach?

The answer is affirmative for both questions. The Earth is so small compared to the dimensions of the celestial sphere that we consider it as just a point at middle of this sphere. The figure above shows an exaggerated size of Earth; it must appear just like a small point at the centre of the sphere.

We know that Earth rotates around its axis from West to East. Hence, we assume the celestial sphere is rotating from East to West, as everything in the celestial sphere is considered from our point of view. Sunrise, moonrise, sunset, moonset, etc., all occur at specific periods of the day. In this type of "motion", the stars do not change their positions in respect of each other. The celestial sphere rotates from East to West like a single body. The imaginary axis PP' of this rotation is collinear to Earth's self-rotation axis. For people living in North hemisphere of Earth (about 90% of world population) the imaginary axis of celestial sphere "punches" the celestial sphere near a very bright star known as the Pole Star (or Polaris). This star is part of the Ursa Minor constellation, which we cover later in this tutorial.

The rotation axis PP' of the celestial sphere is known as the "world axis"; the points where this axis punch the celestial sphere are known as "world poles", namely north and south pole. Stars perform a circular motion during the rotation of the celestial sphere. The perpendicular plane to world axis is called the equatorial plane. Its intersection with the celestial sphere is called celestial equator.

## Equatorial Coordinates

The most used coordinates for representing the objects position in the celestial sphere are equatorial coordinates. These coordinates offer a big advantage over other types of coordinates; they are independent of the observer's location and the time of the observation. This means that only one set of coordinates is sufficient for each object, and the same coordinates can be used by observers in different locations and at different times.

The equatorial coordinate system is basically the projection onto the celestial sphere of the latitude and longitude coordinate system we use here on Earth. By direct analogy, lines of latitude become lines of declination (Dec; measured in degrees, arcminutes and arcseconds) and indicate how far north or south of the celestial equator (defined by projecting the Earth's equator onto the celestial sphere) a celestial body lies. Lines of longitude have their equivalent in lines of right ascension (RA), but unlike in geography, where longitude is measured in degrees, minutes and seconds east the Greenwich meridian, RA here is measured in hours, minutes and seconds east from where the celestial equator intersects the ecliptic (the vernal equinox or vernal point Vp).

In other words, RA represents the angle (expressed in units similar to clock ones) between the meridian plane passing through a given star - the coordinates of which we want to find - and the plane of the zero meridian passing in the direction of Vernal Equinox that acts as a reference meridian. Look at the figure.

Right ascension normally takes the values from 0 to 360°. However, the clock-type values are often preferred for right ascension because the Earth makes one revolution around itself in 24h, the celestial sphere completes one revolution in the same time as well. Therefore, right ascension is often expressed in hours (from 0 to 24 h) with values that increase from West to East.

Regardless of whether the Earth rotates around its own axis or around the the Sun, inclination and right ascension are two immutable values in all hours of the day and in all days of the year. This is because the change in distance due to the Earth revolution around the Sun is so small compared to the distance of stars, that it does not change anything in the position of stars on the celestial sphere. This does not occur when considering the celestial bodies of our solar system because their position in the celestial sphere changes a lot during the year due to orbital revolution of the Earth and planets movement around the the Sun.

### Example 1

Express the RA angle in degrees if RA = 10 hours.

### Solution 1

From theory, we know that a rotation by 360° of Earth around its axis corresponds to 24 h. Hence, we have for the required RA angle in degrees if RA(in hours) = 10 h

RA (in degree) = 3600 × 10 h/24 h = 1500

## Horizontal Coordinates

The Earth has a spherical shape and therefore, an observer cannot see what lies below (or beyond) the horizon. By definition, the horizon is the intersection of the plane tangent with Earth surface and the celestial sphere. More precisely, this represents the true or mathematical horizon, while the observer's horizon is more limited because of obsticles like mountains, hills, etc. We can consider the mathematical horizon as the junction line of sky and sea we observe when we are at middle of the ocean.

We say a star rises when it appears above the horizon (in the evening) and it sets when it disappears from the horizon (in the morning). The highest position of a star in the sky is called the zenith. It is at mid-path of the star's trajectory from east to west in the sky. The star makes the same trajectory from west to east as well, but an observer cannot see this movement because it occurs from the other side of the globe. When the star is at mid-path of this invisible trajectory, we say it is in the nadir (the opposite of zenith).

From the points identified above, it is clear that the position of a star can also be determined in reference to the horizon; in this case, we use the horizontal coordinates to express the position of a star.

The horizon is related to the geographic position of the observer, as the tangent planes in two different locations provides different designs of the sky. Look at the figure.

An observer at the location A can only see the stars above the horizon A (s1, s2, s3, etc.), while another observer at the location B can only see the stars above the horizon B (S4, S5, S6, etc.). After a while, both observers will see a different view of the sky due to the rotation of the Earth around its axis. Likewise, the position of the Earth in different seasons changes in respect to the Sun. Hence, again we have a different view of sky in two different dates despite the hour being the same.

## Ecliptics

We have described the ecliptics as a big circle of celestial sphere obtained by its intersection with the orbital plan of the Earths revolution around the Sun. We assume all planets of the solar system as being on the ecliptics or very close to it, as their orbit forms a very small (negligible) angle to that of the Earth. The Moon also moves very close to ecliptics. We have explained that eclipses occur when the Moon is exactly on ecliptics (hence the name "ecliptics").

The Sun is at different points of ecliptics in various periods of year. It completes one West-to-East revolution in a year that is a whole ecliptic per year. Since ecliptics does not fit to celestial equator, everyday the Sun occupies different positions in the celestial sphere. In other words, the values of right ascension and declination of the Sun (as a common star) are never the same during a year. We have to wait until the same day of the following year to obtain the same identical values of RA and Dec. The same thing is true for planets as well. Moreover, the movement of planets is more complicated than that of the Sun (because of synodic period etc.). Last, the Moon completes one ecliptic every 29 days due to its period of revolution around the Earth.

Vernal points represent the intercept of ecliptic with the celestial sphere. There are two vernal points, which correspond to the two equinoxes (spring and autumn ones).

## The Brightest Stars and Constellations

It is a well established fact that there are billions of stars in the universe. However, we can see only a few thousands of them (the brightest ones) even on a clear moonless night sky. Some stars that appear closer to each other form different patterns when we connect them usinf our mind. Since antiquity, people have associated specific patterns to each group of stars. In general, these patterns bear the names of famous mythological figures of ancient civilization. They had their own method of sky division in pictorial elements. The sets of stars forming such imaginary figures were called constellations. All of them are in the Milky Way galaxy.

Constellations were very useful for the orientation of people travelling at night. However, there is a serious drawback in their use as each nation used their own names and patterns for constellations. Hence, an international agreement was reached at the beginning of 19th century to unify the names and patterns formed by the constellations. By agreement there are, in total, 88 constellations that divide the sky into regions according to the most confirmed figures formed in the sky. These constellations are similar to addresses for the sky.

## Observation of the Sky

Constellations help us orient ourselves in the infinity of stars in the sky. Some patterns (constellations) are more visible than the others. In the following paragraphs, we will introduce the most important ones, which you can use as a reference when needed. For example, the most visible constellation present in the sky in all seasons in the night sky is the Ursa Major constellation, which lies in the northern sky. Its name means "the great bear," or "the larger bear," in Latin. It looks like a saucepan and is located in the Northern Hemisphere of the sky. Ursa Major is formed by 7 stars. Ursa Minor is another constellation very close to Ursa Major in the direction of its body, as shown in the figure.

Between Ursa Major and Ursa Minor there is a long series of stars that form a bent line known as the Draco (Dragon) Constellation as shown in the figure below.

## Spring Constellations

As we explained earlier, we see different stars during different periods of the year. The following figure shows how the sky in the Northern hemisphere looks in summer.

And the following figure shows how the sky of Northern hemisphere looks in summer.

## Zodiac Constellations. The Non-Veracity of Horoscope

The Zodiac is a belt of stars comprising of 12 constellations located near the ecliptics in the celestial sphere. The Latin names of Zodiac constellations with their meaning in English given inside braces are Aries (Ram), Taurus (Bull), Gemini (Twins), Cancer (Crab), Leo (Lion), Virgo (Virgin), Libra (Balance), Scorpius (Scorpion), Sagittarius (Archer), Capricorn (Goat), Aquarius (Water bearer) and Pisces (Fishes). The following figure shows all constellations contained in the Zodiac Belt.

The combination in positions of the Sun, Moon, planets and stars in the Zodiac constellations is misused by certain individuals (astrologers) who claim to know the future of people by "reading" the hidden messages these celestial bodies reveal to humanity through their alignment in the sky. They have invented the "12 Zodiac Signs" that divide people into 12 groups according to their birthday. Astrologers claim that the fate of people is related to the position of stars in the sky. Obviously, such claims are total nonsense, as no sound mind can accept the idea that the fate of humans is related to the position of celestial bodies. Astrology (the pseudo-science that deals with the relationship between humans future and celestial bodies) has no scientific base and the term "astrology" has nothing to do with astronomy - the science dealing with the study of celestial bodies.

## Summary

We consider (for convenience) the sky as a very large sphere where all stars lie on its surfaces with the Earth located at its centre, this sphere is known as the celestial sphere. We know that the Earth rotates around its axis from West to East. Hence, we assume the celestial sphere as rotating from East to West.

The rotation axis PP' of celestial sphere is known as the "world axis"; the points where this axis punch the celestial sphere are known as "world poles", namely north and south pole. Stars perform a circular motion during the rotation of the celestial sphere. The perpendicular plane to world axis is called the equatorial plane. Its intersection with the celestial sphere is called the celestial equator.

The most used coordinates for representing the objects position in the celestial sphere are the equatorial coordinates. The equatorial coordinate system is basically the projection onto the celestial sphere of the latitude and longitude coordinate system we use here on Earth. By direct analogy, lines of latitude become lines of declination (Dec; measured in degrees, arcminutes and arcseconds) and indicate how far north or south of the celestial equator (defined by projecting the Earth's equator onto the celestial sphere) a celestial body lies. Lines of longitude have their equivalent in lines of right ascension (RA), but unlike in geography, where longitude is measured in degrees, minutes and seconds east the Greenwich meridian, RA here is measured in hours, minutes and seconds east from where the celestial equator intersects the ecliptic (the vernal equinox or vernal point Vp).

Horizon is the intersection of the plane tangent with Earth surface and the celestial sphere. We say a star rises when it appears above the horizon (in the evening) and it sets when disappears from the horizon (in the morning). The highest position of a star in the sky is called the zenith. It is at mid-path of the star's trajectory from east to west in the sky. The star makes the same trajectory from west to east as well, but an observer cannot see this movement because it occurs from the other side of the globe. When the star is at mid-path of this invisible trajectory, we say it is in the nadir (the opposite of zenith).

The position of a star can also be determined in reference to the horizon; in this instance, we use the horizontal coordinates to express the position of a star.

Ecliptics is a big circle of celestial sphere obtained by its intersection with the orbital plan of the Earth revolution around the Sun, which is at different points of ecliptics in various periods of year. The values of right ascension and declination of the Sun, planets and Moons are never the same during a year. We have to wait until the same day of the following year to obtain the same identical values of RA and Dec.

Vernal points represent the intercept of ecliptic with the celestial sphere. There are two vernal points, which correspond to the two equinoxes (spring and autumn ones).

Some of the most visible stars that appear close to each other form different patterns, which when we connect them with our mind, form imaginary figures called constellations. They are important to help us find navigate during moonless nights. There are, in total, 88 constellations that divide the sky into regions according to the most confirmed figures formed in the sky.

The most visible constellation present in the night sky is Ursa Major which lies in the northern sky. Ursa Major consists of 7 stars. Ursa Minor is another constellation very close to Ursa Major. Between Ursa Major and Ursa Minor there is a long series of stars that form a bent line known as Draco (Dragon) Constellation.

The Zodiac is a belt of stars comprising 12 constellations located near the ecliptics in the celestial sphere. The Latin names of Zodiac constellations with their meaning in English given inside braces are Aries (Ram), Taurus (Bull), Gemini (Twins), Cancer (Crab), Leo (Lion), Virgo (Virgin), Libra (Balance), Scorpius (Scorpion), Sagittarius (Archer), Capricorn (Goat), Aquarius (Water bearer) and Pisces (Fishes). The following figure shows all constellations contained in the Zodiac Belt.

The combination in positions of the Sun, Moon, planets and stars in the Zodiac constellations is misused by certain individuals (astrologers) who claim to know the future of people by "reading" the hidden messages these celestial bodies reveal to humanity through their alignment in the sky. They have invented the "12 Zodiac Signs" that divide people in 12 groups according their birthday. Astrologers claim that the fate of people is related to the position of stars in the sky. Obviously, such claims are complete nonsense, as no sound mind can accept the idea that the fate of humans is related to the position of celestial bodies. Astrology (the pseudo-science that deals with the relationship between humans future and celestial bodies) has no scientific base and the term "astrology" has nothing to do with astronomy - the science dealing with the study of celestial bodies.

## Orientation in the Sky and Constellations Revision Questions

1. The angle formed by a star to Earth direction has changed by 45° during two observations made. If the first observation was made at 11.30 PM, at what time the second observation is made?

1. 12.00 AM
2. 12.30 AM
3. 1.30 AM
4. 2.30 AM

2. The values of declination and right ascension of a star at a certain instant of the night are 40° North and 10 h West respectively. What will be the horizontal coordinates of the same star after 4 hours? (Consider the fact that the celestial sphere rotates from East to West)

1. 100° North 14 h West
2. 40° North 2 h West
3. 40° North 14 h West
4. 100° South 2 h East

3. A star is actually on its zenith in the sky. When it will be at nadir for the first time after this event?

1. After 6 hours
2. After 12 hours
3. After 26 hours
4. After 48 hours