Star Patterns, Constellations and Celestial Coordinates – General Structure of the Solar System (Senior 4 Physics) | Ganzaa

General Structure of the Solar System

Lessons

Senior 4 · Physics

General Structure of the Solar System

4 lessons

Lesson 4 of 4

Star Patterns, Constellations and Celestial Coordinates

25 min

One sky, seen from the middle

Rwanda lies only about 2° south of the equator. That gives its stargazers a rare gift: over a year, almost the whole sky passes overhead. The Southern Cross, a symbol of the far-southern sky, and the Plough (Big Dipper), a symbol of the far north, can both be seen from Kigali at the right season, although each only low over its horizon. Only one famous star is missing: Polaris, the North Star, lies less than 1° from the north celestial pole, which from Rwanda is 2° below the northern horizon, so it never rises. In this lesson you learn how the sky is divided into constellations and how a star's position is given by two kinds of coordinates, one tied to your horizon and one tied to the sky itself.

Star patterns and constellations

People in every culture have joined the brighter stars into pictures: hunters, animals, tools. These patterns made the sky easier to learn and helped people to track the seasons and to navigate. Astronomers needed a single system, so at its first General Assembly, in Rome in 1922, the International Astronomical Union (IAU) agreed a list of 88 constellations covering the whole sky, and in 1930 it published official boundaries for each (IAU). Today a constellation is a defined area of the sky, like a country on a map, and every star lies in exactly one of them. A smaller, familiar pattern inside or across constellations, such as the three stars of Orion's Belt or the Plough, is called an asterism.

The stars of a constellation usually have nothing to do with each other. They only lie in nearly the same direction from Earth; some may be ten times further away than others. Because the Earth turns, the whole pattern rises in the east and sets in the west each night without changing shape, and because the Earth goes round the Sun, different constellations are in the night sky in different months.

Definition

A constellation is one of the 88 regions into which the IAU divides the sky, named after the traditional star pattern within it. An asterism is a recognisable star pattern that is not one of the 88, such as Orion's Belt. The celestial sphere is an imaginary sphere centred on the Earth on which the stars appear to lie; its celestial poles are directly above the Earth's poles and its celestial equator directly above the Earth's equator. Example: Crux, the Southern Cross, is the smallest of the 88 constellations.

The horizontal system: altitude and azimuth

The simplest way to tell a friend where to look uses your own horizon (Figure 4.1):

altitude $h$ : the angle of the star above the horizon, from $0^\circ$ on the horizon to $90^\circ$ at the zenith, the point straight overhead;
azimuth $A$ : the angle measured round the horizon from north, through east, to the point directly below the star, from $0^\circ$ to $360^\circ$ (east is $90^\circ$ , south $180^\circ$ , west $270^\circ$ ).

The horizontal system is easy to use with a simple instrument, but a star's altitude and azimuth change all the time as the Earth turns, and they are different for observers in different places.

Figure 4.1: The horizontal system: altitude above the horizon and azimuth from north through east.

The equatorial system: declination and right ascension

For a catalogue that is the same for everyone at all times, astronomers use coordinates fixed to the celestial sphere, just as latitude and longitude are fixed to the Earth:

declination $\delta$ : the angle of a star north (+) or south (−) of the celestial equator, from $+90^\circ$ at the north celestial pole to $-90^\circ$ at the south celestial pole;
right ascension $\alpha$ : the angle measured eastwards along the celestial equator from a reference point, the March equinox point (where the Sun crosses the celestial equator going north each March), usually given in hours, minutes and seconds, from 0 h to 24 h ( $1\,\mathrm{h} = 15^\circ$ ).

A star's right ascension and declination hardly change over a human lifetime, so they are printed in star catalogues. Right ascension is measured in hours because the sky turns once in a day: a star with right ascension 6 h crosses your meridian (the north–south line through the zenith) 6 hours after a star with right ascension 0 h. More precisely, the stars return to the same place every 23 h 56 min (Unit 7, Lesson 3), so each star rises about 4 minutes earlier each night.

What you see depends on your latitude

The altitude of the celestial pole above your horizon equals your latitude: at the North Pole, Polaris is overhead; at the equator, both celestial poles lie on the horizon. A star crosses your meridian at its highest altitude,

h_{\max} = 90^\circ - |\varphi - \delta|

where $\varphi$ is your latitude (negative in the south) and $\delta$ the star's declination. From Kigali ( $\varphi \approx -2^\circ$ ) the south celestial pole is just $2^\circ$ above the southern horizon, the celestial equator passes $2^\circ$ north of the zenith, and stars rise and set almost vertically (Figure 4.2). Every star with declination between about $-88^\circ$ and $+88^\circ$ rises at some time of year: almost the whole sky.

Figure 4.2: The meridian seen from latitude 2° S: the celestial poles lie almost on the horizon and the celestial equator almost through the zenith.

Definition

Altitude is the angle of a star above the horizon; azimuth is the angle round the horizon from north through east to the point below the star. Declination is the angle of a star north or south of the celestial equator; right ascension is the angle eastwards along the celestial equator from the March equinox point, in hours ( $1\,\mathrm{h} = 15^\circ$ ). The meridian is the imaginary line across the sky from north to south through the zenith. Example: a star with $\delta = 0^\circ$ lies on the celestial equator; seen from the equator itself it passes through the zenith.

Worked example 1: the celestial poles from Kigali and from further south

Find the altitude of the south celestial pole seen from (a) Kigali, latitude $2^\circ$ S, (b) a town at latitude $26^\circ$ S. From which can Polaris be seen?

(a) The altitude of the visible pole equals the latitude: $2^\circ$ above the southern horizon. (b) $26^\circ$ above the southern horizon. From both, the north celestial pole is below the northern horizon (by $2^\circ$ and $26^\circ$ ); Polaris, less than $1^\circ$ from it, stays below the horizon in both places, though only just from Kigali.

Worked example 2: how high will a star climb?

Find the greatest altitude reached by stars of declination (a) $-40^\circ$ , (b) $+60^\circ$ , (c) $-2^\circ$ , seen from Kigali ( $\varphi = -2^\circ$ ).

\text{(a) } h_{\max} = 90^\circ - |-2^\circ - (-40^\circ)| = 90^\circ - 38^\circ = 52^\circ \text{ (above the southern horizon)}

\text{(b) } h_{\max} = 90^\circ - |-2^\circ - 60^\circ| = 90^\circ - 62^\circ = 28^\circ \text{ (above the northern horizon)}

Worked example 3: the sky as a clock

(a) Star X has right ascension 2 h 30 min and star Y has 8 h 00 min. How long after X does Y cross the meridian? (b) A star rises at 21:00 tonight. At about what time will it rise 30 days later?

(a) $8\,\mathrm{h}\,00 - 2\,\mathrm{h}\,30 = 5\,\mathrm{h}\,30\,\mathrm{min}$ later (to within about a minute, since the sky turns once in 23 h 56 min rather than 24 h). In angle, the two stars are $5.5 \times 15^\circ = 82.5^\circ$ apart in right ascension.

(b) Each night the star rises about 4 minutes earlier: $30 \times 4 = 120$ min earlier, at about 19:00. Over a year the shift adds up to a whole day, which is why the constellations visible in the evening change with the seasons.

Warning

Common mistakes. (1) Thinking the stars of a constellation are close together in space: they only lie in the same direction. (2) Measuring azimuth from south or anticlockwise: in this course it is measured from north through east. (3) Treating altitude and azimuth as fixed: they change by the minute; declination and right ascension do not. (4) Forgetting that southern latitudes and declinations are negative in $h_{\max} = 90^\circ - |\varphi - \delta|$ .

Tip

Your latitude is the height of the pole. From Kigali the poles sit on the horizon and the celestial equator runs overhead, so stars rise straight up from the east and set straight down in the west. The equatorial system is the sky's map grid (like latitude and longitude); the horizontal system is your personal "how high, which way".

Naked Eye Observations: Crash Course Astronomy #2, presented by Phil Plait. Watch how the stars appear to turn around the celestial poles, how the constellations change through the year, and how right ascension and declination fix positions on the celestial sphere.

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Practice

Explain why the stars of a constellation need not be close together in space, and why the constellations seen in the evening change through the year.
Find the altitude of the south celestial pole seen from Kigali ( $2^\circ$ S) and from a place at $34^\circ$ S. Which place has more circumpolar stars (stars that never set)?
Find the greatest altitude, seen from Kigali, of stars of declination (a) $+20^\circ$ , (b) $-70^\circ$ .
Which stars can never be seen from Kigali? Which can never be seen from the North Pole?
A star has altitude $30^\circ$ and azimuth $270^\circ$ . Describe where to look.
Two stars have right ascensions 3 h and 11 h. How long after the first does the second cross the meridian, and how many degrees apart are they in right ascension?
A constellation is just rising at 22:00 tonight. At about what time will it rise 45 days from now?
A student argues that a star catalogue should list each star's altitude and azimuth, "because that is what you measure". Evaluate this argument.

Show answersHide answers

The stars only lie in nearly the same direction; their distances can differ greatly. As the Earth moves round the Sun, the night side faces different directions in space, so different constellations are above the horizon at night; each star rises about 4 minutes earlier each night.
$2^\circ$ and $34^\circ$ . The place at $34^\circ$ S: every star within $34^\circ$ of the south celestial pole never sets there, while from Kigali only stars within $2^\circ$ of it are circumpolar.
(a) $90^\circ - |-2^\circ - 20^\circ| = 68^\circ$ above the northern horizon; (b) $90^\circ - |-2^\circ + 70^\circ| = 22^\circ$ above the southern horizon.
From Kigali, only stars within about $2^\circ$ of the north celestial pole ( $\delta \gt +88^\circ$ ), such as Polaris. From the North Pole, every star south of the celestial equator ( $\delta \lt 0^\circ$ ) is never seen.
Azimuth $270^\circ$ is due west; face west and look a third of the way up from the horizon towards the zenith.
8 hours later; $8 \times 15^\circ = 120^\circ$ apart.
$45 \times 4 = 180$ min earlier: at about 19:00.
Altitude and azimuth are what an observer measures, but they change continuously as the Earth turns and differ from place to place, so a catalogue of them would be useful only for one place and one moment. Right ascension and declination are fixed on the celestial sphere and the same for everyone; an observer can convert them to altitude and azimuth for any place and time. The equatorial system is the right choice for catalogues.

Quick check

From Kigali, about 2° south of the equator, where is the south celestial pole?

Key points

The IAU divides the sky into 88 constellations (list agreed in 1922, boundaries published in 1930); their stars lie in the same direction, not necessarily close together.
Horizontal system: altitude (above the horizon) and azimuth (from north through east); it changes with time and place.
Equatorial system: declination (from the celestial equator) and right ascension (eastwards from the March equinox point, in hours, 1 h = 15°); fixed for each star.
Altitude of the celestial pole = latitude; $h_{\max} = 90^\circ - |\varphi - \delta|$ . From Kigali (2° S) almost the whole sky is visible, but Polaris never rises.

1One sky, seen from the middle

2Star patterns and constellations

3The horizontal system: altitude and azimuth

4The equatorial system: declination and right ascension

5What you see depends on your latitude

One sky, seen from the middle

Star patterns and constellations

The horizontal system: altitude and azimuth

The equatorial system: declination and right ascension

What you see depends on your latitude