Explain the terms right ascension and declination and use a star map and planisphere.
There are many ways of locating stars and constellations in the night sky. Two of these are by using
star maps and planispheres.
Here are some example sky maps for the northern hemisphere:
One useful feature of these star maps is that the grid lines (not shown in the examples above) are
similar to those on a conventional map.
Latitude and Longitude are terrestrial co-ordinates, in that they describe location on the surface of
the Earth. Their celestial equivalents are called right ascension and declination (usually
abbreviated RA and dec). The grid lines are drawn on an imaginary sphere centred on the Earth
known as the celestial sphere.
Declination is the angular distance north or south of the celestial equator (the projection of the
Earth's equator onto the celestial sphere) and is expressed in degrees, minutes and seconds with
plus and minus signs indicating north or south of the equator.
Right Ascension is rather more complex. It is the angular distance measured eastwards from a point
on the celestial equator known as the Vernal Equinox or the First Point of Aries. The path taken by
the Sun along the ecliptic during the course of a year crosses the celestial equator at two points. The
First Point of Aries corresponds to the intersection on the Sun's northward journey. (Owing to
precession this point is now actually in Pisces). RA is usually expresses in hours, minutes and
Explain that if a star is circumpolar from latitude L, then the declination D of the star must be
greater than or equal to 90 - L.
Whether a star is circumpolar depends on both the declination (D) of the star and the latitude (L) of
• If an observer is at latitude L then the angle of elevation of Polaris above the northern
horizon will also be L.
• It follows that if a star's angular distance from Polaris is less than L, then it will not set
(i.e. will be circumpolar).
• Polaris has a declination of 90 degrees, and so a star's angular distance from Polaris
will be 90 - D.
• Rewriting this is symbols, if 90 - D is less than L then the star will be circumpolar.
• This could be rearranged as:
Describe the method of heliocentric parallax for determining the distances of nearby stars.
Heliocentric parallax is used to measure distances of nearby stars. Uncertainty of 10%.
Has a useful maximum distance of 20 parsecs as the angle is otherwise too small.
Angle is measured using mathematic formulae relating the apparent movement of the star against
the background constellations over the course of a year.
"The angular shift gives the angle at the star. From that angle the distance from the sun to the star
can be calculated, using the known distance of the earth to the sun."
State how a parsec is defined and show how it is used as a unit of distance in our Galaxy and
Distance is measured in AU within the Solar System
Measured in Parsecs when discussing Stars. NOT light years.
A Parsec = 200,000 AU or 3.26 Light Years
A Parsec: When angle is found to be only one arcsec then k = 1 parsec (referring to the above
1° = 60 arcmins
1 arcmin = 60 arcsecs
1 arcsec = 1/3600 of a degree
e.g. 0.01 arcsecs gives 100 parsecs
Identify the light curves of eclipsing binaries, Cepheid variables, novae and supernovae.
Extremely similar light curve to a Supernova (see below) but may have more than one outburst.
Explain the causes of variability in the light from eclipsing binaries, Cepheid variables, novae
There are hundreds of different variable stars known.
Two reasons for their causes are:
1. Eclipse - one is orbiting the other
2. The actual star changes internally in apparent magnitude, or physically changes its
An eclipsing binary consists of two stars of, usually, unequal brightness, in orbit around their common
centre of mass (gravity). The orbital plane of the two stars is in, or close to, the line of sight between
ourselves and the binary system.
For the majority of the time, light from both stars can be detected, but twice during every orbit the
stars are aligned with the observer and an eclipse occurs.
The deeper (primary) minimum occurs when the dimmer star is directly in front of the brighter star
(blocking out much of its light), and the secondary minimum occurs when the stars' positions are
reversed half an orbit later.
These are luminous (about 10,000 times more than the Sun) yellow giant stars which periodically
expand and contract over timescales of several days.
The fluctuations in size (by up to 30%) and surface temperature (by up to 1500K) cause regular
changes in their luminosity and therefore magnitude, which can be observed.
The first of this type of variable star was discovered by the English astronomer John Goodricke in
1784. This was Delta-Cephei after which the type of star is named.
Must not be confused with a Supernova (see below) as they share many similarities in light curve but
may have more than one outburst.
A nova may suddenly increase in brightness by about 10 magnitudes in a few days followed by a slow
decline over several months.
The term nova means "new star" and comes from early beliefs as to their nature, but it is now known
that they are mainly close binary systems in which matter from one star (a giant) is pulled onto the
other star (a white dwarf) by its strong gravitational force. This matter erupts in a violent explosion on
the surface of the white dwarf and causes the sudden increase in brightness (by a factor of approx
10,000). Both stars remain intact, however, and it has been estimated that the giant star loses only
one ten thousandth of the mass of the white dwarf.
In supergiants of large masses the temperature of the core is hot enough for further fusion reactions
involving nuclei of elements up to iron to occur. Once these are depleted, a violent explosion occurs
at the outer part of the core and the supergiant blows away its outer layers at speeds of approx 5000
km/s in a supernova.
The typical light curve shown later shows a sudden rise in brightness over a few days and is followed
by a slow decline lasting for several months. For a brief period of time supernovae can appear and
outshine all other stars before fading from view.
Demonstrate a qualitative understanding of the scale of apparent magnitude, and how it
relates to observed brightness, by recalling that:
• for a faint star apparent magnitude m = 6
• for a bright star m = 1
• for a bright planet m = -2.
Greeks invented the concept of apparent magnitude, for stars only.
o 1 = brightest
o 6 = faintest with naked eye
They didn't take into consideration planets, moons, sun, or the naked eye limit.
Our modified system is:
o Sun = -26
o Full Moon = -12
o Venus = -4.4
o Sirius = -1.4
o Brightest star with naked eyes = +1
o Faintest star with naked eyes = +6
o Naked Eye Limit = +6
o Binocular Limit = +9
o Most Telescopes = +14.4
o Expensive 200" Telescope = +24
Describe the discovery of and evidence for planets orbiting other stars.
Stars, other than our own Sun, are very far away - the closest is 4 light years, or 23,514,800,000,000
miles, away. Any planets orbiting other stars would really be too small to see. Also, planets, unlike
stars, don't give out their own light - they don't shine. The only reason we can see the other planets in
our Solar System is because, like a mirror, they reflect the light from the Sun. Planets orbiting other
stars would also reflect light from their stars, but because they are so far away this light would be lost
in the glare of light from their star. It would be like trying to spot a candle next to a floodlight in
Brighton from somewhere in London.
So, there are ways of finding planets orbiting other stars that don't involve trying to directly see the
planet. The first uses the fact that our Solar System was formed from a cloud of debris orbiting the
Sun - the 'circumstellar disc'. Since 1983 scientists have been looking for evidence of such a disc
around our nearest stars which would suggest that planets are forming there too. One such disc has
been observed around Beta Pictoris (50 light years away) using infrared wavelengths.
The Proper Motion of a star can also give us a clue. All stars, including our Sun, are whizzing about
in space in different directions. It's only because they are so far away that they appear to stay still
from night to night. This real motion of the stars is called proper motion. If a star has a large planet
orbiting it, it will wobble slightly as the big planet pulls it from side to side. These wobbles have been
studied since 1937 and there is some evidence to suggest that Bernard's Star (the third nearest star
to the Sun) might have a planet or two orbiting it. But these deviations are very small and often
indistinguishable from measurement errors so the evidence isn't conclusive.
Even so, this method has allowed scientists to discover upwards of 70 planets orbiting other stars.
The first extrasolar planet ever discovered was found by the Swiss team of Michel Mayor and Didier
Queloz in 1995, and in 2001 8 more were discovered. The earliest planets discovered were very
different from our own, but these more recent ones range in mass from 0.8 to 10 times the mass of
Jupiter, the largest planet in our Solar System.
The long-term goal of this ongoing project is the detection of Solar System analogs - that is Jupiter-
like planets in Jupiter-like orbits. The discovery of such planets within the next decade will help
astronomers assess the Solar System's place in our galaxy and whether planetary systems like our
own are common or rare.
We can also use a star's Doppler Shift or redshift (discussed elsewhere) to see if it has a planet in
orbit around it. The light waves emitted by a star can be effected if there is a planet orbiting it. This
technique suggest that Gamma Cephei has a planet orbiting it.
We can also look at pulsars. These are stars that act like radio beacons and usually pulse with
amazing regularity. They spin, like lighthouses of the Universe, sending out their signal with each
revolution. Recently, scientists have discovered some which sometimes pulse irregularly. It is now
believed that there are planets orbiting them which distort their spin like the moon pulling the seas of
Explain the meaning of the term absolute magnitude.
Magnitude = Luminosity
(m) Apparent = how we see it
(M) Absolute = how seen from 10 parsecs
Use the scale of apparent magnitude.
You will need to recall that:
• a magnitude difference of 1 is equal to a brightness ratio of 2.5
• a magnitude difference of 5 is equal to a brightness ratio of 100
• 2.55 is approximately equal to 100.
Use the relationship between absolute magnitude M, apparent magnitude m and distance d:
M = m + 5 - 5 lg d
performing simple calculations involving powers of 10 only.
This is known as the distance modulus equation and is a calculation for finding the absolute mag.
(M) when you know the apparent mag. (m) and the distance (d).
M = 5 + m - 5logd
(You will only be asked to find logs of d for 10, 100, & 1000. i.e.:
• log10 = 1
• log100 = 2
• log1000 = 3
Count the 0's!!)
2 stars each have apparent magnitude (m) of 4. Find the absolute magnitude (M) of each star if the
distances (d) are:
• Star 1 = 10 parsecs (pc)
• Star 2 = 100 pc
M = 5 + m - 5logd
For Star 1:
M = 5 + 4 - 5(1)
For Star 2:
M = 5 + 4 - 5(2)
M = -1
Explain how Cepheid variables are used as distance indicators.
In 1912 a simple connection between a star's pulsation period and its mean absolute magnitude was
established. This relationship is called the period-luminosity law and astronomers can use
observations of Cepheid variables to measure the pulsation period, determine the absolute magnitude
and calculate the star's distance. This type of star is found in globular clusters and nearby galaxies,
and so the distances to these classes of object can also be determined.
As has been said, the period of a Cepheid variable is linked with its luminosity. That is to say, a
Cepheid with a period of 5.3 days will have the same luminosity as any other Cepheid with a 5.3 day
period. The longer the period, the greater the luminosity. Once we know the real luminosity, as well as
the apparent magnitude, we can work out the distance.
For instance, consider Delta Cephei and Eta Aquilae. The apparent magnitude of both of these are
exactly the same, but since Eta Aquilae is more luminous (as it has a longer period) it must also be
Describe how a stellar spectrum is obtained at the telescope.
The spectrum of a star can be obtained by focusing the light from a telescope onto a glass prism or
diffraction grating. The prism or grating will then disperse the rainbow of colours present in the
starlight onto a photographic plate or ccd camera.
Describe the appearance of a stellar spectrum, including emission and absorption lines.
All are familiar with the formation of a spectrum of white light. The "rainbow" pattern of colours is
called a continuous spectrum. If light from a star such as the Sun is dispersed in the same way
(white light passing through a prism of glass), a series of sharp, dark lines at well defined wavelengths
(generally called absorption lines) is superimposed on the continuous background.
The spectral lines in the Sun were first studied by Joseph Von Fraunhofer in 1814 and are named
In relatively cool stars the temperature is low enough for molecules to exist, and these give rise to
wider absorption bands.
In relatively hot stars, the temperature is high enough for bright emission lines to be present in their
spectra. The emission lines are based on the same principle as the absorption lines. Each element in
the star gives off its own distinctive lines which are often absorbed by the gases in the chromosphere.
Therefore the emission lines are normally reversed and show up as absorption lines.
Classify stars according to their spectral type (colour, surface temperature and composition).
According to the modern system of classification, the stars are divided into various spectral types,
each denoted by a letter of the alphabet. The sequence of letters is alphabetically chaotic - W, O, B,
A, F, G, K, M, R, N, S. Many people remember this as "O Be A Fine Girl Kiss Me Right Now Sweetie".
Spectral Main Spectral
Temp / K Colour Examples
O 25,000 - 40,000 helium with weaker Puppis
neutral helium with
B 11,000 - 25,000 stronger hydrogen
white Regulus, Rigel
lines with ionised Sirius, Deneb,
A 7,500 - 11,000 white
calcium becoming Vega
F 6,000 - 7,500 white Polaris,
hydrogen weaker Sun, Capella,
G 5,000 - 6,000 yellow
with iron becoming Alpha-Centauri
lines and bands of Arcturus,
K 3,500 - 5,000 orange
CH and CN Aldebaran
M 3,000 - 3,500 red strong and titanium
oxide bands strong
Describe how information can be obtained from a spectrum, including the resolving of the
components of a spectroscopic binary, and the differential rotation of the Sun.
Dark absorption lines in a star's spectral band originate in the lower atmosphere of a star where
atoms and ions of chemical elements absorb light of certain wavelengths on its way outwards. Each
element has its own unique set of spectral lines, and so a study of a star's spectrum enables
astronomers to deduce what chemical elements and in what proportions, are present in the outer
regions of a star.
One method to determine differential motion (like the bands of Jupiter moving at different speeds at
different latitudes) is to examine the spectrum line shapes. Subtle differences exist between the line
profiles of a rigidly rotating star and that of a differentially rotating star.
Absorption line profiles are influenced by a number of different effects. At any point on a star the
profile is determined by temperature, gravity, element abundances, and atomic parameters.
The Sun rotates at different speeds at different latitudes. It varies between 25 days at the equator to
36 days at the polar latitudes.
Describe the evolutionary cycle of a star with solar mass and of stars with greater mass.
A star begins its career by condensing out of the material in a nebula. As it shrinks, because of the
force of gravity, it heats up. What happens next depends entirely on its initial mass.
If this mass is less than 8 times that of Jupiter it will never become a "proper star", though its surface
will become hot. These objects are known as brown dwarfs.
If the initial mass is less than 0.1 that of the Sun, the core temperature will never rise high enough for
nuclear reactions to be triggered off, and the star will shine as a dim red dwarf until it loses its
If the mass is between 0.1 and 1.4 times that of the Sun the whole story will be different. The
"protostar" will be cool and red (though not necessarily a red giant) and it will be varying irregularly; it
has not settled down into a steady, stable existence. As they go on condensing, they heat up. WHen
the core has passed the critical temperature of 10,000,000 degrees C, nuclear reactions start, with
hydrogen as fuel. The star then joins the main sequence and remains there for a very long time.
The Sun has been a main sequence star for around 5 million years, and will be for another 5 million
years or so before its available hydrogen is used up and it has to change its structure drastically.
Helium, formed from the hydrogen, collects at the star's core. When there is no hydrogen left, gravity
takes over again. There is more shrinking, which causes a new rise in temperature and the helium
starts to react, building up heavier elements such as carbon. More reactions build up heavier and
The inside of the star shrinks, while the outer layers expand, so that the star leaves the main
sequence and moves into the giant branch of the H-R diagram. The core temperature rises to
fantastic values, and the star throws off its outer layers altogether, turning into a planetary nebula.
Eventually all nuclear reactions stop. The core, all that is left of the original star, is now inert. The star
has become a white dwarf.
In a white dwarf all the atoms are crushed and broken, and packed together so tightly that there is
almost no wasted space. This means that the density is very high and may reach a million times that
of water. A tablespoon of white dwarf material may weigh as much as a thousand tons. Eventually a
white dwarf loses the last of its energy, ending up as a cold, dead globe.
If the original star is more than 1.4 times as massive as the Sun, everything will happen at a quicker
pace. The star will condense out of a nebula and join the main sequence, as before, but the greater
mass means that when the hydrogen "fuel" is exhausted still heavier elements are produced, and the
temperature rises to around 3,000,000,000 degree C. The core is by now made of mainly iron, which
will not react. Suddenly the nuclear processes stop; there is an "implosion", followed by a rebound
and an explosion, as the star blows up in a cataclysmic outburst which we call a supernova. Much of
the material is hurled away into space, and the end product is a cloud of expanding gas in the midst of
which is a very small, super-dense object made up of neutrons. The atomic protons and electrons are
forced together to produce neutrons.
A neutron star is only a few kilometres across, but its density may be of the order of a thousand
million million tons per cubic centimetre. The star has an immensely powerful magnetic field, and is
spinning round rapidly, often many times per second, sending out radio pulses. We see these radio
pulses from Earth much in the same way we see the light from a lighthouse, which is why neutron
stars are often called pulsars.
As a pulsar spins it loses energy and slows down. Eventually it too will become cold and dead.
If the initial mass of the star is even greater, at least 8 times that of the Sun, an even stranger fate will
overtake it. When the final collapse starts, it is so sudden and so violent that nothing can stop it.
There cannot even be a supernova outburst. The star just keeps collapsing and collapsing, become
more and more dense. As it does so, the escape velocity rises and there comes a time when the
escape velocity is equal to the speed of light. If light cannot escape from the star then nothing else
can either as light is the fastest thing in the Universe. The old star has surrounded itself with a
"forbidden area" from which nothing can break free. It has become a black hole.
Describe and identify the main components of the Hertzsprung-Russell diagram.
One of the most useful ways of studying the different types of star is to use the Hertzsprung-Russell
diagram (or H-R diagram) shown above. This is a chart of absolute magnitude (or luminosity) against
spectral type (or surface temp). It is clear from this diagram that most stars belong to one of four
Most stars, including the Sun, lie on a diagonal band called the main sequence. Generally speaking
the more mass a star has the further up and to the left its location. The remaining stars mostly lie in
three groups occupied by (red) giants, (red) supergiants and white dwarfs. In many respects main
sequence stars are 'normal' stars like the Sun; the other main groups contain stars which are in their
later stages of evolution, with giants and supergiants being much larger and cooler than the Sun, and
white dwarfs being relatively small but extremely hot.
One useful purpose of the H-R diagram is the ability to determine the absolute magnitude of a star
with reasonable accuracy. Once a star's spectral type is known, its magnitude can simply be read off
the graph, provided it is a main sequence star. This can then be combined with the distance
modulus equation (M = m +5 - 5 lg d) mentioned earlier to determine its distance.
Describe the observational evidence for black holes, including accretion discs or orbiting
It is not possible to observe black holes directly as their immense gravitational pull does not allow light
and other EM radiation to escape.
However, their presence is detectable by the X-Rays that are emitted from accreting matter from a
nearby companion star in a binary system. Material from a binary companion star to the black hole is
pulled off into the black hole, but before being sucked in it is so strongly heated that it gives off X-
Rays which we can detect.
Another piece of observational evidence is the gravitational effect the black hole has on its
surroundings. For example a neighbouring star would show gravitational disturbances due to the
proximity of the black hole.