Stellar Distances

3.1. Define parsec.
The distance from Earth of a star that has a parallax angle of one second. The word parsec comes from one parallax angle per second and it is usually abbreviated to pc. 

3.2 Describe the stellar parallax method of determining a distance to a star.


The parallax angle can be measured by observing changes in the star's position over a period of a year. We can use trigonometry  to work out the distance of the star from the Earth (as we know the distance between the Earth and the Sun).

The parallax angle and distance from the Earth to star are always inversely proportional.

Units:

1. The distance from the Earth to the Sun can be described as 1 Au (Astronomical Unit) = 1.5 x 10^11m.
2. Calculations show that a star with an parallax angle of 1 second of arc must be 3.08 x 10^16m away (3.26 light years or ly).
3. This distance is defined as parsec (see above) 

3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs.
The parallax angles for stars are greater distances are too small to measure accurately. The smallest -parallax angle that can currently be measured is 0.01 arc-second. The limitation on ability to measure the angle accurately therefore, limits the method in that it can only be used to measure the distances of close stars.
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3.4 Solve problems involving stellar parallax

3.5 Describe the apparent magnitude scale.

• Apparent magnitude: Its apparent brightness viewed by an observer on Earth.
• Each magnitude is 2.51 times brighter than the next.
• The Ancient Greeks: classified stars according to brightness, 1 = the brightest, 6= the dimmest magnitude, m=1. A magnitude 1 star was first considered to be twice as bright as a magnitude 2 star, which was in turn as bright as a magnitude 3 star and so on (simple logarithmic scale). 
• A magnitude 1 star = 2.51^5 = 100 times brighter than a magnitude 6 star.
• Modern magnitude scale: Star of brightness 2.52 x 10^-8 Wm^-2 is given an apparent magnitude of 0.
• Note: Apparent brightness has unit whereas apparent magnitude is a ratio.
• Apparent magnitude of star depends on LUMINOSITY and its DISTANCE FROM EARTH.
• The brightest objects have MORE NEGATIVE values whereas the dimmest objects are MORE POSITIVE.

3.6 Define absolute magnitude

Absolute magnitude (M) the apparent magnitude of a star if it were 10 parsecs (pc) from Earth.

Most stars are further away than only 10 pc from Earth therefore they would appear brighter if they were only 10pc away. Therefore for most stars their absolute magnitudes are more negative than their apparent magnitudes (more brightness in absolute).

3.7 Solve problems involving apparent magnitude, absolute magnitude and distance.
(below)
3.8 Solve problems involving apparent magnitude and apparent brightness.

Some Images and diagrams from: Heinemenn HL Physics Course Companion, IB Physics study guide by Tim Kirk

E.2.7 to E.2.11: Astrophysics

E.2.7 Explain how atomic spectra may be used to deduce chemical and physical data for stars.


The radiation from stars is not a perfectly continuous spectrum-- some wavelengths are missing. The missing wavelengths correspond to a number of elements. The absorption takes place in the outer layers of the star therefore this means that we have a way of telling which elements are in the star (or at least in its outer layers).

A star that is moving relative to Earth will show a Doppler shift in spectrum.

Red shift: light from stars that are receding
Blue shift: light from stars which are approaching.



E.2.8 Describe the overall classification system of spectral classes.


Different stars give out different spectra of light which allows us to classify stars by their spectral class. Stars that emit the same type of spectrum are allocated to the same spectral class.

There are several main spectral classes in order of decreasing surface temperature.

O: Oh

B: Be

A: A

F: Fine

G: Guy

K: Kiss

M: Me

E.2.9 Describe the different types of star.


BINARY STARS:

• Some stars like our Sun exist by themselves, but many have a partner
• Binary stars rotate around their own common centre of mass
• By analysing the orbital period and separation, the mass of each star in the binary system can be found

RED GIANT STARS: 

• Large in size
• Red in colour
• Comparatively cool
• Later possible stages for a star
• Source of energy: Fusion of some elements other than hydrogen
• Red supergiants are even larger

WHITE DWARF STARS:

• Small in size
• White in colour
• White therefore comparatively hot
• One of the final stages for some stars
• Fusion is no longer taking place - white dwarf is just a hot remnant that is cooling down
• Eventually it will cease to give out light when it becomes cold enough
• After ceasing to give out light (cold) it is called a brown dwarf 

CEPHEID VARIABLES:

• They are stars that are a little unstable.
• Observed to have a regular variation in brightness and (therefore) luminosity
• Aforementioned variation due to oscillation in the size of the star
• Rare but useful because there is a link between period of brightness variation and average luminosity
• Astronomers can therefore use them to help calculate the distances to some galaxies

E.2.10 Discuss the characteristics of spectroscopic and eclipsing binary stars.


VISUAL BINARIES
Binary stars (e.g. Sirius A) that can be seen with the naked eye of with a telescope are called visual binaries, when they are further away from us or closer together, resolution become difficult.

SPECTROSCOPIC BINARY STARS
In some cases, stellar spectra can be used to deduce the presence of two stars - these are called spectroscopic binary stars. As stars move around their common centre of mass, one star will be approaching whilst the other is receding.

The diagram above shows a spectroscopic binary system. In the right hand diagram, Star A approaches and Star B recedes from our line of sight. Therefore the absorption lines of A are blue shifted  and the absorption lines of B are red shifted (moving away so longer wavelength, therefore red). In the left hand diagram, because the motion of the stars relative to our line of sight is opposite, the shift is reversed.

ECLIPSING BINARY STARS
Show a periodic variation in the brightness of light emitted from the star system. This occurs because during their rotation, one star periodically obscures, or eclipses, the other.

The diagram above shows an eclipsing binary system.
Position-
1 and 3: light is reaching us at a maximum, because it is arriving directly from both stars
2 and 4: reduction in brightness as the stars are eclipsing each other.

E.2.11 Identify the general regions of star types on a Hertzsprung-Russell (HR) diagram.


Discovery by Hertzsprung and Russell in 1910: For most stars, there is a relationship between surface temperature and luminosity. 

Dots on diagram below represent stars, scales are not linear.

Temperature scale: Runs backwards, high temperatures on the left.
Absolute magnitude: The apparent magnitude it would have if it were observed from a distance of 10 parsecs. Absolute magnitudes are much more negative than the apparent magnitudes of the stars.

• 90% of stars fall into the diagonal band known as the main sequence. It can be shown using the Stefan-Boltzmann Law that stars increase in size as we move up the main sequence.
• Lower right: The coolest stars, reddish in colour.
• In the middle: (further towards the left than lower right) hotter, more luminous stars that are yellow and white.
• Lower left: more luminous blue stars.

Mass of star increases moving up the main sequence so the gravitational pressure increases with mass. Therefore, to maintain equilibrium, fusion reactions in the core must generate a greater radiation pressure. The star has to burn at a higher temperature, giving it a greater luminosity.


9% of stars = red giants and supergiants. From Stefan-Boltzmann Law we can see that their high luminosity and low temperature means that they must have a very large area - they are therefore giants. 


WHITE DWARFS are very hot but not luminous, therefore they are much smaller than their counterparts on the main sequence.

The cepheids, congregate in a great band of instability that appears between the main sequence and the red giants.

Images and diagrams from: Heinemenn HL Physics Course Companion, IB Physics study guide by Tim Kirk

E2 Stellar Radiation

E.2.1 State that fusion is the main energy source for stars.

Fusion is the main energy source for stars.

E.2.2. Explain that in a stable star (for example, the Sun), there is an equilibrium between radiation pressure and gravitational pressure.

A stable star is a star in which there is an equilibrium between the radiation pressure and the gravitational pressure. The reason why the powerful reactions in the Sun have not forced away the outer layers of the Sun is because of this balance between the outward pressure and inward gravitational force.

E.2.3. Define the luminosity of a star.

Luminosity is the total power radiated by a star, it is measured in Watts (W). It depends on both the surface temperature of the star and its radius or surface area. If the radius of the two stars is the same, the one with the higher temperature will have the greater luminosity. If the temeperature of the stars is the same, the one with the larger radius will have the great luminosity.

E.2.4 Define apparent brightness and state how it's measured.

Apparent brightness: The power received per unit area. The SI units are Wm^-2.

E.2.5 Apply the Stefan-Boltzmann Law to compare the luminosities of different stars

The radiation from a perfect emitter is known as black body radiation. The graph below shows a spectrum of radiation from black-body emitters at different temperatures. A hot object emits radiation across a broad range and there is a peak in intensity at a particular wavelength. For a hotter body, the peak is at a higher intensity and shorter wavelength.

The peak wavelength (at which the maximum amount of energy is radiated) is related to the surface temperature by Wien's displacement law.

E.2.6 State Wien's (displacement) law and apply it to explain the connection between the colour and temperature of stars.

Questions 5 & 6

5.

Astrophysics

3) Make a pneumonic for the order of the planets:

Mercury

Venus

Earth

Mars

Jupiter

Saturn

Uranus

Neptune

My Very Educated Monkey Just Sat Uncomfortably Naked

4) Compare sizes of planets with circles

http://www.google.co.th/imglanding?q=planet%20sizes&imgurl=http://hyperphysics.phy-astr.gsu.edu/hbase/solar/imgsol/psize.gif&imgrefurl=http://hyperphysics.phy-astr.gsu.edu/hbase/solar/sizes.html&usg=__KzUp-rOcpR2Kx8pWWukoJPWSTJI=&h=335&w=342&sz=5&hl=th&zoom=1&um=1&itbs=1&tbnid=X0xyO42EuscbNM:&tbnh=118&tbnw=120&prev=/images%3Fq%3Dplanet%2Bsizes%26um%3D1%26hl%3Dth%26sa%3DN%26tbs%3Disch:1&ei=8g9iTa_MOo3NrQfIm4SxAQ&um=1&sa=N&tbs=isch:1&start=12#tbnid=X0xyO42EuscbNM&start=16

5) Define:

Asteroid: Small rocky body that drifts around the Solar System.

Meteoroid: An asteroid on a collision course with another planet.

Meteorite: Small meteors can be vaporized due to the friction with the atmosphere (‘shooting stars’) whereas larger ones can land on Earth. The bits that arrive are called meteroties.

Comet: Mixtures of rock and ice (a ‘dirty snowball’) in very elliptical around the Sun. Their ‘tails’ always point away from the Sun.

Stellar Cluster: Group of stars that are physically close to each other, created by the collapse of the same gas cloud.

Constellation: Patterns of stars.

Light year: The distance light travels in 1 year.

6) Compare distances between stars and between galaxies

(From Physics IB Study Guide by Tim Kirk) 

7) Describe the motion of constellations over

1 night

They appear to rotate around in one direction. In the Northern hemisphere, everything seems to rotate around the North Star.

1 year

(From Physics IB Study Guide by Tim Kirk)