E3 - Stellar Distances

As we move, objects appear to change their relative distances. Objects closer to us appear to move more than those further away that might appear stationary. This apparent movement is called parallax and this effect can be used to measure stellar distances as the closer the star is to the earth the greater the parallax shift will be.

Angles: 3600 arc seconds (3600") = 1° = 2π/360 radians

Using distant stars as a reference the angle that the moving star makes with the earth is observed over a six month period (why? it gives the maximum angle) as shown:

Here we can see that:

tanq = 1 Au/ d

using small angle approximation we can see that this means:

q = 1 Au/ d

If q was 1 second ( (2π/360 * 60 * 60) radians ) then the distance d would be given by 1 parsec. 

  p = 1/d

where p = angle in arcsecs 

               d = distance in parsecs

This method can be used for stars up to a few 100 parsecs away after which the angle becomes so small that the uncertainties become significant.

Apparent magnitude: This is a scale to measure the apparent brightness of a celestial body where each level is equivalent to a rise of 2.51 times the brightness of the previous one and the brightness increases with the negativity of the numbers. This means that the brightest star ( sun) will have the largest negative value of all the stars.

The ratio of the apparent brightnesses of two stars bA and bB is related to their apparent magnitudes MB adn MA by:

Absolute magnitude: This is the apparent magnitude of the celestial bodies at a distance of 10 parsecs from earth. 

E2- Stellar Radiation

Fusion is the main source of energy for fusion.

When fusion occurs this leads to the production of heat which gives the molecules greater kinetic energy. As a result they exert an outward force that forces that would force the star to expand. As this force acts over the surface area of the star, it is called radiation pressure. However, the gravitational force caused of the star also exerts an opposing force that ensures that the start does not expand. This is referred to as gravitational pressure as it acts over the surface area of the star. In stable starts like the sun, the gravitational pressure is equal to the radiation pressure which ensures that the size of the star remains constant.


Luminosity (L) is defined as the total power emitted radiated by the star (units: W). It is affected by the star and its surface temperature. Stars with higher surface temperatures and radii will have greater luminosities. This is however  not the power received by, us the observer. The per received per unit area by an observer is called the apparent brightness (b) of a star. As power is emitted as a sphere, the apparent brightness is given by:

The units are W m^-2.

If two stars are different distances apart then, for them to have the same apparent brightness, the one further away needs to have a greater luminosity.

The apparent brightness of a star can be measured using a charge coupled device (CCD) which works on the principle of the photoelectric effect. 

Wien's and Stefan-Boltzmann Law

Radiation from a perfect emitter is known as black-body radiation. 

Wien's displacement law states that the peak wavelength of the emission of a black body is inversely proportional to the temperature.

Energy emitted per unit time is known as power but also luminosity and is given by:

E2.7: Absorption spectra for stars are observed and using the characteristic absorption spectra for the different elements, the elements that the star is composed of are discerned.  Observing the absorption spectra of stars can give us the peak wavelength which can be used to calculate the surface temperature using Wien's law. This temperature can be used to calculate the luminosity of stars using the Stefan-Boltzmann law. This can be used to calculate the distance between the star and the earth if the apparent brightness is known.


However depending on whether the star is moving away from us or towards us, the entire spectrum maybe be shifted towards higher or lower frequencies due to the Doppler effect. As stars move away, their wavelengths increase causing the frequency to decrease. This is called a red shift. If stars are coming towards us, their wavelength is compressed causing an increase in frequency causing a blue shift. A red shift in the majority of the spectra observed, is evidence for the expansion of the universe.

E2.8: As different stars give out different spectra of light, this allows us to classify stars on the basis of spectral classes. Stars emitting the same types of spectra are allocated to the same spectral class. The seven main classes are: OBAFGKM

As the temperature of the sun is around 5800 K, this means that  it is a group G star which are yellow.

Mnemonic: Oh be a fine guy, kiss me.

For looking at spectra:

http://astro.unl.edu/classaction/animations/light/spectrum010.html 

Sun's spectra:

Different types of stars:

Red Giant:  Large size, red colour, comparatively cooler as red light has a lower frequency, source of energy is fusion but of elements other than hydrogen.

White Dwarfs: Small in size, white in colour, comparatively hot, fusion is no longer taking place. Eventually it will cool down to make a brown dwarf.
Cepheid variables: They are observed to have regular variation in brightness and luminosity which is due to oscillations in the size of the star. They are rare, but useful in determining large distances in galaxies as there is a link between the period of brightness and average luminosity.


Binary Star systems: consisting of two stars revolving around a common centre of mass
Spectroscopic Binary systems:  As stars move around one star appears to be receding while the other appears to be approaching which means that there is a  red/blue shift in their adsorption spectra

Eclipsing Binary systems: This occurs due to a periodic variation in brightness as one stars obscures of overlaps the other. When the less bright star comes before the brighter star there is a decrease in the apparent brightness:

Position 2 = less apparent brightness


Hertzsprung-Russell diagram:


(memorize...)

Astrophysics: Introduction to the Universe

Planets Mnemonics:
My  : Mercury
Very  : Venus
Educated  : Earth
Mother  : Mars
Just  : Jupiter
Served : Saturn
Us  : Uranus
Nothing :Neptune

Relative Planet Sizes

hyperphysics.phy-astr.gsu.edu

Asteroids: A small rocky body that drifts around the Solar system

Meteorite: An asteroid on a collision course with the planet is known as a meteoroid. Small meteors can be vaporized due to friction with the atmosphere. The bits that arrive are called meteorites.

Comet: are mixtures of rock and ice

Stellar Constellation: Are a group of stars that are physically close to each other, created by the collapse of the same gas cloud

Constellation: These are patterns of stars that have been identified.

Light Star: The distance light travels in one year.

Comparing Distances:
Distance of the visible universe: 10^26m

Distance between local galaxies: 10^22 m

Distance of our galaxy: 10^21m

Distance of our solar system: 10^13 m 

Movement of constellations:

Over one night: They appear to be rotating in the sky around a fixed point (the pole star) due to the rotation of the earth

This shows the movement of Orion over one night.

Over a year: The pivot of rotation (i.e.) the pole star appears to have changed position in the sky which is due to the revolution of earth. This means that the constellations appear at different places in the sky depending on the time of the year.