.. ion of radiation is. Luminosity (L) is the total power emitted by a body. The Stefan-Boltzmann law states that the total energy radiated per unit time by a black body is proportional to the fourth power of its absolute temperature; it also depends on the surface area (A): L = s A T4 Stefans constant (s) = 5.67 x 10-8 W m-2 K-4 The amount of power received per unit area is flux (equal to power / area). Light emitted from an object spreads out in all directions, the further away it gets the less intense it becomes according to the inverse square law: L = d-2 E.g., As Saturn is ten times the distance from the Sun as Earth, the intensity of radiation is receives is 1/100 th of that for Earth.

The light reaching Earth from the sun can be analysed using a technique called spectroscopy. It is used to identify the chemical composition of stars (which is mostly hydrogen and helium), and their surface temperature. Once these are known, stars can be classified accurately. An emission spectrum is the spectrum of wavelengths of light emitted from atoms or molecules. They do this when they lose energy, which corresponds to a specific frequency of the electromagnetic spectrum. An atom or molecule may become electronically excited, electrons transfer to higher energy levels, and then later drop back to their normal, lower energy states, emitting this extra energy as photons of light in the process.

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Molecules gain translational, rotational, vibrational or electronic energy, depending on how much energy they first absorb. They must emit this quantised amount of energy again. Different elements and have different energy levels, this is why we can associate certain wavelengths with the physical behaviour of a particular atom. Even small molecules cannot withstand the high temperatures of stars, their spectra are only visible for cool stars. An absorption spectrum is apparent when wavelengths of light are missing against the continuous background of emitted light.

These missing wavelengths have firstly been emitted from atoms in the inner layers of the star, but then absorbed by different chemicals in the outer layers. Thus we can identify the elements in the outer layers of a star. The Balmer series refers to the emission spectrum of hydrogen, specifically for high energy level electrons dropping back to the second energy level (n=2). Light emitted falls in the visible region of the electromagnetic spectrum, and the intensity of this light is an indication of a stars surface temperature. The Balmer series is due to atoms being excited by kinetic collisions.

The electrons of cool atoms occupy their ground state (n=1), as there are few collisions to excite the electrons. The hotter the atoms, the more energetic the collisions; more electrons are excited to even higher levels (n=3, 4,.etc). These electrons now absorb wavelengths beyond the Balmer series. The most intense Balmer emission spectra are from stars with intermediate surface temperatures at around 10 000K. Most electrons can absorb and re-emit wavelengths of the visible spectrum at this temperature.

The light from stars travels very great distances, taking a long time, to reach Earth. Unsurprisingly, it can be affected by the time it reaches us. Of course, our nearest star is the Sun, and our nearest neighbour is the moon. However, near in space is nowhere near close enough to actually measure by hand. The first logical estimates used simple trigonometry in a method called parallax. This is where a distant object will appear at a different spot when viewed from a different angle. Simply, the position of a star is measured relative to the background, at the two times when the apparent distance between these viewing positions is as great as possible. As the Earth rotates around the Sun, with a radius of 1 astronomical unit (1AU = 1.496 x 1011 m), the greatest possible angle between two different views of a star is achieved at six month intervals, when the distance between these two times is 2AU: The further away the object, the smaller the parallax angle would be, as: Distance (d) = 1AU Tan (r) Distance (d) in parsec (pc) = 1 Parallax angle (r) in arc-seconds Measuring parallax in this way is called annual parallax.

It is suitable for objects up to about a distance of 100pc from us. Earth based instruments are less reliable as the parallax angle being measured gets smaller, greater measurements have been made by Earth orbiting telescopes such as 1989 ESA Hipparcus which avoid atmospheric limitations. We can only estimate the distances of more distant objects such as supernovae. One method is called spectroscopic parallax, where we can make the assumption that all stars are equally bright (although we know of course that they are not), and so the brighter a star the closer it is. The apparent magnitude (m) of a star is related to its intensity (I); its is an observational logarithmic scale.

The absolute magnitude is a comparative scale based on the assumption that all objects are at a distance (d) of 10 pc. The two measurements are related: d = 10pc x 10 (m M) / 5 The distance of an object is related to its intensity (using the inverse square law): I = L 4pD2 For objects further away than 10 megaparsecs, astronomers have made use of more unusual objects as reference points in the sky. Cepheid variable stars have luminosity which varies periodically. They vary in brightness as their surface temperature rises and falls. The absolute magnitude is directly proportional to the period, and using the above formula the distance of these stars can be calculated.

These stars are present in distant galaxies, we can deduce how far away these are. Some supernovae behave in the same way. We know that stars and galaxies are moving away from us, because the spectra lines from some are shown to have been shifted. This is the Doppler effect, where the spectrum lines are displaced, because their wavelengths have been changed. The change in wavelength is related to the velocity: Df = Dl = v f l c The Doppler shift can occur when something is moving towards or away from us, however receding galaxies is evidence that our Universe is expanding (their light is shifted towards the red / longer wavelength part of the spectrum). It can also be used to determine the distance of an object from us.

Hubble made the important finding that the further away a galaxy is, the greater its velocity. Also, all galaxies are generally moving apart from each other, including ours. Hubbles law depends on the Hubble constant (Ho), but there is no accurate value for this, due to the inaccurate estimates for distances by other methods. v = Ho x d It is speculated that Ho lies between 40 and 100 km s-1 Mpc-1 The Doppler effect is also used to measure how fast stars and galaxies are rotating, and the orbital period of binary stars. A pair of binary stars each orbit a common centre of mass, as they are attracted by each others gravity.

The stars usually have different masses, and will have different orbits (the radius of which is inversely proportional to the mass). When the stars are close to each other, it is difficult to distinguish between them, except by their different spectra (these are spectroscopic binary stars). Each is identified to be receding or approaching as they rotate, by Doppler shifting. We can find the combined mass of the two stars (M), based on Keplers third law of planetary motion: M = 4p2r3 GT2 G = Universal gravitational constant = 6.67 x 10-11 N m2 kg-2 The mass of each star can be calculated, as they are known to be in ratio of the distance to the centre of mass. We can see that there is so much to be discovered about the sky, over the years physicists have somewhat overcome the problem of sheer distance across the Universe. We have catalogued data about many stars, and crucially we can compare other stars to ones we already know about.

We can learn how stars evolve from our observations, however we can only view a tiny part of history. Star populations are mapped on the Hertzsprung-Russell diagram, basically a graph of luminosity against surface temperature: From it we can examine the life sequences of a star, deduce a stars absolute magnitude, and then their spectral class according to their surface temperature and other properties. We can identify what stage in its life a star it. Bibliography : Astrophysics, Nigel Ingham ; Physics Passcards, Graham Booth, Letts.