Chapter 10 Measuring the Stars 10 1 The First Step Measuring the Brightness Distance and Luminosity of Stars stereoscopic vision the brain judges distances to objects by comparing the view from the left eye with the view from the right fingers moves a lot when at your nose and blinking each eye moves less if blinking each eye with finger at arm s length it s the way we perceive distance anything more than ten meters away won t really change positions when using a different eye because eyes are only separated by 6 cm if separated further we could see judge further distances this is done by pictures taken at different sides of Earth s orbit 6 months distance of 2 AU between both pic tures Earth Sun and Star form a right angle small angle at the end of the triangle near the star is the parallax of the star over a year the star seems to move and move back against background of dis tant stars the apparent shift is equal to twice the parallax more distant stars make longer skinnier triangles smaller parallaxes parallax is inversely proportional to distance most are so tiny scientists use arcseconds not de grees where d is distance and p is parallax d parsecs 1 p arcsecs distances to stars and galaxies is measured generally with the parsec 3 26 light years first successful parallax measurement was made by the German astronomer F W Bessel in 1838 for 61 Cygni 3 2 pc away increased the known universe 10 000 fold today only 60 stars within 15 light years of the sun are known in the neighbor hood of the Sun each star has 360 cubic LY of space to itself knowledge of stellar neighborhood increased in 1990s Hipparcos Satellite has observational uncertainty measurements of distances to stars aren t perfect we can t reliably measure stellar distances of more than a few hundred parsecs using par allax two thousand years ago Hipparchus classified stars by brightnesses 1 through 6 brightest objects have the smallest magnitudes objects brighter than the first magni tude have magnitudes of less than one magnitude of a star is the star s apparent magnitude brightness of the star as it appears in our sky its luminosity is its intrinsic brightness for which we must know the distance absolute magnitude if we know distance we can put it on a scale with all the other stars and calculate how bright they would be if they were all located 10 pc from us brightness varies with wavelength region symbols are used to represent magni tudes at certain colors V and B are those in the visual yellow green and blue regions brightness doesn t tell us much could seem bright but actually dim just close by apparent brightness the intensity of starlight that reaches us is inversely propor tional to the square of our distance from the star knowing the distance allows us to find luminosity vast majority of stars are far less luminous than our Sun only a few are at the upper range of luminosities Sun falls near the middle 10 2 Radiation Tells Us the Temperature Size and Composition of Stars Stereoscopic vision and the fact that closer objects appear brighter allow us to measure distance and luminosity of the closest stars stars are gaseous fairly dense we can use blackbody radiation like the Stefan Boltzmann law hotter at same size means more luminous and Wien s law hotter means bluer to understand stellar radiation their temperature and size Wien s law the temp of an object determines the peak wavelength of its spec trum hotter stars are blue cooler are red sun is middle yellow the law tells temp of the surface because color only indicates the temp of the surface interiors are much hotter brightness of a star usually measured through a filter piece of colored glass lets in only a small range of wavelengths usually either blue or visual we find more cool stars than hot stars the spectra of stars are not smooth continuous blackbody spectra but dark and bright lines at specific wavelengths How does light interact with matter Almost all mass in an atom is in the nucleus this image of orbiting electrons around a nucleus is the Bohr model 1913 is incor rect Particles of matter have wavelike properties just like waves of light the positive nucleus isn t surrounded by electron orbits but by electron clouds or waves We can imagine the energy states of an atom as a set of shelves in a bookcase the energy of an atom might correspond to the energy of one shelf or the next but will never be found between two shelves ground state lowest possible energy state of an atom electron has minimum en ergy has nothing more to give up will remain here unless it gets external energy excited states levels above the ground state can move to ground state by get ting rid of energy all at once atoms falling from a higher energy state to a lower energy state lose an amount of energy exactly equal to the distance in energy levels the energy level structure of an atom determines the wavelengths of the photons emitted by it the color of light it gives off it can emit photons with energies corre sponding only to the difference between two of its allowed energy states the atom either absorbs the energy of a photon or it collides with another atom or unattached electron or absorbs some of the other particle s energy in a cloud of hot gas with atoms of only two energy states where the atoms are zooming and colliding and getting kicked into the higher energy state any atom in the higher energy state quickly decays and emits a photon in a random direction all light coming from the cloud is the same color because emitted light only con tains photons with the specific energy between those two states if passed through a slit and prism it form a single line of color an emission line Example neon signs each color comes from a different class not necessarily neon trapped inside the glass tubes absorption line if there is a white light in a cool cloud of gas most photons will be unaffected because they don t have the right amount of energy those that do are ab sorbed missing from spectrum represented by sharp dark line at the wavelength of this energy when an atom absorbs a photon it quickly returns to its previous energy state emitting a photon with the same energy as the one it absorbed essentially photon was replaced but all the absorbed photons travel in the same direction where as emitted travel in random direction most photons are diverted from their original path In summary white light contains all wavelengths so its spectrum contains all the colors of the rainbow