Note: some of the photos onthis page were duplicated from Nick Strobel"s Astronomy Notes internet site. Theofficial, updated version is available at his net site. Selectthislink to walk to his net site.Stars

Cleverness with LightWe stated that starsare simply tiny clues of light, however we have the right to tell plenty of things around stars.We can tellwhat they room made of,how hot they are,how big they are (their radius),how quick they rotate,whether castle are widening orcontracting,...and plenty of other things (liketheir masses, even if it is they have actually planets, etc.).How can we do all of this?It is by gift clever with light -- by understanding every little thing we canabout just how light works, how it interacts v matter, etc. We alreadylearned exactly how to carry out several of the points in the above list. Because that example,weuse spectral currently to determine what stars space made of. We use thecontinuum spectrum (or the star"s color) to recognize how hot they are.We usage doppler move of spectral currently to identify whether they are expandingor contracting, and also "doppler broadening" to recognize how fast they rotate.Luminosity and also Distance What we have actually not talked around yet is how to call how huge they are. This is a an extremely important point, yet it take away a pair of measures we haven"t learned yet. If a star shows up only together a suggest of light, how deserve to be tell how huge the star really is? we cannot just measure that is size. It transforms out the we require two bits of details -- the distance, and also its luminosity. Us earlier characterized the Sun"s luminosity as the full power calculation of the sunlight (3.8 x 1026 watts). We will refer to the luminosity of various other stars in units of the Sun"s luminosity, therefore let"s provide it a symbol, Lsun. A star through twice the strength output the the sun would have actually a luminosity the 2 Lsun. Keep in mind that luminosity is an intrinsic residential or commercial property of a star, definition that it does not depend on how much away the star is. In fact, we regularly emphasize this by making use of the hatchet intrinsic luminosity. Together it transforms out, the nearest star other than the Sun, alpha Centauri, has actually slightly better luminosity as the Sun. However note the the sun lights up our work on Earth, when Alpha Centauri shows up only as a faint point of light, invisible other than at night. Obviously the factor is that Alpha Centauri is really far away, if the sunlight is nearby. If us knew just how the evident brightness of things changes v distance, could we compare the evident brightness the the Sun and Alpha Centauri and tell how far it is to Alpha Centauri?
 The sky focused on the star Kappa Orionis. Return Kappa Orionis watch much larger than the other stars in this image, the is an illusion resulted in by overexposure that the film. Without the overexposure, the photo of Kappa Orionis would be the very same size as the faintest the theother stars in the photo -- a single point oflight. Is Kappa Orionis brightest because it is the star nearest to us in this image? No, the is around 815 ly distant, if the star just above it is just 75 ly away!

It is simple to figure out how apparent brightness drops off v distance. Consider the surface ar of a star, and also all the energy passing v this surface each second. This is the luminosity. Currently imagine one more sphere focused on the star, but at some better size. The same energy per second must also pass through this larger sphere -- none of the power disappears. Now imaging a collection of spheres, each one happen the same amount of energy per second. The surface ar area that each round grows together the radius squared, and also since the power is the same through each sphere, it complies with that the power per unit area (= brightness) drops as 1 over street squared: 1/d2. The is, the brightness (energy flux) complies with an station square law. figure 15.1 from the text. The area of each sphere boosts as the square the the distance, so the flux per unit area drops as the square the the distance. The obvious brightness is the exact same as the flux every unit area, therefore the apparent brightness likewise falls together the square of the distance. This provides the luminosity-distance formula: apparent brightness = luminosity / (4p x distance2) so of 2 stars through the same luminosity, the one that is aside from that away definitely has a smaller sized brightness. But stars do not all have the same luminosity, together is shown by the situation of Kappa Orionis, above.

Lecture inquiry #1

Measuring distance To sort out which stars space faint because they are far away, and which stars room faint due to the fact that they have a short luminosity, we have actually to uncover some way to measure ranges to stars. This is a lot harder 보다 it might seem. The whole difficulty of ranges to objects in the world is a an essential one, and it has actually a surname -- the street scale. The distance scale is a collection of dimensions going from little distances to larger and also larger ones. The an initial step in the expensive distance scale is to recognize the street to the Sun, 1 AU, which we now recognize to be 150 million km. Once we understand this distance, we deserve to use the activity of the Earth around the sun to look at for tiny annual place variations as result of parallax. (Note that this is precisely the same cause as retrograde motion of distant planets). measuring the place of adjacent stars relative to street stars over 6 month (January to July in the number above), us can find that the star appears to change a little angle p, referred to as the parallax angle. This turns out to it is in a very tiny angle, even for the nearest stars -- much less than 1 arcsecond (1/3600 of a degree) because that Alpha Centauri. If a star were close enough to cause a transition of specifically 1 arcsecond, we would certainly say that it is 1 parsec or 1 computer away. The word parsec originates from the words parallax and also arcsecond. Astronomers measure up all distances in parsecs, no light-years. However there is a simple relationship, 1 computer = 3.26 ly. The reason astronomers usage parsecs is that there is a an especially simple relationship in between parallax and distance: d (in parsecs) = 1 / ns (in arcseconds) We can measure angles to about 0.01 arcsecond, which way we deserve to measure star ranges using stellar parallax only to distances d = 1/0.01 = 100 parsecs (about 326 light-years). Stars farther away than that present no measurable transition as the planet orbits the Sun. Stellar parallax offers the second step in the distance scale. There are more steps the we will learn around later. When we look in ~ which stars in the sky present parallax, and so are the closest stars to us, we may be surprised to find out that countless are very dim -- not also visible without a telescope. Some brighter stars rotate out to be pretty close, prefer Sirius (2.6 pc), Altair (5 pc), and also Fomalhaut (7 pc), but many bright stars are so far away that they display no parallax. That way the intrinsic luminosity the stars have to vary enormously. In the 1990"s the Hipparchos satellite measure the parallax of nearly 1 million stars at distances out come 200 pc (parallax the 0.005 arcsec). Prior to that, only a few thousand stars had actually accurately known parallaxes. Proposed room missions the the future are expected to be able to measure parallaxes the end to 25000 pc--almost the whole distance throughout the galaxy!

Hipparchus and also the Magnitude device

Astronomers measure up the brightness of stars in magnitudes. That is based on a mechanism devised by the old Greek astronomer Hipparchus (c. 150 BC), who separated the brightness the stars into those that the very first magnitude (the brightest), next brightest to 2nd magnitude, and also so on under to those just visible v the nude eye as the sixth magnitude. Modern-day astronomers have a problem, however, since they can see far fainter stars through the assist of telescopes and cameras. They wanted to prolong this mechanism to fainter stars, for this reason to perform that they listed that it spanned a selection of about 100 in brightness (the brightest stars are 100 times brighter than the faintest). To be quantitative, they collection a range of 5 magnitudes as precisely equal to a factor of 100. This has the result of making part bright stars have also lower (brighter) magnitude than 1, therefore they walk to zero, and also even become negative. We can assign a brightness come the Sun, and find that it is -26th magnitude! therefore remember the the magnitude range is type of backwards -- the brighter stars have actually smaller magnitudes.