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Chapter 19 The Stars Distances to stars are measured using parallax. This is not effective for very distant stars. The angle formed by parallax is measured in arc seconds. A circle is divided into 360°. One degree is divided into 60 minutes, and one minute is divided into 60 seconds.

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## Chapter 19 The Stars Distances to stars are measured using parallax .

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**Chapter 19 The StarsDistances to stars are measured**using parallax.**This is not effective for very distant stars. The angle**formed by parallax is measured in arc seconds.**A circle is divided into 360°. One degree is divided into**60 minutes, and one minute is divided into 60 seconds.**Therefore, one arc second is 1/(360 x 60 x 60) of a circle,**or 1/1296000 of a circle.**The distance a star must be to have a parallax of one arc**second is 20,265 A.U.’s, 3.1 x 1018 cm. This distance is called a parsec(parallax in arc seconds).**The farther away a star is the smaller the angle becomes,**so:distance (in parsecs) = 1/parallax (in arc seconds)**The closest star to Earth is Proxima Centauri. It is a**member of a triple star system called the Alpha Centauri System.Proxima Centauri has the largest known stellar parallax at 0.76”.**1/0.76 = 1.3 parsecs; 4.3 light years, or 270,000 A.U.’s.**This is a typical interstellar distance in the Milky Way galaxy.**If the Earth were a grain of sand orbiting a golf ball sized**Sun at a distance of 1 meter, Proxima Centauri would be another golf ball over 100 km distant.**The next nearest star is Barnard’s Star at 1.8 parsecs**(pc), 6.0 light years. There are about 30 stars within 4 pc of Earth.**The annual movement of a star across the sky, relative to**other stars, is called proper motion. It is measured by angular displacement.**Barnard’s Star moved 227” over 22 years. This solves to**10.3”/yr. This is the largest known proper motion of any star.**Proper motion is only the transverse velocity (perpendicular**to Earth). The other component of motion is radial velocity (found from the Doppler Effect).**True space motion can be found from the Pythagorean Theorem.****Finding Stellar Size –One way is by speckle**interferometry. Many short exposure images of a star are pieced together producing a high resolution map of the star.**Another way to find the size of stars is by using the**Radius-Luminosity-Temperature Relationship.Energy flux is the energy emitted by a star per unit area per unit time. Energy flux increases proportional to increases in temperature and stellar radius.**_________√ luminosityradiusis proportional to**----------------------temperature2This is used to indirectly determine stellar size.**Example: Omicron Cetitemp: 3000K 1/2**Sun’sLuminosity: 1.6 x 1036 erg/sec400x Sun’s √400Therefore: radius = --------- = 0.52 80X Sun’s radius**80X Sun’s radius would put the photosphere at Mercury’s**orbit. This makes Omicron Ceti a Red Giant. A Giant is 10 to 100x the Sun’s size. A Supergiantis 1000x the Sun’s size.**Example: Sirius Btemp: 12,000K 2x Sun’sLuminosity:**1031 erg/sec0.002x Sun’s√0.002Therefore: radius = ------------ = 22 0.01X Sun’s radius**Sirius B is much hotter and much smaller than our Sun. It is**roughly the size of Earth. It is a white dwarf star. Any star smaller than our Sun is called a dwarf.**Luminosity is the rate of energy emission by a star. The**apparent brightness of a star is how bright it appears from Earth.**A bright star is a powerful emitter, is near Earth, or both.**A dim star is a weak emitter, is far from Earth, or both.**The apparent brightness of a star decreases in an inverse**square relationship as its distance from the Earth increases.**Doubling the distance from a star makes it appear 22, or 4**times dimmer. Tripling the distance makes it appear 32, or 9 times dimmer.**The apparent brightness of a star is directly proportional**to its luminosity and inversely proportional to the square of its distance.**When comparing the luminosity of stars, astronomers imagine**looking at all stars from a standard distance of 10 pc.**The apparent brightness a star would have at 10 pc from**Earth is called its absolute brightness.**A star closer than 10 pc from Earth will have an absolute**brightness less than its apparent brightness. A star greater than 10 pc will have an absolute brightness greater than its apparent brightness.**The surface temperature of a star can be determined from**measurements of its brightness at different frequencies. This is usually measured at a certain frequency of blue light (B) and a certain frequency of visible light (V) to which human vision is most sensitive.**The color index of a luminous object is the ratio of its B**to V intensities. It is directly related to the object’s surface temperature and to its color.**Color IndexB/VTemp ColorExample1.7 30,000K electric blue**1.3 20,000K blue Rigel 1.0 10,000K white Vega, Sirius 0.8 8,000K yellow-white Canopus 0.6 6,000K yellow the Sun, Alpha Centauri 0.4 4,000K orange Arcturus, Aldebaran 0.2 3,000K red Betelgeuse**This intensity measurement through a series of filters is**called photometry. The UBV system uses Ultraviolet, Blue, and Visible filters to determine a star’s properties.

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