chapter 19 the stars distances to stars are measured using parallax
TRANSCRIPT
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Chapter 19 The StarsDistances to stars are measured using parallax.
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This is not effective for very distant stars. The angle formed by parallax is measured in arc seconds.
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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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Therefore, one arc second is 1/(360 x 60 x 60) of a circle, or 1/1296000 of a circle.
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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).
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The farther away a star is the smaller the angle becomes, so:
distance (in parsecs) = 1/parallax (in arc seconds)
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One parsec is approximately equal to 3.3 light years.
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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”.
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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.
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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.
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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.
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The annual movement of a star across the sky, relative to other stars, is called proper motion. It is measured by angular displacement.
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Barnard’s Star moved 227” over 22 years. This solves to 10.3”/yr. This is the largest known proper motion of any star.
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Proper motion is only the transverse velocity (perpendicular to Earth). The other component of motion is radial velocity (found from the Doppler Effect).
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True space motion can be found from the Pythagorean Theorem.
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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.
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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.
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_________ √ luminosity
radius is proportional to ----------------------
temperature2
This is used to indirectly determine stellar size.
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Example: Omicron Cetitemp: 3000K 1/2 Sun’sLuminosity: 1.6 x 1036 erg/sec
400x Sun’s
√400Therefore: radius = --------- =
0.52
80X Sun’s radius
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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 Supergiant is 1000x the Sun’s size.
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Example: Sirius Btemp: 12,000K 2x Sun’sLuminosity: 1031 erg/sec
0.002x Sun’s
√0.002Therefore: radius = ------------ =
22
0.01X Sun’s radius
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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.
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Luminosity is the rate of energy emission by a star. The apparent brightness of a star is how bright it appears from Earth.
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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.
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The apparent brightness of a star decreases in an inverse square relationship as its distance from the Earth increases.
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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.
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The apparent brightness of a star is directly proportional to its luminosity and inversely proportional to the square of its distance.
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When comparing the luminosity of stars, astronomers imagine looking at all stars from a standard distance of 10 pc.
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The apparent brightness a star would have at 10 pc from Earth is called its absolute brightness.
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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.
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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.
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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.
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Color Index
B/V Temp Color Example 1.7 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
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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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