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Nature of Stars • Parallax is denoted by ‘p’. • Distance (d) is measured in parsec. • d = 1 parsec = the distance at which a star has a parallax (p) of 1 arc second. 1 parsec = 3.26 light years. Also d = 1/p Closest star, Proxima centauri, p = 0.772 arc seconds. Hence distance ‘d’ in parsec is d = 1/p = 1/0.772 = 1.3 parsec = 4.2 light years • Limitations on stellar parallax method • 1. p = 0.01 arc seconds from Earth. So max. distance = 100 parsecs • 2. Hipparcos, p = 0.001 arc seconds. So max. distance = 1000 parsecs. • Other distance methods. Luminosity and Inverse square Law. • Show weblink Brightness to Distance • If you know the apparent brightness, you know its luminosity (total energy output per second) • b = L /(4d2) • Comparing to the Sun, can determine distance to star Time to think…… Two stars have the same luminosity. As seen from Earth, one star has an apparent brightness of four times the other. The dimmer star a. is eight times farther away than the brighter star. b. is four times farther away than the brighter star. c. is two times farther away than the brighter star. d. is two times closer than the brighter star. Time to think…… Work out class activity ‘Parallax and Distance’ Magnitude • Introduced by the Greek astronomer Hipparchus – Based on naked eye observations • Brightest stars – first magnitude • Half as bright – second magnitude • Dimmest stars – sixth magnitude Magnitude • First magnitude stars are 100 times brighter than sixth magnitude stars • Magnitude difference of 1 corresponds to brightness difference factor of 2.512 !!!!! CAUTION !!!!! • Larger number in magnitude means the star is dimmer. • Apparent magnitude (m): How bright an object “appears” to a person on Earth. • Absolute magnitude (M): This is the apparent magnitude a star has it is placed at a distance of 10 parsecs from Earth. • m-M = 5 log(d) – 5 d = distance to the star in parsec Time to think…… How bright is a star with a magnitude of +4.0 compared to a star with magnitude +5.0? a. b. c. d. 2.5 times brighter 1/2.5 times as bright 1.25 times brighter 10 times brighter Time to think…… Star A’s V magnitude is brighter than its B magnitude, Star B’s U magnitude is brighter than its B magnitude, and Star C’s B magnitude is brighter than its V magnitude. Which of the following lists the stars from hottest to coolest? a) A,B,C b) C,B,A c) A,C,B d) B,C,A e) B,A,C Time to think…… Betelgeuse has a very high luminosity (40,000 times as bright as our Sun), but its surface is cool (below 4000 K). Which of the following explains this? a. The star must have a much smaller surface area than the Sun. b. The star is at the lower end of the main sequence. c. The star is at the upper end of the main sequence. d. The star must have a much larger surface area than the Sun. Time to think…… You observe an eclipsing binary. You have a measure of how long it takes the dip in the light curve to reach a minimum from when the eclipse begins. What information can you obtain from this measure? a) distance from the primary b) mass ratio of the primary and secondary c) size ratio of the primary and secondary d) size of the secondary only