Astronomy Problems: Help Solve Now!

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The discussion focuses on several astronomy problems related to stellar characteristics. Key questions include comparing the luminosity of a star with a temperature of 70% that of the Sun and a radius ten times larger, determining the main sequence lifetime of stars with masses 11 times and 0.09 times that of the Sun, and calculating the distance to a star with a parallax of 0.015 arc seconds. Additional inquiries involve using Wien's Law to find the peak wavelength for a star at 7800 K and identifying its spectral class and absolute magnitude. The thread emphasizes the importance of not multi-posting for clarity in responses.
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Astronomy Problems: Please Help!

THESE ARE ALSO POSTED ON THE HOMEWORK PAGE WITH NOTES ABOUT WHAT I HAVE DONE.
1.) If a star has a temperature only 7/10 that of our Sun but a radius 10 times our Sun's, how would its luminosity compare to our Sun?

2.) If a star has a mass 11 times our Sun's mass, what would be its lifetime on the main sequence? What if the mass were 0.09 that of our Sun?

3.) If the parallax for a star is 0.015 arc sec (as measured by the Hipparchus satellite) how far away is it in parsec? In Light Years? If it has an absolute magnitude of 3, how bright would it appear from Earth?

4.) If the temperature of a star is 7800 K, where is the peak wavelength from Wien's Law? Assuming that it is a Main Sequence star, what spectral class and absolute magnitude would it have?

5.) If a star has an Absolute Magnitude 50 times brighter than our Sun, what would it be? If it appears as a 5 magnitude star, how far away is it?
 
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