How Do You Solve These Astronomy Homework Problems?

[PhysicsMajor86]

I cannot figure out the answers for the following problems:

1) If a star has a parrallax of 0.016 second of arc and an apparent magnitude of 6, how far away is it, and what is its absolute magnitude?

7) If a star is 10 times the radius of the sun and half as hot, what will its luminosity be?

13) If the orbital velocity of the eclipsing binary in Figure 8-17 is 153 km/s and the smaller star becomes completely eclipsed in 2.5 hours, what is its diameter?

 

[mgb_phys]

1, A star at a distance of 1 parsec has a parallax of 1 arc second.
Calculating absolute magnitude is explained very well here http://en.wikipedia.org/wiki/Absolute_magnitude

 

[Blueshift5]

Hello,

I am happy to help you with your astronomy homework. For problem 1, we can use the formula d=1/p, where d is the distance in parsecs and p is the parallax in arcseconds. Plugging in the given values, we get d= 1/0.016 = 62.5 parsecs. To find the absolute magnitude, we can use the formula M = m - 5(log(d) - 1), where M is the absolute magnitude, m is the apparent magnitude, and d is the distance in parsecs. Plugging in the values, we get M = 6 - 5(log(62.5) - 1) = 2.88. Therefore, the star is 62.5 parsecs away and its absolute magnitude is 2.88.

For problem 7, we can use the Stefan-Boltzmann Law (L = 4πR^2σT^4) to calculate the luminosity of the star. Here, L is the luminosity, R is the radius, σ is the Stefan-Boltzmann constant, and T is the temperature. Since the star is half as hot as the sun, we can assume its temperature to be half of the sun's temperature, which is approximately 5778 K. Plugging in the values, we get L = 4π(10R)^2(5.67 x 10^-8)(5778/2)^4 = 1.18 x 10^32 watts.

Finally, for problem 13, we can use the formula v = 2πr/P, where v is the orbital velocity, r is the distance between the stars, and P is the orbital period. Since the smaller star becomes completely eclipsed in 2.5 hours, we can assume that the orbital period is 2.5 hours. Plugging in the values, we get 153 km/s = 2πr/(2.5 hours) = 2πr/(2.5 x 3600 seconds). Solving for r, we get r = 7.31 x 10^8 km. Since the diameter of a star is roughly twice its radius, the diameter of the smaller star would be approximately 1.46 x 10^9 km.

I hope this helps you with your homework. Let me know if you have any other questions. Keep exploring the