Download Astronomy 10 Measuring Stars

Astronomy 10 Measuring Stars
d = p1
L
b = 4πd
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λpeak T = 3 × 107 ÅK
L = 4πR2 σT 4
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P 2 = G(M4π+M ) r3
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Let’s examine the star Sirius. Sirius is the bright star southeast of Orion in the winter sky. It’s the
brightest star in the sky (other than the sun), and is also called the ”Dog Star” since it is the brightest
star in the constellation of Canis Major (the great dog). Sirius has a companion star that orbits around
it, called Sirius B (and the brighter star is called Sirius A).
The pair are measured to have a parallax of about 4/10 of an arcsecond. How far away are they?
Sirius A appears to be 1010 times fainter than the sun. Given that 1 pc is about 200,000 AU, what is
the luminosity of Sirius A in terms of the sun’s luminosity?
Sirius B is seen to be 10,000 times fainter than Sirius A. What is the luminosity of Sirius B in terms of
the sun’s luminosity?
The spectra of the two stars are analyzed. The blackbody spectrum of Sirius A is found to peak at
about 3000 Å. Given that the constant in Wien’s Law is 3 × 107 ÅK, what is the temperature of Sirius A?
Sirius B’s blackbody spectrum is found to peak at about 900 Å. Is it hotter or colder than Sirius A?
What is the temperature of Sirius B?
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The sun has a temperature of about 6000K. Given the data you have calculated so far, what is the ratio
of the radius of Sirius A to that of the sun?
What about the same for Sirius B? How does it compare to the size of the Earth? (REarth = 9 × 10−3
Rsun )
From just looking at the spectrum, the apparent brightness, and the parallax of the stars, we have
now found their surface temperature, intrinsic brightness, and physical size! Since these two stars are in a
binary system, lets see what more we can measure. Some simple geometry can show us that the physical
distance seperating Sirius A and Sirius B can be found by: r = d × θ, where r is the actual physical distance
between the two stars (in AU), d is the distance they are from us (in parsecs), and θ is the apparant angular
separation of the pair (in arcseconds). Given that Sirius A and Sirius B appear to be separated by about
8 arcseconds, how far are they really apart from each other?
By watching the pair over time, we can see them orbiting each other. It is observed that the period
of this orbit is about 50 years. Using Kepler’s 3rd Law, find the sum of the masses of Sirius A and B in
terms of the mass of the sun.
We can also observe that Sirius B moves more than Sirius A in this orbit. Which of the two is more
massive?
By carefully measuring their motions, we find that Sirius A is a bit more than twice the mass of the
sun, and Sirius B is a little less than the mass of the sun. Sirius A turns out to be more massive, larger,
hotter, and brighter than the sun. Sirius B, however, is about the same mass, much smaller, much hotter,
and much less bright than the sun. This little star contains about as much mass as the sun in an object
about the size of the Earth! It turns out that Sirius B is the dead core of a star, called a white dwarf,
which you’ll learn more about in about a week or so.
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