Question

section 27.1 review

1. what do astronomers analyze to determine the composition and surface temperature of a star?
2. as you observe the night sky, why do stars appear to move west - ward across the sky?
3. how do astronomers measure the distance to stars that are less than 1,000 light - years from the earth?
4. assume that a star has an apparent magnitude of +2 and an absolute magnitude of +4. what do you know about the distance of that star from the earth?

Explanation:

1. Astronomers analyze a star's spectrum to determine its composition and surface temperature. Different elements emit or absorb light at specific wavelengths in the spectrum, and the peak - wavelength of the emitted light is related to the star's temperature by Wien's law.
2. Stars appear to move westward across the sky because the Earth rotates east - ward on its axis. From our perspective on Earth, it seems as if the stars are moving in the opposite direction.
3. For stars less than 1,000 light - years from the Earth, astronomers use parallax. Parallax is the apparent shift in the position of a star against more distant background stars as the Earth orbits the Sun. The closer a star is, the larger its parallax angle.
4. The difference between apparent magnitude ($m$) and absolute magnitude ($M$) is related to the distance ($d$) of the star from the Earth by the distance - modulus formula $m - M=5\log_{10}(\frac{d}{10})$. Given $m = + 2$ and $M=+4$, we have $2 - 4=5\log_{10}(\frac{d}{10})$, so $- 2 = 5\log_{10}(\frac{d}{10})$, $\log_{10}(\frac{d}{10})=-\frac{2}{5}=-0.4$, $\frac{d}{10}=10^{- 0.4}\approx0.398$, and $d\approx3.98$ parsecs. Since 1 parsec is about 3.26 light - years, the star is closer than 10 light - years from the Earth.

Answer:

1. A star's spectrum.
2. Because the Earth rotates east - ward on its axis.
3. Parallax.
4. The star is closer than 10 light - years from the Earth.