Question

1. what do astronomers analyze to determine the composition and surface temperature of a star?
2. if 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:

Step1: Analyze star composition

Astronomers analyze starlight through spectroscopy. Different elements and compounds in a star's atmosphere absorb or emit light at specific wavelengths. By studying the absorption or emission lines in the star - light spectrum, they can determine the star's composition and surface temperature.

Step2: Explain star's west - ward motion

The stars appear to move westward across the sky because of the Earth's rotation. The Earth rotates from west to east on its axis. As a result, from our perspective on Earth, the stars seem to move in the opposite direction, which is westward.

Step3: Measure star distance (less than 1,000 light - years)

For stars less than 1,000 light - years from the Earth, astronomers use the method of parallax. Parallax is the apparent shift in the position of a star when observed from two different points in the Earth's orbit around the Sun. By measuring the angle of this shift and knowing the baseline (the diameter of the Earth's orbit), they can calculate the distance to the star using trigonometry.

Step4: Determine star distance from magnitudes

The relationship between apparent magnitude ($m$), absolute magnitude ($M$), and distance ($d$ in parsecs) is given by the formula $m - M=5\log_{10}(\frac{d}{1})$. Given $m = + 2$ and $M = + 4$, we have $2-4 = 5\log_{10}(d)$. So, $- 2=5\log_{10}(d)$, then $\log_{10}(d)=-\frac{2}{5}=-0.4$. Taking the antilog, $d = 10^{- 0.4}\approx0.398$ parsecs. Since 1 parsec is about 3.26 light - years, the star is closer than 1 parsec (and thus relatively close to the Earth).

Answer:

1. Astronomers analyze starlight through spectroscopy to determine the composition and surface temperature of a star.
2. Stars appear to move westward across the sky because of the Earth's rotation from west to east.
3. For stars less than 1,000 light - years from the Earth, astronomers use the method of parallax to measure the distance.
4. The star with an apparent magnitude of + 2 and an absolute magnitude of + 4 is relatively close to the Earth (less than 1 parsec).