What is the ratio of this star luminosity

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Assignment - Basic Astronomy Questions

Q1. If the emitted infrared radiation from Pluto has a wavelength of maximum intensity at 75,000 nm, what is the temperature of Pluto assuming it follows Wien's law? How close is this to the actual surface temperature of Pluto?

Q2. A red giant star has a surface temperature that is 1/2 of the Sun's surface temperature, and its radius is 50 times larger than the Sun's radius. What is the ratio of this star's luminosity to the Sun's luminosity?

Q3. You observe two stars. Star A is at a distance of 100 light years, and its luminosity is equal to 3 times the Sun's luminosity. Star B is at a distance of 200 light years, and its luminosity is equal to 6 times the Sun's luminosity. What is the ratio of the apparent brightnesses of these two stars, as seen from Earth?

Q4. A star is moving away from the Earth at v = 120 km/s. (a) Is its spectrum redshifted or blueshifted, when we observe it from Earth? (b) If a spectral line in the star's spectrum has rest wavelength 400.0 nm, what is the observed wavelength of this spectral line when we measure the star's spectrum?

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