CH6- QP

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University of Michigan *

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101

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Astronomy

Date

Apr 3, 2024

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pdf

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2

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9th Edition Textbook: 50) a. How much greater is the light-collecting area of one of the 10-meter Keck telescopes than that of the 5-meter Hale telescope? 10/5 → 2x the diameter Light-collecting area= 2^2= 4x greater b. Suppose astronomers built a 100-meter telescope. How much greater would its light-collecting area be than that of the 10-meter Keck telescope? 100/10=10x the diameter 10^2= 100x greater 51) Suppose that two stars in a binary star system are separated by a distance of 100 million kilometers and are located at a distance of 100 light-years from Earth. What is the angular separation of the two stars? Give your answer in both degrees and arcseconds. Can the Hubble Space Telescope resolve the two stars? Angular separation= Physical separation * (360/(2pi *distance)) = 100,000,000 (360/(2pi *(9.46*10^14)) =0.00000605663 degrees Arcseconds= 0.00000605663 *3600 = 0.0218 seconds No, an object would need to subtend an angle greater than 0.05 arcseconds for the hubble telescope to resolve it. 52) Suppose you were looking at our own solar system from a distance of 10 light-years. a. What angular resolution would you need to see the Sun and Jupiter as distinct points of light? Sun-Jupiter distance= 778,000,000km Angular separation= Physical separation * (360/(2pi *distance)) = 778,300,000 (360/(2pi *(9.46*10^13)) = 0.000471388 Arcseconds=0.000471388*3600= 1.6969 b. What angular resolution would you need to see the Sun and Earth as distinct points of light?
Sun-Earth distance= 147,770,000km Angular separation= Physical separation * (360/(2pi *distance)) = 147.770,000 (360/(2pi *(9.46*10^13)) =0.00008949891 Arcseconds= 0.00008949891*3600= 0.322 c. How do the angular resolutions you found in parts a and b compare to the angular resolution of the Hubble Space Telescope? Comment on the challenge of making images of planets around other stars. Both planets could be distinguished from the Sun in means of angular resolution as the hubble telescope would need an angle of 0.05 arcseconds or greater in order to be resolved. However, the light from planets could be lost in the glare of the Sun. 54) What is the diffraction limit of a 100- meter radio telescope observing radio waves with a wavelength of 21 centimeters? Compare this to the diffraction limit of the Hubble Space Telescope for visible light. Use your results to explain why, to be useful, radio telescopes must be much larger than optical telescopes. Diffraction limit= 2.5*10^5 (wavelength of light / diameter of telescope) = 2.5*10^5(0.21/100) =525 arcseconds The diffraction limit of the Hubble Space Telescope is 0.05 arcseconds, thus it can be resolved. Also, radio telescopes must be larger than optical telescopes because the wavelengths of radio waves are larger than visible light. Moreover, they have higher telescope diffraction limits.
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