Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 6, Problem 24Q
To determine
(a)
The diffraction limited angular resolution of the telescope.
To determine
(b)
The angular resolution of the telescope as compared with Keck I
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You have been asked to compare four proposals for telescopes to be placed in orbit above the blurring effects of the earth’s atmosphere. Rank the proposed telescopes in order of their ability to resolve small details, from best to worst. (i) A radio telescope 100 m in diameter observing at a wavelength of 21 cm; (ii) an optical telescope 2.0 m in diameter observing at a wavelength of 500 nm; (iii) an ultraviolet telescope 1.0 m in diameter observing at a wavelength of 100 nm; (iv) an infrared telescope 2.0 m in diameter observing at a wavelength of 10 mm.
You are using a telescope is to resolve two distant stars as well as possible.
Which of the following modifications will increase the resolution of the telescope?
Question 8 options:
Use a filter to filter out all but the red light.
Use a filter to filter out all but the blue light.
Use a lens of smaller diameter
Use a lens of larger diameter
None of these modifications will impact the resolution of the telescope.
What is the limit of resolution for a telescope lens with a diameter of 120 cm when it observes a star at a distance of 4 light-years? Use the wavelength of l = 550 nm in your calculations.
Chapter 6 Solutions
Universe: Stars And Galaxies
Ch. 6 - Prob. 1QCh. 6 - Prob. 2QCh. 6 - Prob. 3QCh. 6 - Prob. 4QCh. 6 - Prob. 5QCh. 6 - Prob. 6QCh. 6 - Prob. 7QCh. 6 - Prob. 8QCh. 6 - Prob. 9QCh. 6 - Prob. 10Q
Ch. 6 - Prob. 11QCh. 6 - Prob. 12QCh. 6 - Prob. 13QCh. 6 - Prob. 14QCh. 6 - Prob. 15QCh. 6 - Prob. 16QCh. 6 - Prob. 17QCh. 6 - Prob. 18QCh. 6 - Prob. 19QCh. 6 - Prob. 20QCh. 6 - Prob. 21QCh. 6 - Prob. 22QCh. 6 - Prob. 23QCh. 6 - Prob. 24QCh. 6 - Prob. 25QCh. 6 - Prob. 26QCh. 6 - Prob. 27QCh. 6 - Prob. 28QCh. 6 - Prob. 29QCh. 6 - Prob. 30QCh. 6 - Prob. 31QCh. 6 - Prob. 32QCh. 6 - Prob. 33QCh. 6 - Prob. 34QCh. 6 - Prob. 35QCh. 6 - Prob. 36QCh. 6 - Prob. 37QCh. 6 - Prob. 38QCh. 6 - Prob. 39QCh. 6 - Prob. 40QCh. 6 - Prob. 41QCh. 6 - Prob. 42QCh. 6 - Prob. 43QCh. 6 - Prob. 44QCh. 6 - Prob. 45Q
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- What kind of visible-light and infrared telescopes on the ground are astronomers planning for the future? Why are they building them on the ground and not in space?arrow_forwardThe HST cost about $1.7 billion for construction and $300 million for its shuttle launch, and it costs $250 million per year to operate. If the telescope lasts for 20 years, what is the total cost per year? Per day? If the telescope can be used just 30% of the time for actual observations, what is the cost per hour and per minute for the astronomer’s observing time on this instrument? What is the cost per person in the United States? Was your investment in the Hubble Space telescope worth it?arrow_forwardWhat is the resolving power of a 25-cm (10-in.) telescope at a wavelength of 550 nm (in the middle of the visual band)?arrow_forward
- Which of the following pairings of telescope diameter and observational wavelength would give the best resolution images of an object with a telescope? Explain why you chose the telescope and wavelength combination you did, and calculate the angular resolution you could achieve with it. It would be best to observe with... Option 1: a 10 m diameter optical telescope on the ground with λ= 550 nm Option 2: a 2.4 m diameter optical telescope in space with λ=500 nm Option 3: a 100 m radio telescope on the ground with λ=100 cmarrow_forwardThe large space telescope that has been placed into an Earth orbit has an aperture diameter of 1.4 meters. What angular resolution will this telescope achieve for visible light of wavelength 2 = 6.5 x 10-7 m? Write your answer in "seconds of arc".arrow_forwardspy satellite orbiting 410 km above Earth is supposedly capable of counting individual people in a crowd in visual-wavelength images. Assume that the satellite's cameras operate at a wavelength of 550 nm. Assume an average person has a size of 0.6 m as seen from above. Estimate the minimum telescope diameter that the satellite must carry. (Hint: Use The small-angle formula angular diameter (arc seconds) 2.06 105 = linear diameter distance to convert linear size to angular size.)arrow_forward
- The SST's planned operating temperature is 5.5 K. At what wavelength (in micrometers, µm) does the telescope's own blackbody emission peak? How does this wavelength compare with the wavelength range in which the telescope is designed to operate?arrow_forwardThe telescope of a spy satellite is reputed to be able to resolve objects 9 cm apart from an altitude of 180 km above the surface of Earth. 1) What is the diameter, in meters, of the telescope’s aperture, if its resolution is limited only by diffraction effects? Take 550 nm for the wavelength of light.arrow_forwardA space-based telescope can achieve a diffraction-limited angular resolution of 0.05" for red light (wavelength 700 nm). What would the resolution of the instrument be in the infrared, at wavelength 3.5 μm.arrow_forward
- You want to create a telescope with a resolving powe of 0.100 arc seconds at a wavelength of 550 nm. Wha diameter (in m) do you need? If you want to increase the light gathering power by a factor of 10, by what factor does the diameter need to increase? What would the new resolving power be (in arc seconds)?arrow_forwardAstronauts observing from a space station need a telescope with a resolving power of 0.6 arc second at a wavelength of 530 nm and a magnifying power of 220. Design a telescope to meet their needs.What will its light-gathering power be, compared with a dark-adapted human eye? (Assume that the pupil of your eye can open to a diameter of about 0.8 cm in dark conditions.)(State the necessary primary diameter of the telescope, in m, and the ratio of the focal lengths below.)arrow_forwardThe Hubble Space Telescope has a primary mirror with diameter 2.4 m. Suppose you were able to point it at Mars when the planct is at its closest point to the Earth in its orbit, which would be about 55.7 million km from the telescope. How close could two features on the Martian surface be and still be resolved (assume a wavelength in the middle of the visible spectrum - a number you should know at this point, at least approximately)?arrow_forward
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