The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter 6, Problem 58EAP
Visible-Light Interferometry. Technological advances are now making it possible to link visible-light telescopes so that they can achieve the same angular resolution as a single telescope over 300 meters in size. What is the angular resolution (diffraction limit) of such a system of telescopes for observations at a wavelength of 500 nanometers?
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Both the Keck Telescope and
Hubble Space Telescope (HST)
observe visible light. Given a
typical visible light wavelength of
500 nm, and the diameters of 10 m
for Keck and 2.4 m for Hubble,
which telescope do you think
would have better angular
resolution? Based on the equation
for angular resolution, what is the
resolution of Keck at 500 nm? Of
HST?
How can we help VIEW
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%D
a) Describe what is meant by the term Point Spread Function (PSF), explain the
relationship between the PSF and the aperture (entrance pupil) of a telescope.
You should refer to the ideas of diffraction and Fourier Optics in your answer.
b) Determine the plate scale and theoretical resolving power at a wavelength of
380 x 10-9 m of a telescope with 2 m aperture diameter and focal length of 4m.
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 cm
Chapter 6 Solutions
The Cosmic Perspective (9th Edition)
Ch. 6 - Prob. 1VSCCh. 6 - Prob. 2VSCCh. 6 - Prob. 3VSCCh. 6 - Prob. 4VSCCh. 6 - How does your eye focus light? How is a glass lens...Ch. 6 - How does a camera record light? How are images...Ch. 6 - What are the two key properties of a telescope,...Ch. 6 - What is the diffraction limit, and how does it...Ch. 6 - How do reflecting telescopes differ from...Ch. 6 - What are the three basic categories of...
Ch. 6 - Prob. 7EAPCh. 6 - What do we mean by spectral resolution? Why is...Ch. 6 - List at least three ways in which Earth's...Ch. 6 - 10. Describe how deeply each portion of the...Ch. 6 - Prob. 11EAPCh. 6 - Prob. 12EAPCh. 6 - Prob. 13EAPCh. 6 - Prob. 14EAPCh. 6 - Prob. 15EAPCh. 6 - Prob. 16EAPCh. 6 - Prob. 17EAPCh. 6 - Prob. 18EAPCh. 6 - Prob. 19EAPCh. 6 - Prob. 20EAPCh. 6 - Prob. 21EAPCh. 6 - Prob. 22EAPCh. 6 - Prob. 23EAPCh. 6 - Prob. 24EAPCh. 6 - Prob. 25EAPCh. 6 - Prob. 26EAPCh. 6 - Prob. 27EAPCh. 6 - Prob. 28EAPCh. 6 - Prob. 29EAPCh. 6 - Prob. 30EAPCh. 6 - Prob. 31EAPCh. 6 - Prob. 32EAPCh. 6 - Prob. 37EAPCh. 6 - Prob. 38EAPCh. 6 - Prob. 39EAPCh. 6 - Prob. 40EAPCh. 6 - Prob. 41EAPCh. 6 - Prob. 42EAPCh. 6 - Prob. 43EAPCh. 6 - Prob. 44EAPCh. 6 - Prob. 45EAPCh. 6 - Prob. 46EAPCh. 6 - Prob. 50EAPCh. 6 - Close Binary System. Suppose that two stars in a...Ch. 6 - Prob. 52EAPCh. 6 - Diffraction Limit of the Eye. Calculate the...Ch. 6 - Prob. 54EAPCh. 6 - Prob. 55EAPCh. 6 - Hubble’s Field of View. Large telescopes often...Ch. 6 - Prob. 57EAPCh. 6 - Visible-Light Interferometry. Technological...
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- The 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_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_forwardYou 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_forward
- Can you please assist with Part 2 of 5?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_forwardYou 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.arrow_forward
- 1. If the cross-track angular resolution of a satellite sensor at nadir is given by 1.4 /D where is the wavelength being observed and D is the aperture size of the sensor, what is the cross-track spatial resolution on the ground if D = 80 cm and the satellite sensor is at an orbital height of 600 km? (a) for an infrared sensor observing wavelengths at 20 microns? (b) for a microwave sensor observing wavelengths at 1.5 cm? =arrow_forwardA series of optical telescopes produced an image that has a resolution of about 0.00350 arc second. What is the smallest diameter telescope that could theoretically resolve these features using light with a wavelength of 1.90 μm? (Note: 1arcsec=1/3600∘) Express your answer to three significant figures and include appropriate units.arrow_forwardWhat is the resolving power of an 8-inch telescope (if necessary, you may assume λ=550 nm)? By the way, this is the aperture size of the telescopes we use in the outdoor labs. Will two stars 1 arcsecond apart appear as two separate stars or one big blob? In other words can the two stars be clearly resolved by this telescope?arrow_forward
- A 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_forwardYou 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.arrow_forward4. For a space-based imaging system that uses a fixed size aperture for both visible and infrared sensors, given the characteristics listed, what would be the theoretical resolution for each of the sensors? Aperture diameter = 1.1 m. Visible wavelength = 0.5 micron. IR wavelength = 2.0 micron. Altitude = 400 km. (note: 1 micron = 1E-6 m)arrow_forward
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