Horizons: Exploring the Universe (MindTap Course List)
14th Edition
ISBN: 9781305960961
Author: Michael A. Seeds, Dana Backman
Publisher: Cengage Learning
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Chapter 5, Problem 10P
To determine
Minimum diameter of the telescope the satellite must carry.
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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)?
spy 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.)
Estimate the angular resolutions of a radio interferometer with a 5000-km baseline, operating at a frequency of 5 GHz.
Chapter 5 Solutions
Horizons: Exploring the Universe (MindTap Course List)
Ch. 5 - Prob. 1RQCh. 5 - Prob. 2RQCh. 5 - Prob. 3RQCh. 5 - Prob. 4RQCh. 5 - Prob. 5RQCh. 5 - Prob. 6RQCh. 5 - Prob. 7RQCh. 5 - Prob. 8RQCh. 5 - Prob. 9RQCh. 5 - Prob. 10RQ
Ch. 5 - Prob. 11RQCh. 5 - Prob. 12RQCh. 5 - Prob. 13RQCh. 5 - Prob. 14RQCh. 5 - Prob. 1DQCh. 5 - Consider the “atmospheric windows” of Earth’s...Ch. 5 - The thickness of the plastic in plastic bags is...Ch. 5 - What is the wavelength of radio waves transmitted...Ch. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - H does the resolving power of the 5-rn telescope...Ch. 5 - If you build a telescope with a focal length of...Ch. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 1LTLCh. 5 - The star images in the photo in Figure UN 5-4 are...Ch. 5 - The X-ray image in Figure UN 5-5 shows the remains...
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- In the dark, your pupil (the aperture of your eye) expands to a diameter of 7 mm. How many times more light can be gathered by a telescope with a 5.5 m diameter than by a fully dark- adapted eye? Increase in light gathered = I timesarrow_forwardFor a human eye with a pupil diameter (aperture diameter D) of 0.005 meters, and a focal length of 0.022 meters, there will be a resolution limit due to diffraction at 0.6 microns (10^-6 meters) wavelength. If we space light-sensitive cells on the retina at this spacing, how many retina cells per meter (of retina) are there? cells/meter. Now suppose there are giants which are exactly twice the size of humans in each dimension. So giant eyes have pupils of 0.01 meters, and a focal length of 0.044 meters. How many retina cells per meter should the giants have? cells/meterarrow_forwardWhat diameter telescope is needed to resolve the separation between an Earth-like planet and its star at 550 nm if the linear separation between them is 1 AU and the star system is 4 pc from Earth? (Give your answer in m.) marrow_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_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_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
- the SETI project's Allen Telescope Array will have 350 radio dishes, each with an individual diameter of 6 m, spread out over a circle whose diameter is 1 km. What would this array's spatial resolution be when it operates at 6,000 MHz?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_forwardA charged-couple device (CCD) detector ismounted at the focus of an f/7 reflecting telescope with a D= 50 cm mirror. The CCD chip contains 1024×1024 pixels, with each square pixel being 10μm on a side. How many separate exposures would be required to cover the entire celestial sphere (4π steradians)?arrow_forward
- Theoretically (that is, if seeing were not an issue), the resolution of a telescope is inversely proportional to its diameter. How much better is the resolution of the ALMA when operating at its longest baseline than the resolution of the Arecibo telescope?arrow_forwardHow much more light can the Keck telescope (with its 10-m diameter mirror) gather than an amateur telescope whose mirror is 25 cm (0.25 m) across?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_forward
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