The Solar System
10th Edition
ISBN: 9781337672252
Author: The Solar System
Publisher: Cengage
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Chapter 6, Problem 15P
To determine
The minimum value of the diameter f the telescope.
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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.)
What 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.)
m
Estimate the angular resolutions of a radio interferometer with a 5000-km baseline, operating at a frequency of 5 GHz.
Chapter 6 Solutions
The Solar System
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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_forwardTwo identical stars are moving in a circular orbit around one another with an orbital separation of 2 AU. The system lies 200 light-years from Earth. If we happen to view the orbit head-on, how large a telescope would we need to resolve the stars, assuming diffraction-limited optics at a wavelength of 2 μm?arrow_forwardTheoretically (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_forward
- How 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_forwardIn broad daylight, the size of your pupil is typically 3 mm. In dark situations, it expands to about 7 mm. How much more light can it gather?arrow_forwardThe unaided human eye has a resolution of about 100 arc seconds in bright lighting conditions. Could someone looking out the command module window have seen the astronauts on the Moon yes or no?arrow_forward
- The Mars Reconnaissance Orbiter (MRO) flies at an average altitude of 280km above the Martian Surface. If its cameras have an angular resolution of 0.2 arc seconds, what is the size of the smallest objects that the MRO can detect on the Martian surface? Use the equation: S =x × d / 206265 arcseconds / radian , where S is the true size of the object, d is the distance from the detector to the object, and x is the angular size of the object. Your answer will be in km (you can ignore the radians unit (it should appear, but the equation made a simplifying assumption that dropped it out.arrow_forwardConsider a telescope with a primary mirror diameter of 10 inches compared to one which has a primary mirror diameter of 15 inches. Assuming both are of excellent optical quality, the larger telescope has ---- O one and a half times the light gathering power but worse resolution O over twice the light gathering power and better resolution O one and a half times the light gathering power and better resolution O over twice the light gathering power but worse resolution O the same light gathering power but much better reesolution O the same light gathering power but much better resolutionarrow_forwardThe James Webb Space Telescope has a primary mirror of diameter ? = 6.5metres. When observing at 1100nm wavelength, calculate the minimum angular separation between two stars which can just be resolved; give your answer in arcseconds (arcsec), where 1 arcsec = 1/3600 degree, to 3 decimal places.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_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_forwardCan you please assist with Part 2 of 5?arrow_forward
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