Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 6, Problem 28Q
To determine
The reason behind using the Hobby-Eberly Telescope (HET) at the McDonald Observatory in Texas, despite it being a spherical mirror. Also explain why HET is useful for spectroscopy even though it may have spherical aberration which is common in spherical mirrors.
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A certain telescope has a 10' × 10' field of view that is re-
corded using a CCD chip having 2048 x 2048 pixels. What
angle on the sky corresponds to 1 pixel? What would be the di-
ameter of a typical seeing disk (1" radius), in pixels?
Many years ago, a lunar lander was sent to the moon given the base of the lunar lander is roughly 4 m wide and the moon is on average 380 000 km away from Earth, what is the angular size of the lunar lander in Arcseconds? how does this compare to the diffraction-limited resolution of the Hubble Space Telescope (2.4 m aperture) when observing at the wavelength of 700 nm? can the HST resolve the lander of the moon?
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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?
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Chapter 6 Solutions
Universe
Ch. 6 - Prob. 1CCCh. 6 - Prob. 2CCCh. 6 - Prob. 3CCCh. 6 - Prob. 4CCCh. 6 - Prob. 5CCCh. 6 - Prob. 6CCCh. 6 - Prob. 7CCCh. 6 - Prob. 8CCCh. 6 - Prob. 9CCCh. 6 - Prob. 10CC
Ch. 6 - Prob. 11CCCh. 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. 10QCh. 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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- in the question: A spy satellite orbiting 600 km above Earth is supposedly capable of counting individual people in a crowd in visual- wavelength images. Assume that the middle of the visual wavelength band is at 550 nm . Assume an average person has a size of 0.8 m as seen from above. Estimate the minimum telescope diameter that the satellite must carry. The previous expert used 1,22 instead of 2.06 to convert to angular distance. I thinkn he has to use the small-angular formula.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_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 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_forward(a) What is the angular separation of two stars if their images are barely resolved by the Thaw refracting telescope at the Allegheny Observatory in Pittsburgh? The lens diameter is 76 cm and its focal length is 14 m. Assume l = 550 nm. (b) Find the distance between these barely resolved stars if each of them is 10 light-years distant from Earth. (c) For the image of a single star in this telescope, find the diameter of the first dark ring in the diffraction pattern, as measured on a photographic plate placed at the focal plane of the telescope lens. Assume that the structure of the image is associated entirely with diffraction at the lens aperture and not with lens “errors.”arrow_forwardThe nearest neighboring star to the Sun is about 4 lightyears away. If a planet happened to be orbiting this star atan orbital radius equal to that of the Earth–Sun distance,what minimum diameter would an Earth-based telescope’saperture have to be in order to obtain an image that resolvedthis star–planet system? Assume the light emitted by thestar and planet has a wavelength of 550 nm.arrow_forward
- Please answer both:The brightest star in the Pointers is α Centauri. It is actually a binary star, with two components known as α Cen A and α Cen B. They orbit each other for a period of about 80 years. At the moment they are separated by about 5 arcseconds in the sky. a) The average eye has a pupil diameter of 3mm, increasing to about 7mm at night. What is the theoretical best resolution for the human eye, at 500 nm? (Enter your answer in arc seconds, to the nearest whole number) b) Could you separate the two components with your naked eye (at 500 nm)?arrow_forwardCompare the angular resolving power of the following imaging instruments (details of the italicized instruments are to be covered later). Take the wavelength of light as 5 × 10-7 m. (a) the eye with an effective aperture of 0.5 cm (b) a pair of binoculars using a typical aperture of the front lenses (c) the Yerkes Observatory optical telescope, with a diameter of roughly 1.0 m (d) the Manchester radiotelescope, with a diameter of 76.2 m, using microwave radiation of wavelength 22 cm Oarrow_forwardThe Very Large Array (VLA) is a set of 27 radio telescope dishes in Catron and Socorro counties, New Mexico (as shown). The antennas can be moved apart on railroad tracks, and their combined signals give the resolvingpower of a synthetic aperture 36.0 km in diameter. (a) If the detectors are tuned to a frequency of 1.40 GHz, what is the angular resolution of the VLA? (b) Clouds of interstellar hydrogen radiate at the frequency used in part (a). What must be the separation distance of two clouds at the center of the galaxy, 26 000 light-years away, if they are to be resolved? (c) What If? As the telescope looks up, a circling hawk looks down. Assume the hawk is most sensitive to green light having a wavelength of 500 nm and has apupil of diameter 12.0 mm. Find the angular resolution of the hawk’s eye. (d) A mouse is on the ground 30.0 m below. By what distance must the mouse’s whiskers be separated if the hawk can resolve them?arrow_forward
- Astronauts 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_forward(a) How far apart must two objects be on the moon to be resolved by the human eye? Take the diameter of the pupil of the eye to be 6 mm, the wavelength of the light to be 500 nm, and the distance from the earth to the moon to be 380 000 km. Number Units (b) How far apart must the objects be on the moon be to be resolved by a telescope that has a mirror diameter of 6 m? Number Unitsarrow_forwardThe primary mirror of a telescope is 2.4 m in diameter. At what altitude will you need to pilot the telescope in order to resolve things on a 3.0 cm scale?arrow_forward
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