(a) The planet Pluto and its Moon Charon are separatedby 19,600 km. Neglecting atmospheric effects, should the5.08-m-diameter Mount Palomar telescope be able to resolvethese bodies when they are 4.50×109km from Earth?Assume an average wavelength of 550 nm.(b) In actuality, it is just barely possible to discern that Plutoand Charon are separate bodies using an Earth-basedtelescope. What are the reasons for this?

(a) The planet Pluto and its Moon Charon are separatedby 19,600 km. Neglecting atmospheric effects, should the5.08-m-diameter Mount Palomar telescope be able to resolvethese bodies when they are 4.50×109km from Earth?Assume an average wavelength of 550 nm.(b) In actuality, it is just barely possible to discern that Plutoand Charon are separate bodies using an Earth-basedtelescope. What are the reasons for this?

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter4: Diffraction

Section: Chapter Questions

Problem 86AP: How far apart must two objects be on the moon to be distinguishable by eye if only the diffraction...

See similar textbooks

Similar questions

How far apart must two objects be on the moon to be distinguishable by eye if only the diffraction effects of the eye’s pupil limit the resolution? Assume 550 nm for the wavelength of light, the pupil diameter 5.0 mm, and 400,000 km for the distance to the moon.
A spy satellite is reputed to be able to resolve objects 10. cm apart while operating 197 km above the surface of Earth. What is the diameter of the aperture of the telescope if the resolution is only limited by the diffraction effects? Use 550 nm for light.
The 305-m-diameter Arecibo radio telescope pictured in Figure 4.20 detects radio waves with a 4.00-cm average wavelength. (a) What is the angle between two just-resolvable point sources for this telescope? (b) How close together could these point sources be at the 2 million light-year distance of the Andromeda Galaxy? Figure 4.20 A 305-m-diameter paraboloid at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D for Arecibo is much larger than for the Hubble Telescope, it detects radiation of a much longer wavelength and its diffraction limit is significantly poorer than Hubble’s. The Arecibo telescope is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Jeff Hitchcock)
Check Your Understanding What is the angular resolution of the Arecibo telescope shown in Figure 4.20 when operated at 21-cm wavelength? How does it compare to the resolution of the Hubble Telescope? Figure 4.20 A 305-m-diameter paraboloid at Arecibo in Puerto Rico is lined with reflective material, making it into a radio telescope. It is the largest curved focusing dish in the world. Although D for Arecibo is much larger than for the Hubble Telescope, it detects radiation of a much longer wavelength and its diffraction limit is significantly poorer than Hubble’s. The Arecibo telescope is still very useful, because important information is carried by radio waves that is not carried by visible light. (credit: Jeff Hitchcock)
Assuming the angular resolution found for the Hubble Telescope in Example 4.6, what is the smallest detail that could be observed on the moon?
Radio telescopes are telescopes used for the detection of radio emission from space. Because radio waves have much longer wavelengths than visible light, the diameter of a radio telescope must be very large to provide good resolution. For example, the radio telescope in Penticton, BC in Canada, has a diameter of 26 m and can be operated at frequencies as high as 6.6 GHz. (a) What is the wavelength corresponding to this frequency? (b) What is the angular separation of two radio sources that can be resolved by this telescope? (c) Compare the telescope’s resolution with the angular size of the moon.
A telescope can be used to enlarge the diameter of a laser beam and limit diffraction spreading. The laser beam is sent through the telescope in opposite the normal direction and can then be projected onto a satellite or the moon. (a) If this is done with the Mount Wilson telescope, producing a 2.54-m-diameter beam of 633-nm light, what is the minimum angular spread of the beam? (b) Neglecting atmospheric effects, what is the size of the spot this beam would make on the moon, assuming a lunar distance of 3.84108 m?
A camera uses a lens with aperture 2.0 cm. What is the angular resolution of a photograph taken at 700 nm wavelength? Can it resolve the millimeter markings of a ruler placed 35 m away?
An amateur astronomer wants to build a telescope with adiffraction limit that will allow him to see if there are people onthe moons of Jupiter.(a) What diameter mirror is needed to be able to see 1.00 mdetail on a Jovian Moon at a distance of 7.50×108km fromEarth? The wavelength of light averages 600 nm.(b) What is unreasonable about this result?(c) Which assumptions are unreasonable or inconsistent?
The 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.
One important goal of astronomers is to have a telescope inspace that can resolve planets like the earth orbiting other stars. If aplanet orbits its star at a distance of 1.5 * 10^11 m (the radius of theearth’s orbit around the sun) and the telescope has a mirror of diameter8.0 m, how far from the telescope could the star and its planet be if thewavelength used was (a) 690 nm and (b) 1400 nm? Use the Rayleighcriterion and give your answers in light-years (1 ly = 9.46 * 1015 m).
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.