Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 6, Problem 40Q
To determine
Whether the Hubble space telescope can distinguish any feature on Pluto, if Pluto is
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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.
What diameter telescope (in m) would you need to observe Olympus Mons (624 kmin diameter) from Earth at a wavelength of 550 nm when Mars is2.55×106km away?xUse the small angle formula to calculate the angular size of Olympus Mons. Then use the telescope resolution formula to calculate the diameter needed to resolve it m
What diameter telescope is needed to see the separation between Uranus and its largest moon, Titania, from Earth at 550 nm, when Earth is 19.7 AU away? The moon is 436,300 km from the center of the planet. (Enter your
answer in m.)
m
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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- The angular separation in degrees of two objects is (physical separation × 360°) / (2 π × distance). If an individual was observing our solar system from Castor at a distance of 7.2 light years. What angular resolution, in arcsecond, is needed to resolve the Sun-Jupiter system (5.46 AU) as distinct points of light?arrow_forwardTutorial You want to resolve 9.5 m features on Mercury with a 2 m telescope using 550 nm light. How close (in km) do you need to be? How does the orbital velocity (in km/s) at this altitude on Mercury compare to the orbital velocity at this altitude on Earth? (MẸ = 5.97 x 1024 kg, Re = 6.38 x 10 km, M = 3.30 x 1023 kg, R = 2440 km.) Part 1 of 4 The small angle formula tells us how distance and linear size are related to the angular size of an object. 2.06 x 105 D And the diameter of a telescope is related to the resolving power by: a- 2.06 x 105 diameter Part 2 of 4 First we should determine the resolving power of our 2 m telescope. a = 2.06 x 10 What is the wavelength you are trying to observe at? m diameter arc secondsarrow_forwardThe 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_forward
- Suppose you send a probe to land on Mercury, and the probe transmits radio signals to earth at a wavelength of 52.0000 cm. You listen for the probe when Mercury is moving away from Earth at its full orbital velocity of 48 km/s around the Sun. What wavelength (in cm) would you have to tune your radio telescope to detect that signal? Use the doppler shift formula Note: the speed of light is 3.0 ✕ 105 km/s. Give your answer to at least four decimal places.)arrow_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 1 pc from Earth? (Give your answer in m.)arrow_forwardWhat are the arguments for building the TMT telescope?arrow_forward
- Suppose you send a probe to land on Mercury, and the probe transmits radio signals to earth at a wavelength of 40.0000 cm. You listen for the probe when Mercury is moving away from Earth at its full orbital velocity of 48 km/s around the Sun. What wavelength (in cm) would you have to tune your radio telescope to detect that signal?arrow_forwardVoyager 2. When the Voyager 2 spacecraft was approaching towards its Neptune encounter in 1989, it was 4.5 × 10° km away from the earth. Its radio transmitter, with which it communicated with us (and we communicated with it), broadcast with a mere 22 Watt of power at the S-band (2.1 GHz). (Your home wi-fi router emits around 2 Watt at 2.4 GHz wi-fi band). Assuming the Voyager transmitter broadcast equally in all directions, (a) What signal intensity was received on the earth? (b) What electric and magnetic field amplitudes were detected? (c) How many 2.1 GHz photons were arriving per second on a radio-receiver antenna with a circular cross-section of diameter 34 meters? Two counter-propagating plane waves (a) Let E(z, t) = E0 cos(kz – wt)â + E, cos(kz + wt)x. Write E(z, t) in simpler form and find the associated magnetic field. (b) For the fields in part (a), find the instantaneous and time-averaged electric and magnetic field energy densities. (c) Let E(z, t) = E, cos(kz – wt)x + E,…arrow_forwardYou have a radio telescope that you are designing to observe the fine details of the ring of hydrogen around Jupiter (yes, Jupiter does have rings, but not as pretty as Saturn.) Jupiter is about 5.93E8 km from Earth. If you are trying to observe gas structures the size of a small town (about 1.0 km across) and the wavelength of hydrogen alpha is 656.28 nm, then what is the minimum diameter that you would need to have for your telescope to resolve the needed details to Rayleigh criterion?arrow_forward
- The 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_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 1 pc from Earth?arrow_forwardYou are working for a new assistant professor in astronomy who is interested in exoplanets. One day, a scientific rumor begins circulating that there is a Jupiter-sized planet around Alpha Centauri, 4.28 light-years away. Your professor has access to viewing privileges for the Hubble Space Telescope (aperture diameter 2.4 m, 100 nm to 2 400 nm), the Hale Telescope on Palomar Mountain in California (aperture diameter 5.08 m, visible light), the Keck Telescope on Mauna Lea, Hawaii (aperture diameter 10.0 m, visible light), and the Arecibo Radio Telescope in Puerto Rico (aperture diameter 305 m, 75-cm radio waves). He asks you to advisehim as soon as possible as to which telescope he should request time on in order to resolve an image of the planet.arrow_forward
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