Horizons: Exploring the Universe (MindTap Course List)
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 17, Problem 1P

Imagine that a spacecraft has landed on Mercury and is transmitting radio signals to Earth at a wavelength of 10.000 cm. When Mercury is seen from Earth in the evening sky, at its greatest angular distance east of the Sun, it is moving toward Earth at its maximum possible relative speed of 47.9 km/s. To what wavelength must you tune your radio telescope to detect the signals? (Hint: Use the Doppler formula in Reasoning with Numbers 6-2.)

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Suppose you send a probe to land on Mercury, and the probe transmits radio signals to Earth at a wavelength of 59.0000 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 the signal? (Hint: Use the Doppler shift formula .) (Note: the speed of light if 3.0 x 10^5 km/s. Give your answer to at least four decimal places.)  ______ cm
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.)
At an average opposition, the Earth and Mars are separated by 0.52 AU. Suppose an astronomer observes Mars at opposition and that seeing blurs the images to a resolution of 1.0 seconds of arc. What is the smallest surface feature the astronomer would be able to resolve on Mars? How does this size compare with the diameter of Mars?
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