Temperature of Mars At a wavelength of 31.5 mm, the 15 meter radio telescope at the U.S. Naval Research Laboratory has a beamwidth of 0.116◦. From this antenna, the planet Mars subtends an angle of...

Temperature of Mars At a wavelength of 31.5 mm, the 15 meter radio telescope at the U.S. Naval Research Laboratory has a beamwidth of 0.116◦. From this antenna, the planet Mars subtends an angle of 0.005◦. When this antenna is focused on cold sky (interstellar space), the antenna noise temperature is measured to be 3◦K. When this antenna is focused on Mars, the antenna noise temperature of the antenna increases to 3.24◦K.

a. What is the frequency of observation corresponding to the given wavelength?

b. What is the gain of the antenna at the frequency of observation? Be sure to include your units.

c. What would be the gain of an antenna that would view only Mars?

d. Find the average temperature of Mars at a wavelength of 31.5 mm. (Hint: The antenna subtends an area of the sky. Mars subtends a smaller area of the sky. The increase in noise temperature of the observing antenna is caused by a “hot” Mars being present in a small portion of the view of the sky.)

e. Comment on the effect of polarization in this measurement. If the antenna is polarized, does the measured temperature of Mars increase or decrease?