Homework Assignment
1
Due Wednesday September 5, 2003
Problem
2.TZD
1.14
Problem
3.TZD
1.15
Problem
4.TZD
1.17.
Problem
5.Radar
ranging to asteroids.Radar is
a tool used for measuring distance and velocity through the use of electromagnetic
waves in the radio and microwave spectrum, typically at frequencies of
several hundred Megahertz to several Gigahertz. Recently, radar has been
applied to the imaging of near-Earth orbiting asteroids. This problem investigates
the use of round-trip radar pulses to measure the shapes of asteroids.
Useful
sites: http://echo.jpl.nasa.gov,
http://neo.jpl.nasa.gov/1950da,
http://www.eecs.wsu.edu/~hudson/Research/Asteroids/index.htm.
Here
is a radar image of one particular asteroid, Asteroid 1950da, which has
been in the news lately. To learn more about this object, check out the
website at the Jet Propulsion Laboratory, http://neo.jpl.nasa.gov/1950da/.
This asteroid was discovered by optical telescopes in 1950, and then was
lost for roughly 50 years, when it was rediscovered. During a recent close
approach, March 3-7, 2001, radar observations were taken from the Goldstone
and Arecibo radio telescopes. The images show an asteroid that is roughly
1.1 km in diameter. The image shows pock marks roughly 100 meters across.
The overall distance to the asteroid is determined by sending a radio pulse
out towards the asteroid, and then running a clock to see how long it takes
for the reflected pulse to return. If the asteroid is shaped like a flat
mirror, pointed directly back at the Earth, then the reflected pulse would
look just like a smaller amplitude version of the original pulse. However,
due to the shape of the asteroid, the parts that are closer to the Earth
send the reflected pulse back earlier than part that are farther from the
Earth.
Assume
that the asteroid is 7.8 million kilometers from the Earth. What is the
typical round trip time between launching the pulse and receiving the reflected
pulse? Suppose that the asteroid has a crater 100 meters deep. At some
time, the rim of the crater is closest to Earth and the bottom of the crater
is 100 meters further away. What is the time between receiving the return
pulse from the rim and from the bottom?
By
tracking this asteroid, radio astronomers now know that there is a 1:300
chance that this rock will hit the Earth squarely in the year 2880.