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Lesson Five - Geometry of Radio Meteor Reflections
*All requirements in this section are quoted directly from the new Science 9 curriculum from Alberta Learning. The full curriculum can be seen here.
a) constructing and interpreting drawings and physical models that illustrate the motion of objects in space;
b) describing the position of objects in space, using angular coordinates.
Background information for the teacher
Geometry of radio meteor reflections
· Calculating the distance to the horizon. Graph the curve of the Earth's surface. Use distance to Earth's centre, height of the burn zone for meteors.
Outline the activity
Activity #1 – Calculating Distance to the Horizon
For demonstration: Large ball such as an exercise ball, basketball or beach ball. Penny. Ruler.
For group activity: 6 basketballs, 6 rulers
Demonstration: Finding the distance to the horizon on a ball. Take a ball and have a student put their eye as close to the top surface of the ball as possible. Have another student gradually move a penny standing on end between their thumb and finger along the surface of the ball until the first student sees the top of the penny appear above the horizon of the ball. The purpose is to demonstrate that the distance to the horizon depends on how high one is above the surface of the Earth.
a) The Earth is perfectly spherical. It is not.
b) For our purposes here, treat the surface of the Earth as perfectly smooth with no variations - no mountains or valleys or other obstructions.
What is the distance to the visual horizon from a point a certain distance off the surface of the Earth?
In six groups:
a) Measure the diameter of the ball. Calculate the radius of the ball based on this measurement.
b) Measure the distance of the student’s eye from the surface of the ball.
c) Mark the spot on the surface of the ball beyond which the person cannot see anything on the surface of the ball (the horizon).
d) Lay a ruler on the spot on the ball that is the horizon. The ruler should point to where the pupil of the observer's eye was. Note that the ruler is laying tangent to the surface of the ball. That is, the ruler is at 90 degrees to the radius line of the ball.
d) Measure the distance between the eye and the horizon mark on the ball. This is the distance to the horizon.
e) Draw the geometry of this setup including the measurements. Include the radius of the ball, the height of your eye above the ball, and note the distance to the mark (horizon) on the ball.
f) Using the diagram and the formula at this link plug your measurements into the formula to see how your measurements compare with the calculated results.
g) Translate the geometry of this model to that of the Earth using the diagram and the formula. The radius of the Earth is approximately 6370 km. Instead of using your eye, replace its position on the diagram with a transmitting antenna 100 meters high, with the horizon being the location of a radio receiver.
h) What is the distance to the horizon as seen from the top of the transmitting antenna?
Activity #2 – Calculating the Correct Antenna Elevation Angle
Six 6.37 meter lengths of string, 6 protractors, 12 sheets of paper, tape, protractor.
What is the correct angle measured from the horizon to a point above the horizon that will give the optimal reception of a signal from a transmitter at a given distance from the student radio observatory.
On the morning of November 18, 2001, a Radio Meteor was detected at about 3:45 am at an Edmonton based radio observatory. In the audio recording of the bounce the FM radio station gave its frequency as 92.1 FM, a Calgary radio station. Calgary and Edmonton are approximately 300 kilometers apart as the crow flies. The best spot to aim an antenna is mid-point between the receiver and transmitter (150 km away). Meteors typically form ionization trails capable of reflecting radio signals at an altitude of between 85 and 105 kilometers above the Earth’s surface (use an average of 95 km).
a) Review the geometrical model developed using the ball demonstration. See the illustration at this link.
b) Translate the geometry of this model to that of the Earth using a long string, sheet of paper and protractor. The radius of the Earth is approximately 6370 km. If you use 1 mm to stand for 1 kilometer, how long does the string need to be to represent the radius of the Earth? Take a string that long and tape one end to the floor. At the other end, tape two pieces of paper to the floor end to end so that you can draw an arc at the end of the string that crosses the middle of the paper. Draw the arc.
c) Mark two points along the arc 300 mm (30 cm) apart representing the distance between Edmonton and Calgary. Then bisect the arc at 150 mm between Edmonton and Calgary. Measure a distance of 95 mm above the midpoint of the arc and mark that spot. This represents the zone at which meteors create ionization trails.
d) Take a ruler and draw a line between Edmonton and the ionization zone midpoint between Edmonton and Calgary. Draw another line from Calgary to the same point. With the protractor, measure the angle at Edmonton between the Earth's surface and the line from Edmonton to the ionization zone. This is the elevation at which you should set your antenna if you are using a Yagi antenna.
e) Optional: Using trigonometry and the geometry of right angle triangles, determine the elevation angle for a Yagi antenna where the receiver and transmitter are separated by 2100 km.
Teacher notes and debriefing