help please! A satellite circling the Earth is transmitting microwaves if 15 cm
ID: 2108569 • Letter: H
Question
help please!
A satellite circling the Earth is transmitting microwaves if 15 cm wavelength. When the satellite is above a ground station which has two antennae connected together 100m apart and located in the plane of the orbit, a signal is received that fluctuates in intensity with a period of 1/10 s. If we know that the satellite is 400 km high, and if we neglect the curvature of the Earth, what is the velocity of the satellite? A concept that may be useful here is reciprocity: the sensitivity pattern of a receiving antenna system is exactly the same as the intensity pattern it would produce if transmitting.Explanation / Answer
The idea is that you can imagine the satellite passing through a double slit interference pattern, and the time from one maximum to the next is 1/10 of a second. So we find the distance from one maximum to the next, divide by the time... and that's the speed! We can use the double slit formula for small angles: m*wavelength = d y / L , where m = 1 in this case and we want to solve for y. y = L * wavelength / d = 400 km * 15 cm / 100 m = 400000 * 0.15 / 100 = = 600 meters Finally, speed = distance / time = 600 m / 0.10 sec = 6000 m/s is the speed of the satellite.
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