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Echoes from the Moon
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Image of Fig. 1.
Fig. 1.

Audio output of the words “… Houston, AOS, over,” as displayed using the opensource software Audacity (Ref. 8). The pattern clearly reveals the echo effect. The small signal at about is a beep (“Quindar tone”) used to trigger ground station transmitters. The time scale can be arbitrarily expanded allowing an accurate determination of the echo delay.

Image of Fig. 2.
Fig. 2.

Distance between Houston and the astronauts on the Moon in meters. The data points show the results of our measurements. The open squares show the students’ results, obtained from the data shown in column 3 of Table II. The solid squares, with much smaller error bars, are obtained from the times listed in column 4 of Table II. The curve is obtained by using the Moon ephemerides (Ref. 10) and refers to the distance between Houston and the center of the Moon.


Generic image for table
Table I.

Time delays of the replies in the conversation between Houston and Armstrong during which the famous sentence “one small step for man, one giant leap for Mankind” can be heard. The time delays were measured using chronometers. The errors reflect the range of values measured by the ten groups of students. The very short delay in the second column corresponds to a radio check requested by Armstrong. The mp3 file of this famous conversation is available at the NASA web site (Ref. 9).

Generic image for table
Table II.

Time delays of the echoes during the radio communications between Houston and the Apollo 17 astronauts on the Moon. The delays were measured by ten groups of students. In column 3 the average of the ten measurements is shown, with the error representing the maximum deviation from the average. A more proper statistical treatment of the data, using a maximum likelihood fit, yields the results shown in column 4. The times in column 2 are relative to the “ignition time.” Column 5 shows the differences between the measured times and the times obtained from the Moon ephemerides (Ref. 10). The mp3 files of the registration are available at the NASA web site (Ref. 9).


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Scitation: Echoes from the Moon