2. Refraction by the Ionosphere 
The Doppler shift exhibited in the reception of a trans- 
mission from an earth satellite is not strictly proportional to the 
rate of change of the true slant range but rather is proportional to 
the rate of change of the transmission path length. If, as is 
normally the case, the satellite is above the ionosphere, then the 
transmission path is not the straight line joining the transmitter 
and receiver but instead is some longer curved (or bent) path due 
to the refraction effect of the ionosphere. Hence, for a precision 
analysis of the Doppler shift, account must be taken of the effect 
of this ionospheric refraction on the Doppler. A rough model of the 
ionosphere indicates that the effect of ionospheric refraction on 
the Doppler shift should be inversely proportional to the square of 
the transmitter frequency. This suggests that refraction can be 
made negligible by going to a sufficiently high frequency. And, 
indeed, at microwave frequencies (and above) the ionosphere has a 
negligible effect on the received Doppler shift. Unfortunately the 
use of microwave frequencies would require either the use of large 
directional antennas for reception or of very high transmitter powers. 
The first solution would be undesirable for many potential users of 
TRANSIT (e.g., Submarines or aircraft) and the second is unavailable 
with small, easily launched satellites. Accordingly, it has been 
considered wise to restrict the TRANSIT frequencies to the range 
(hundreds of megacycles) where solid state amplifiers were usable. 
In this range, ionospheric refraction cannot be neglected with high 
accuracy. The technique used in TRANSIT is to transmit a pair of 
harmonically related (coherent) frequencies rather than a single 
frequency. From the Doppler shift obtained on each of these fre- 
quencies it is possible to obtain a measure of the integrated 
electron density between the transmitter and the receiver, and then 
to develop a good estimate of the Doppler shift that would have been 
measured in the absence of the ionosphere, It is this so-called 
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