What determines the optimum frequency range for the transmission of signals in a system that's transmitting electromagnetic signals between an antenna on the surface of the earth and an orbiting satellite antenna.
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$\begingroup$ Do you know the frequency the satellite is listening to? $\endgroup$– SDsolarCommented Sep 9, 2017 at 6:05
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Many factors, and since your question is so broad, a broad answer follows:
The signal bandwidth (amount of information per second) will determine a minimum carrier frequency. In practice, the modulated signal should have a bandwidth of not more than say 1% of the carrier frequency.
Then, at lower carrier frequencies, you need to consider antenna size (which can be too large for a satellite), and ionospheric effects (mostly in HF range).
Commercial satellites communicate in the microwave range (L band, all the way to the K bands and above).
At high carrier frequencies, atmospheric attenuation becomes a problem. Also clouds and rain provide attenuation in the K bands.
Small amateur radio satellites normally operate in UHF and VHF, but those frequencies allow for a very small bandwidth (1200 or 9600 bits per second).
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1$\begingroup$ Note that "bandwidth" has two distinct meanings which are both useful in this context: signal processing bandwidth (maximum minus minimum frequency of the RF output of the transmitter), and transmission bandwidth or bit rate. In analog radio we are most often concerned with how wide the signal is (RF bandwidth), whereas in digital communications one is most often concerned with how much data can be transmitted (bit rate). $\endgroup$– userCommented Apr 9, 2015 at 7:11
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$\begingroup$ I think the limitation to 9600 kb/s on amateur satellites is due more to the archaic technology employed than the frequency. AFSK has horrible efficiency and sensitivity by modern standards. $\endgroup$ Commented Apr 9, 2015 at 16:18
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$\begingroup$ I've upvoted this answer because the information is good, considering how broad the subject is - and how concise the answer is. I do agree that "those frequencies allow for a very small bandwidth" is incorrect though - I would rather that it said that by convention amateur use of those frequencies is at excruciatingly slow bit-rates, that were actually slow 20 years ago. Otherwise, this is a great general answer to a broad question. $\endgroup$– Scott Earle ♦Commented May 11, 2015 at 1:51