TL;DR: Based on the below information, and given 4 assumptions, the maximum number of stations one could legibly hear would be 42 or less.
Not sure if there is a factual answer to this question. But as the OP has indicated a "Gedankenexperiment" as the basis of the question. We may theorize, how many stations you can receive.
Lets concentrate on the FM broadcast band, which in many countries goes from 87 MHz to 108 MHz, some countries lower, and some countries higher. However, looking at the picture of the proposed radio receiver, I think this is the band we need to concentrate on. These frequencies are not reflected by the Ionosphere back to earth, so we are good to receive them.
It is mentioned in the comments, that the main broadcasting antenna's will have their main directivity pointed to their intended audience, which certainly is not up to the Ionosphere, but horizontal, parrallel to ground, or even in a downward angle.
However RF is a strange beast, and antenna's are far from ideal. Most antenna's will have something which is called "side lobes". And it is in theory possible that some of these side lobes are pointing more upwards, with a larger angle, therefore some of the signal is "going into space".
As the ISS is roughly 406 km above earth, the radius of earth is about 6371 km, it is simple to calculate the theoretical area which is "visible" from the ISS.
A = 50%/(1+R/d)
Which brings A to about 3%.
This brings us to:
- how many stations in the 3% of the visible earth,
- and how many of those stations have antenna's with side lobes which are radiating signal to the location and path of the ISS
- and are strong enough to be received/demodulated above the noise floor.
From here it is guessing, as factual calculation is not possible.
- At least some
- Probably many
- Possibly a lot
Now, some more information, there seems to be 44,000 radio stations in the world, well if you believe the source, as the deep link seems to be gone.
Lets take this 44000 and with this, there are AM and FM stations. With AM in decline, lets apply an 80/20 rule on this [assumption 1] and put the total number of FM stations to 35200.
Lets say that these staions are equally distributed on the surface of the earth [assumption 2], and 3% of that is visible. This will bring the number of visible stations to 1056 stations.
The afore mentioned side lobes are not all directly pointing to the ISS, it is a bit of hit-and-miss, so lets apply a 20/80 rule on those [assumption 3], which now brings the number of receivable stations to 211.
However, as this is FM: if two, or more, stations are on the same frequency, you will not be able to hear any (likely) or only the strongest. This needs to be seen in comparrisson to AM; if more than one station is on the same frequency then you can still hear all stations... just like you can hear multiple people talk simultaneously. (This is one of the reasons that Aviation traffic on 110 MHz - 135 MHz is still on AM, the flight controllers can hear more than one plane on the same frequency)
Now, the band we have chosen is 87 MHz to 108 MHz, and with a 200 KHz bandwidth for an FM station, this means that there are 105 possible "slots" for non-overlapping broadcasts.
These "slots" are actually the most limiting factor. The stations will not be evenly spread, many will have "popular sounding frequencies", and overlaps will happen. For this purpose lets apply another 20/80 rule to the equation [assumption 4]. Which will bring the number down from 211 to 42.
Suppose you take the radio receiver as indicated, and "tune" in to a station which is receivable. The fact that the ISS is traveling at an orbital speed of 27000 km/h, it would mean that the received signal is influenced by a doppler effect. You will have to tune higher when approaching the transmitter location, constantly lowering the frequency during your listening experience. It is debatable if the estimated 2.6 kHz drift doppler will introduce, is significant or not. The radio receiver used may even have an AFC circuit which may correct this.
How many stations could one hear with an AM/FM radio in front of the ISS' cupola window?
Based on the above information, and given 4 assumptions, the maximum number of stations one could legibly hear would be 42 or less.