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Given a planet otherwise similar to Earth, but which has (for reasons outside the scope of this question) no ionosphere, what would be the effective range of radio communication?

I understand radio communication on Earth has effective range much longer than the distance to the horizon, because radio waves bounce off the ionosphere. Without that, is it strictly line of sight only, or are there other effects that enable communication over the horizon?

And how much does the ionosphere matter to short-range communication, such as military backpack radios on a battlefield over distances of tens of miles?

Of course, technological measures could be used: building taller broadcasting masts, chains of relay stations, putting transmitters on tethered balloons, just investing earlier in extensive telephone networks. I'm trying to figure out just how necessary these would be.

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I understand radio communication on Earth has effective range much longer than the distance to the horizon, because radio waves bounce off the ionosphere. Without that, is it strictly line of sight only, or are there other effects that enable communication over the horizon?

This is rather well known, radio propagates effectively by ground waves for long and medium wave and the top of shortwave, with the distance progressively shorter and shorter - from thousands of kilometres for the LW. Note that even UHF is not quite line of sight only, but can diffract slightly around the horizon, hills and buildings. Note that you need rather high powered transmitters.

Then there are several more exotic and much less reliable sporadic ways, like meteor scatter or Moon bounce, but we can perhaps disregard them for pre-modern communication. Using contemporary technology (DSP, computers, low noise amplifiers, SDR), modes like JT65 can be very efficient for extremely long range, low power and low bandwidth communication.

And how much does the ionosphere matter to short-range communication, such as military backpack radios on a battlefield over distances of tens of miles?

Not at all. Modern communication is in frequencies well over ionosphere reflection threshold, and let's say WWII shortwave+short range communication would be affected negatively (from the military point of view), by enabling remote enemy listening stations to monitor your communication from potentially very far away.

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Tropospheric ducting.

This occurs at any moderately high frequencies (not so much in longer wave radio) and in visible light. The cause is to do with layers of different atmospheric density lying over each other such as happens in an inversion (AKA temperature inversion).

It's familiar to most people as the kind of mirage that can occur on a road in the hot sun.

This can allow for spotty and inconsistent reception as it depends on weather conditions, but can allow travel of radio comms over up to a thousand miles on land. Mountain ranges largely get in the way and prevent even this. The longest consistent travel occurs at dawn or dusk, and in extreme cases can allow up to 3000 miles (4800 kilometers), such as occurs between Brazil and Australia, and California to Hawaii (the oceans not having mountain ranges helps a lot). It has been observed in frequencies below 40 MHz, but is more consistent above 90 MHz.

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