I heard this somewhere but It does not sound right.
We are assuming propagation into space/vacuum.
So, I tried to find any applicable formulas by googling to no end.
Other than the energy decaying per the square of the distance, of course.
This is an interesting question I had never thought of. My gut says that, given the conditions you set forward, all radio waves should have the same range. Radio waves are physics, and with no physical limitations they should all act the same, just as a 50 ton space ship and sheet of tissue paper both weigh the same (zero) in outer space.
But it seems almost too simple. Instead of googling for a variation of
"do all radio frequencies have the same range in space" I instead googled
"Why does NASA use microwaves." If it's all the same, then why don't they talk to the Mars rover on, say, 40 meters? I figured there must be a reason why microwave frequencies are used for space comms and was hoping to find information that verifies not all frequencies are the same.
As it turns out, NASA prefers microwave frequencies for a lot of reasons and none of them have anything to do with range across a vacuum. So I'm going to agree with ghrit, not because I can prove the theory, but because i can't
disprove it. I realize that accepting something as true solely because you can't prove it's false is really bad science, but that's the best I can do without researching deeper into this than I care.
Thanks for the great post.