I've seen statements to the effect of: "the gravity on the surface of Jupiter is about 2.5 times that of Earth". The problem with such a statement is that as essentially a ball of gas, Jupiter is not believed to have a solid surface. Behind the "2.5g" claim there must be some criteria applied to select a radius, which when combined with a figure for Jupiter's mass, will yield an acceleration value according to the classic gravitation formula.
The meat of my question pertains to the criteria which produce radius values for the gas planets which presumably are the basis of statements such as I mentioned. As we know, Earth's atmosphere extends quite far into space, just getting thinner and thinner. So as one approaches a gas giant, one would presumably first encounter an extremely thin atmosphere, getting progressively denser, eventually as dense as a liquid. Somewhere along the way, we crossed a point which represents what we deem to be the planet's radius. What is going on at that point? Is it the same for all gas planets, or do the conditions of each planet necessitate different choices? Are the same criteria applied regardless of endeavor (astronomy vs spacecraft engineering vs exometeorology, etc.)?
Also, for what its worth, how does the planet's deemed radius relate to its visible horizon i.e. the visible but indistinct boundary between planet and space?