JoshuaZ comments on Open thread, Oct. 12 - Oct. 18, 2015 - Less Wrong Discussion
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Highly speculative thoughts off the top of my head (only with what little I can remember from my high school physics):
The main factor that determines escape velocity is the mass of the planet (there's also atmospheric drag, but it's generally manageable unless the world is a perpetual hurricane hell, in which case I doubt it has any civilization). After a certain mass threshold, the planet is likelier to be gaseous than rocky. I don't think Neptune-like or Jupiter-like worlds are suitable for life (but their moons are another story). In general, I'd say if the world is too big to jump out of, it's too gaseous for anything to have walked on it anyway. Edited to add: Inhabited moons of Jupiter-like worlds would also need to take into account the planet's escape velocity, even if it's lower where they are.
If the planet is a big Earth (that is, quite massive but still mostly rocky), the greater gravity will result in a thicker and denser atmosphere, but I don't know enough aerodynamics to tell how much, if any, this detail will add to the problem of escape velocity. But this difference may change the rules as to which fuels will be solid, liquid or gaseous under that planet's normal conditions.
Another, related problem is payload. For example, if the planet's intelligent species is aquatic, the spaceship will need to be filled with water instead of air; this will increase the total mass horribly and require a much more potent fuel (but all this is assuming that an aquatic species has had the opportunity to discover fire in the first place).
In worlds too big to escape by propulsion, people may come up with the idea of the space elevator, but the extra gravity will require taking into account the structure's weight. The counterweight at the upper end will need to be heavier and/or farther. Issues related to which material is best suited for this building scenario and whether there's a limit to how big a space elevator you can build are beyond my knowledge. According to Wikipedia, nanotubes appear to be a workable choice on Earth.
Some world out there may have a ridiculously tall mountain that extends into the upper atmosphere. Gravity at the top will be lower, and if a launch platform can be built there, takeoff will be easier. Of course, this is an "if" bigger than said mountain.
India has a huge coastline, but for mythical/cultural reasons, Hinduism used to have a taboo against sea travel. In the worst scenario, our heavy aliens may stay on ground, not because they can't, but because they won't; maybe their atmosphere looks too scary or their planet attracts too many meteorites or it has several ominous-looking moons or something.
Good analysis! A few remarks:
In practice even for a planet with as thin an atmosphere as Earth, getting past the atmosphere is more difficult than actually reaching escape velocity. One of the most common times for a rocket to break up is near Max Q which is where maximum aerodynamic stress occurs. This is generally in the range of about 10 km to 20 km up.
Getting enough mass up there to build a space elevator is itself a very tough problem.
Whether gravity is stronger or weaker on top of a mountain is surprisingly complicated and depends a lot on the individual planet's makeup. However, at least on Earth-like planets it is weaker. See here. Note though that if a planet is really massive it is less likely to have large mountains. You can more easily get large mountains when a planet is small. (e.g. Olympus Mons on Mars).
This would require everyone on the planet to take this same attitude. This seems unlikely to be common.
You got me curious, and I read a bit more, and found this on Wikipedia:
In lay terms, I guess this means that, unlike a cannon ball, which only gets one initial "push", a rocket is being "pushed" continually and thus doesn't need to worry about escape velocity.
So first they get the rocket high enough to be safe from the air, and then they speed it up.