How could a subterranean alien lifeform develop space travel?

It's actually easier without an Atmosphere

If you strip away most of the atmosphere, it's probably easier for an intelligent species to become space-faring. All the complexities of space travel stem from the tyranny of the rocket: more weight means more fuel, but more fuel adds more weight!

With a non-existent or very rarefied atmosphere, an intelligent species could use mass drivers to get to space.

A mass driver is basically a railgun cross bred with a bullet train: a long track - say 200 miles - that accelerates the ship to orbital velocities. Then you use a small rocket burn to circularize the ship's orbit.

This moves the fuel source off the rocket, thus allowing much higher launch weights.

Mass drivers don't work on Earth, because traveling through the atmosphere at orbital velocities causes the ship to melt / explode / disassemble.

But would they discover Space at all?

Of course.

We use RADAR and X-Ray technology to for a lot of our space research. Neither of these technologies return information in formats that humans can understand natively. We use intervening technologies - visualization software and computer displays - to convert the data into something we can understand.

Likewise, a society that "sees" the world through sonar will develop technologies to interpret X-Ray, RADAR, and even visible light information into some format that they can understand.

When this society reaches the surface world, they will naturally use these existing technologies to understand it, and will therefore invent astronomy.

I like Jann Poppinga's answer, but would like to extend it a bit to respond to the quite valid concerns of "if they can't see the stars, why would they think there's something up there?". That was my first thought too.

Give them a moon to shoot for

While their star (which creates times of different warmth, even if illumination is not noticed) might qualify, giving them a moon (especially a big one like ours) would help a lot.

Once they're using the surface for transportation (by land or air), noticing that at different times - and quite regularly periodical ones - the temperature at the surface is different would only be natural. But there's several ways to explain that - and the "there's more land to conquer/settle in the sky!" theory would have to compete with the "there's a huge ball of fire circling the world" one.

A large moon with easily noticeable tidal effects (even without large bodies of water this would be rather measurable) would give them a notion of "other hard bodies are out there above us", and a target to shoot for.

Light sensors (infrared first)

Of course even without a moon, measuring light with sensors would be a natural development too. The visible (to us) spectrum of light is only a small part of the electromagnetic spectrum - and infrared radiation (aka, "why can I notice that a rock is warm from a distance?") is very close to visible light. Sufficiently advanced measuring equipment aimed at infrared wavelength might even be able to pick up the planets and stars from the ground - giving them the motivational breakthrough they need.

There's no reason why they can't. All they have to do is mine a hole to the surface, and use that to launch rockets. There's no reason why they would have to build a civilization on the surface, just like humans didn't have to build underwater or underground civilizations to send rockets to space.

Like L.Dutch - Reinstate Monica, I don't see a good reason for this population/civilization to get into space. It's not the tech that's necessarily the problem, but psychology is a huge factor when the people can't perceive something. And perception is a huge factor when trying to comprehend something.

It would have to take some very special circumstances to align just right to let this happen. For instance, in the communication or other electrical gear they invent, they may notice interference. This could be interference from the nearby star, but because they can't see it, they would attribute it to something they do understand and can comprehend, the core of the plant.

It would have to take a special kind of thinker to consider putting some kind of direction finder to figure out where the interference is coming from. Most engineers would likely just work to shield or otherwise remove/negate the interference. It would take some really severe interference for more than just a single person to look for the source. If they realize there's likely no way they can do anything to prevent the interference, they won't do anything about finding the source.

And even if they do find that the interference is "up", they probably still have a taboo about going to the surface, due to the circumstances you describe about how they became cave dwellers to begin with.

Even if the thing they discover is deadly radiation, that just plays into the taboo and they are more likely to dig deeper to get away from the radiation, rather than go towards it.

Since their ancestors chose to "run away" from the dangers of the surface, instead of invent technology to deal with it, they likely have a civilization based around this fear. It doesn't even matter if the ancestors had the resources to invent the tech, they still chose to dig down. With any civilization, there's a lot of pressure to "continue to do as the ancestors did". This is how "well we've always done it that way" comes to be as a saying, among more dangerous doctrines, but I won't get into that.

With this taboo, even if the original thinker figured out that the interference/radiation is gradually reduced then disappears completely in an area, then realizes there's nothing causing this below, so it has to be above (a lake or ocean), it would still take quite a bit to convince the people in charge to figure this out.

Then again, they may already be living there and know about the phenomenon without caring why it happens, and literally no one in generations has thought to ask why. It may have even worked into the taboo no to ask that type of question.

And with strong enough taboos, they can work into laws. It may even be against the law to go to the surface.

Maybe all this works into the story, where the original thinker decides to go off on their own to discover "up". They would likely have to work on their own for quite a while, until they secretly convince others to join the venture. It might even become a haven for the "unclean" (or whatever) who make a nuisance of themselves by breaking the taboos/laws about "up".

This is still a tenuous story line, but I've enjoyed even more unrealistic plotlines, as long as it can hook people by their emotions and/or curiosity. :-)

Like others I assume the answer is "yes", and I think Jann Poppinga's answer is very good. But I also think the issue of them being blind is a very interesting one and L.Dutch makes a good point that it's hard to see how they discover any cosmology at all without sight. And while I don't think that would prevent them from flying higher and higher, noticing the atmosphere thinning and disappearing and being curious about going further and further, and figuring out ballistic properties through trial and error, it's still hard to see how and why they'd go further into space beyond a certain point without the notion of other spatial bodies and the ability to know where they are. It's not like they'd just stumble into a neighbouring planet, the distances are ridiculous.

But of course there is no reason they won't be able to sense light, blind as they are: we use technology to sense all kinds of physical entities we cannot sense with our bodies. So what I'm finding interesting is, how would they discover light, what would it seem like to them, what would they do with it?

First, I think at the very latest they will discover light around when they've discovered electricity and developed a theory of electromagnetism, as we discovered radio waves. Actually in your scenario I think that even if the sentient lifeforms in question are blind there would be a sighted biosphere in existence because you only described the surface as having a lot of UV... living things could adapt to that, maybe not a thriving biosphere but some organisms that could be worth sneaking out of the caves to eat (you also don't mention what your biosphere would be based on, energetically speaking. It's quite possible it wouldn't be possible for a biosphere to sustain sentience without using light energy in which case your sighted biosphere would be very significant indeed). It would also be pretty safe to exist around cave openings where it would be easy to avoid direct exposure to UVs, and those would be lit environments where sight would be adaptive. As such, these blind organisms might have become aware much earlier through the science of biology that some organisms have an uncanny ability to hone in on prey, and that this is related to these "eye" organs they have. Once you have that, and you have electromagnetism, you have both the incentive and information necessary to invent a visible-light camera, and once you've done that you can discover that wait, your camera is picking stuff up in that emptiness above the surface????????? (I don't know if you could use the principle of the phone to connect up a light receptor to an ultrasound emitter to allow for some approximation of "direct" light perception, at which point you would just need to adjust either end to get as useful information as you can).

On the other hand we could modify your scenario a bit to have true blindness - the sun's rays are fatal in very short order to all but extremophile micro-organisms, and the biosphere runs happily on some very high-yield chemosynthesis. In this situation maybe it would take until the discovery of electricity before our arthropods had any notion of light at all (though there is always infrared, you don't really form pictures or see stars with it), and I'm curious if they ever would figure out image-forming cameras. Electromagnetic waves would be certainly useful to them for communication, especially once they colonized the surface. They'd also likely use them for sensing the world, as we use radar. They'd already know about the day/night cycle at the surface just from temperature but they'd see a corresponding pattern in other electromagnetic waves. They could figure out the waves have a point source just from shading effects, and that's a discovery of the Sun and at that point they can have a notion of space, as in "stuff happening way beyond the surface of the planet". With more focused and sensitive detectors I suppose you could find stars (even better if there are moons and certainly planets) and then you're off to the races, astronomy-wise.

Because it’s there

This may be a bit of a cop out, but just because biology dictates they be subterranean doesn’t mean they can’t be curious about other environments. Humans aren’t made for living deep underwater, and yet there are sub nautical observatories.

If these creatures view things via echolocation they have a concept of far distance and such. They could use technology to explore the surface, most likely using some form of sonar pings to expand their own echolocation and environment suits. From there a good way of them discovering space would just be them expanding their sonar to map more and more of the surface. And then one day they get a ping off a moon or asteroid or something.

Suddenly there’s a massive “Oh DANG, there’s STUFF in the great nothing above!” Humans have been aware of space because we can look up and see all those things, but modern scientists bounce various waves and signals off celestial bodies all the time. After that initial realization it would be a natural progression for curious scientists to simply start angling their sensors upwards and seeing what gets bounced back. And then building things to get closer and send even more information back.

If they have expansionist tendencies, their exploration and exploitation of the surface and eventually space is functionally inevitable (assuming they don't go extinct before hand). The only known sophonts are humans, who have demonstrated a tendency to and flair for expanding into available space, even ostensibly inhospitable ones. What we don't know for sure is the source of that tendency; it could be cultural, but the latest batch of imperialist expansion wasn't the first, just the most comprehensive. If it's physiological, onmivorism may have played a part, or bipedalism, or visual orientation. It might be a fundamental aspect of all intelligent life, or even just life in general. We don't have the data to know. Decide all intelligent life is expansionist and you're sorted. You can spike the protest by having someone ask how your species realized there was a sky, and having an individual incredulously ask "How could we not?" or otherwise dismiss the question as naïve.

If you want a specific path towards the realization, just have your species encounter radioactive isotopes. They won't be able to smell anything but alpha radiation if even that, but it will rapidly become apparent that something is going on when individuals start dying of acute radiation poisoning even when they're protected from the killer helium. The discovery of any portion of the EM band will eventually lead to the rest of it (they'll just wonder what's going on around and between 380 and 700 nanometers), which will help with a whole bunch of fundamental physics that should inevitably lead to the big questions.

I'm assuming they've got access to their recorded history and know about the time when they were on the surface, or have noticed something unusual (eg gravity waves) and want to go check them out. Basically they know space is there and want to go there.

I see a few paths:

• They find the Star Gate or a buried crashed alien ship, or some other peice of advanced alien tech which either transports them directly, or they can reverse engineer to build a ship.
• They just use FTL underground. Whether that has effects or not is up to your imagination, FTL in the middle of a massive underground chamber sounds loosely plausible.
• Surface mounted big doors. Build pressure suits. Use pressure suits to do work on the surface. Build a big honking space door. Build a big ship underneath it in an airtight chamber. Open outer doors. Fly into space. Close outer doors. Best used at night to minimise radiation.
• Really long underground railgun poking out the surface If they're very good at building big underground structures, they can build StarTram, which is basically a long maglev rail launching something into space or landing it. Since your atmosphere is gone, you can get a vacuum for free inside a tube sticking out of the surface, giving no air resistance during launch.

they can perceive their surroundings by using ultrasounds (like our bats), and a powerful capacity to smell minerals and all types of molecules.

None of those abilities will make them aware that there is something called "space" above their heads.

What is current space science started when some humans started looking up in the sky and noticed the stars, and noticed that some of them were behaving oddly. From that observation came all the theories on cosmology and from there it sprouted space exploration and space science.

Ultrasounds and smell do not help in noticing the sky. They will be blissfully ignorant on anything related to that.