My story features Renaissance-era feudal society with working space travel. Humans are able to travel around the Solar System (Earth, Mars, asteroid belt, moons of Jupiter) in spacecrafts fitted with solar sails. These crafts are manufactured in space and never see the ground.
My question is, how can these people get into and out of space without rockets and without resorting to handwavy magic? What alternatives exist?
Not strictly "medieval", but we're going with sci-fi, so...
There were ancient people at a much higher level of technology. Are they the ancestors of the current feudal society who suffered some sort of disaster? Did they leave and did these new people evolve on what was once their homeworld? Were they only here briefly and installed some stuff?
Doesn't matter, what does matter is that they installed a set of large-capacity space elevators around the globe. Many settlements are located around the bases of these impossible structures because they've become items of worship due to their mind-bending scale. Their maintenance and operation is automated - one need only get in and press "up" and one will be dropped off in space.
Automated energy weapons also kill anyone attempting to damage the elevator with no warning, lending an added element of "gods' wrath" to the worship of these colossal relics.
You could go with the style of The Road Not Taken. Antigravity and/or hyperdrive are easy, we humans just didn't go down the right paths to find them. This is effectively magic, but it's also the only way you're not subject to the rocket equation.
Even with a hand up into space, a medieval technology society with solar sails beggars belief. Making a vessel air-tight would have been near-impossible. Manufacturing the ultra-thin, ultra-light, ultra-huge material for a solar sail would have been completely impossible. Being able to carry sufficient air and provisions for the months of travel between planets would be completely impossible (spoilage would have done them in before arrival). But this is ultra-soft sci-fi, so as long as you don't draw much attention to them, you can probably get away with it.
Julius Verne was a great author, writing steampunk fiction with broken science that sounded logical to the average reader of his time. Any nerd from even a century or two before him could see the errors though.
But supposing that the physics of the Verneverse are valid, take a page from his book From the Earth to the Moon.
In this book there is a club of Americans who fiercely compete to see who can america the most (i.e.: who can make the biggest gun). Goes to show how timeless this piece of work is.
So at one point one guy tries to outamerica his peers by landing a shot on the expletive Moon, as a manner of greeting whatever people might live there (insert the theme song of Team America here). Then out of the sacre bleu a French guy comes along and says "Bonjour, I'm Michel Ardan and this is Jackass!" Just kidding - Jackass hadn't been invented yet. Instead Ardan said "hey, if you make the bullet hollow then you and me can sit inside and use it as an interplanetary vessel", which is a longwinded way to say the same thing.
And then they do it. They dig a 270m (900 ft) hole to act as a barrel, fill the bottom with gunpowder guncotton and load the "vessel". They shoot and, to add insult to insult, they expletive miss.
Now in our own boring universe, any steel from the 1860's would have been obliterated (edit: to make matters worse, they used... tin). Even if the capsule would survive, it wouldn't fly at enough speed to go into space, and if it did, then the americanauts would become a thin paste on the bottom of the projectile. But in the Verneverse they make it alive into space.
As long as your universe follows the same cartoon physics, people should be able to replicate the feat - even with more rudimentary technology.
Naturally occurring space elevators
Your society may live on a world where plant or animal life exists that forms a natural space elevator. For example, giant plants that live in the upper atmosphere that have vines that reach ground level, and seed pods that travel to other worlds to pollinate other space pants that can be used as shuttle craft.
Thinks wind pollination but on a solar system scale
Tame wild space horses
The Reefs of Space (Frederik Pohl and Jack Williamson, 1964) features a whole ecosystem living in the vacuum of space...including air-breathing mammal-like animals (sleeths) that have mysterious internal organ(s) that keep a bubble of air around them as they swim reactionlessly among the reefs of the Oort cloud.
Sleeths occasionally journey close enough to the sun to wander onto the curious large planets. Being mammalian, they can be somewhat domesticated. Their jetless drive works just as well in atmosphere as space.
Create your own space-horses, have some wander close enough to encounter your Medievals, and then chariot across the cosmos.
Usually hyperspace is an alternate dimension where the distances between points is shorter, but that doesn't have to be the case.
In The Long Earth, somebody figures out how to step into an alternate reality Earth with a very simple to reproduce "stepper box." It's a little hand-wavey, but allows for a lot of options. In that story, there are an unlimited number of alternate Earths, but you have to step through them one at a time.
One of them is what's called the "gap Earth," where the planet itself doesn't exist. If you take that to a logical extreme, even if the distances aren't shorter, you're still operating without gravity. You would hop out to that other vacuum and ride your 1000 mph momentum to a spot outside the atmosphere, and accelerate from there.
According to Wikipedia, Vijaypat Singhania set a world record and reached an altitude of over 20,000m in a hot air balloon in 2005.
So, what I would suggest is to have a hot air balloon lift your space faring capsule to an altitude of ~30km, then detaching from the balloon and using an ornithopter mechanism in combination with your solar sails to reach even higher, before dropping the ornithopter mechanism for weight savings, and using only solar sails to take you the rest of the way.
As with all answers, this wouldn't actually work, but I think it would fit your aesthetic very well
About 50 years I had a dream where the Roman Empire had a space program and other advances. And I had another dream where the Holy Roman Empire in the time of Frederick I had a space program. While I was dreaming those dreams I believed they were real history. I was really disappointed when I woke up. And if you write a really good story about space travel with medieval tech, readers may believe you while reading, and not realize how implausible it is until after reading.
I can add one more way for medieval people to acquire space travel.
Poul Anderson's classic novel The High Crusade (1960) opens with an alien spaceship landing in Medieval England. The English people capture the spaceship and become lost in space. They lead a revolt to overthrow the alien space empire and replace it a new space empire, but can't find their way home to Earth.
And in Larry Niven's Known Space series, the Thrint and the Kzinti acquired space travel the same way, stealing spaceships from visitors and conquering them.
So possibly in your story a group of people with medieval technology have managed to conquer and rule at least one world with advanced interplanetary or interstellar travel.
And they have to live at least part time in a world or worlds with advanced technology they don't understand in order to supervise their more advanced subjects. But they take long vacations from that work, spending vacations on less advanced worlds which are more understandable to them and which may be their main homes. And they travel between medieval and advanced worlds and societies in spacecraft they don't understand and which they decorate to look like they were built by medieval craftsmen.
I also point out at a society with a medieval level of technology doesn't have to be medieval European. And of course technology was different in different parts of Europe at the same time, and usually more advanced in AD 1500 than in 500. Other medieval era societies had technological levels anywhere from stone age hunter-gatherers to Aztecs, Incas, and Mayans, the eastern Roman or "Byzantine" Empire, the Caliphate, the Delhi Sultanate, Song and Ming Dynasty China, etc.
Building stairs might be a very slow process. But trying over the years. I think we can reach the space.
What about biological (living!) rocket ships that can survive in the vacuum of space?
Suppose the inhabitants of your world have bred animals, over many millennia, that can generate propulsion via internal chemical reactions.
Passengers and crew are carried inside a chamber in the organism.
Harry Harrison developed a bio-tech civilization similar to this (although there was no space travel) in his West of Eden science fiction novels.
Babylonian "updraft" tower
Ancestors of your civilization managed to achieve what our did not. Using analogous technology to the solar-sailed craft, they built the hollow tower that extends most of the way you need.
Geothermal energy is used to heat the air at the base to near-lava temperatures. Stack effect gives you whizzing winds in the tower, on which your people would ride in capsules hanging from heat-resistant parashot upwards, even getting considerable momentum at the end, so tower 'shoots' them the last step somewhere, where prepared orbiting craft can dip into sufficiently low orbit to snatch the capsule.
You could use an "active support" structure, like a Space Fountain/Tower or Loftrom/Launch Loop. These look similar to a Space Elevator from the outside, but they don't require super-strong materials. Instead, they contain a stream of mass travelling round and round a loop that's either oriented vertically (for a Fountain/Tower) or otherwise angled upwards (for a Loop). That mass is usually assumed to be steel pellets, so it can be guided with magnets; although a continuous cable or chain could be used in principle (but may suffer from large vibrational modes).
Imagine firing a gun vertically, at a target that's lower than the peak of the bullet's trajectory: we get pushed into the ground by the recoil, whilst the bullet will slam into the bottom of the target, pushing it upwards slightly. Now imagine someone attached to the target, who digs out the bullet and fires it back down to us: they get another upwards push from the recoil, whilst we get pushed down again when it hits us. Now imagine doing that over and over, in a constant stream. A practical device would need to replace those guns with something less destructive: in the real world we'd use electromagnets; a medieval setting could use a rope or chain driven by a wheel, or heavy slugs thrown by catapult, etc. (in general we'd want something mechanically powered, to avoid using up gunpowder)
The advantages over a Space Elevator are:
This last point is interesting, since the system can all be built on the ground, then turned on to gradually lift up the top of the loop. Multiple streams can be used in parallel to support one platform, and towers can be built on top of other towers (as long as the lower towers can support the weight of everything above). The streams can be used to transfer energy up the tower (mechanically or electromagnetically), which is useful for powering the turnaround mechanism at the top. Structures at any point along the stream (either upward or downward) can also "tap into" it to hold themselves up; e.g. wooden or stone architecture that could not support its own weight otherwise.
The main impossibility of such devices is their power requirements. In steady-state we only need to replenish the friction losses; but starting it up and lifting the platforms takes an enormous amount of energy (although, as previously stated, it can be done gradually as desired).
https://en.wikipedia.org/wiki/Space_fountain
https://www.orionsarm.com/eg-article/47e1bb1fc898c
https://hackaday.com/2022/01/01/attack-of-the-eighty-foot-string-shooter/
Depending on your definitions, it could be argued that some nations in the 20th century and even today are both "feudal" and "spacefaring".
Actually rockets may be the most realistic scenario. Primitive forms of rockets (fireworks) already existed in China at that time. The problem is having a fuel which could be used to reach escape velocity, without all the knowledge gained only in later centuries. This however could be achieved, if only we allow using some technology without the actual knowledge why it works.
I would opt here for the nuclear power, as it can be justified without such knowledge, if we assume it were discovered accidentally during researching something else. And it could be: e.g. at that time Venice was leading producer of glass products (Murano glass), yet in later centuries it was superseded by Czechia (bohemian glass).
If we assume bohemian glass was a thing a bit earlier than in our reality, and that uranium glass was accidentally invented at that time, by experimenting with various ores (e.g. in Jachymov), it gives a quite plausible explanation for pure uranium being in active use and research, without any knowledge of modern chemistry or nuclear physics.
Let’s suppose then, some alchemist out of curiosity somehow manages to accidentally enrich it on a centrifuge, and causes a nuclear explosion destroying the whole city.
As renaissance Italy was a bunch of independent cities instantly at war, such weapon would gain instant attention of every ruler. Just in this reality, instead of Leonardo da Vinci’s tanks, they will get Leonardo da Vinci’s nuclear warheads (and probably an excommunication of anybody who actually uses it).
And all this assumes only trial and error (and lot of innocent victims) and no actual need for the XX century physics.
From here we can just assume the trial and error (justified and funded by the usefulness in war) leads to finding that this form of energy can be controlled by neutron reflectors. Since those are substances as simple as the graphite, we could still assume it’s reached without understanding why it works.
And having nuclear reactor that can be manually (!) controlled, and its power directed in one direction, you have a rocket propulsion system capable of reaching escape velocity.
Now you only need some religious explanation, why anybody involved in operating such a vessel has burns, ulcers and dies in pain.
Alternate Earth.
You don't need an Earth sized planet to have sapient life on it. Make it Moon sized and then you can build a space elevator out of steel.
Well, all they need is a cannon and a capsule and way to survive the acceleration.
The canon is easy- its just a long stone channel into an active volcano, with a controllable water reservoir overhead.
The capsule seems doable, although reentry and oxygen would be a problem. Lets assume they have oxygen candles with them, as it pleases the gods (which they are visiting).
Now how to survive this acceleration? There are animals that can recover after large traumas. They would be the first test-pilots.
I have no idea how a ancient civilization with marble benches would survive the thousands of Gs.
Maybe transfer "counter" acceleration Gs into a dozens gimbals whirring with rotational energy that chancel out the redirected acceleration? ;)
