This answer will focus on just a few problems that a proposed society will have. It will also be based on an assumption that somehow this society has been successfully established (whether it is possible or not is another question).
1. Industry and agriculture
It is worth mentioning that Europe was not technologically and culturally homogenous in the 15th century. However, this is beyond the scope of this question, so we will assume that if some technology, know-how, knowledge, etc. was available somewhere in Europe at that time, the proposed society has it.
One of the most used agricultural systems in the 15th century was an open-field system:
The typical planting scheme in a three-field system was that barley, oats, or legumes would be planted in one field in spring, wheat or rye in the second field in the fall and the third field would be left fallow. The following year, the planting in the fields would be rotated. Pasturage was held in common. The tenants pastured their livestock on the fallow field and on the planted fields after harvest.
This system was not very efficient and the yields were somewhat low:
Annual wheat production at Battle Abbey in Sussex in the late 14th century ranged from 2.26 to 5.22 seeds harvested for every seed planted, averaging 4.34 seeds harvested for every seed planted. Barley production averaged 4.01 and oats 2.87 seeds harvested for seeds planted. This translates into yields of 7 to 17 bushels per acre harvested. Battle Abbey, however, may have been atypical, with better management and soils than typical of demesnes in open-field areas.
For comparison, today's wheat yields range from 3 to 8 tonnes per hectare (approximately 44 to 119 bushels per acre). In 1961, the yields were lower and ranged from 1 to 3 tonnes per hectare (approximately 15 to 45 bushels per acre).
In addition to low yields, medieval agriculture was subject to frequent crop failures that led to famines.
The population of Europe reached about 80 million people by the mid-14th century. And the open-field system was struggling to support it. It is speculated that one of the reasons for the Black Death's (1347-1351) high mortality rates was the overall poor health of the population due to insufficient nutrition (this documentary was available for free on some streaming platforms some time ago).
The open-field system persisted for over a thousand years, so keeping it in place for 500 years is not a big deal. It is doable. However, it places a hard limit on population. This limit can be somewhat higher than historically observed if:
- better plough technologies are used (check the Second Agricultural Revolution for details);
- better crops are used (e.g. potatoes, modern varieties of wheat, rye, barley, etc. which all have higher yields and higher nutritional values);
- better land management (can use the same three-field system but manage the land differently);
- better storage solutions are available;
- overall better management of the food stocks (with the focus on managing crop failures).
While it is possible to support a slightly higher population by improving logistics and management, it is doubtful that the population will be able to reach the numbers necessary for supporting the industrial base required for space flight.
For example, Russia is a country with space flight technology, a relatively low population (approx. 145 million), a huge territory, and an abundance of natural resources. It is also reasonable to assume that most space-related technologies are developed and produced within the country (this does not mean that all raw and intermediate materials are sourced or produced within the country, though). Russia, theoretically, can be self-sufficient while maintaining the modern level of technology (some raw materials will still have to be imported; self-sufficiency might also require the abandonment of consumerism).
Please note that the current urbanisation level of the Russian Federation is 74%. It is also the country with 'one of the highest tertiary attainment rates across OECD countries, at 63% of 25-34 year-olds compared with the OECD average of 44%'.
It is also worth mentioning that Russia, China, and Japan (3 historical examples of the rapid increase in industrial and technological capacity) had to rapidly urbanise, modernise agriculture, and adopt universal education in order to accomplish their goal of technological advancement.
2. 1%
A. Historical trends
A popular estimate is that on average1 about 85% of the Medieval European population were peasants, i.e. agricultural labourers with limited land ownership. The rest 15% of the population were nobility, clergy, and townsfolk. Administration, law, trade, crafts, scientific research, war, etc. were the fields that these people specialised in. I would suggest consulting specialised literature for specific details pertaining to various occupations and laws and practices associated with them.
Medieval society was highly structured and did not have many 'freeloaders': Every class, every occupation had its role, obligations, and place in society. There is a good reason why most countries had more than 1% of the population involved in non-agricultural activities.
I am not sure that 1% would be enough to fill all necessary non-agricultural roles even if we eliminate everything not related to space technology and assume that the proposed nation is completely safe from all other countries.
B. Every genius stands on the shoulders of ants
If talent (or high IQ) was the only thing necessary for technological advancement, humanity would've already colonised the entire universe. There are plenty of geniuses in human history.
Real science is nothing like books or TV portrayals of it. A lot of discoveries are accidental, literary: Some clumsy person makes a mistake in an experiment and gets an unusual result that accidentally happens to be important. Other discoveries can be made only because an army of unnamed, unknown, mediocre scientists spent decades gathering data and repeating the same experiments.
A genius may be able to look at things from a different perspective and conceptualise new relationships, but even a genius is not capable to generate knowledge out of the air with no reliance on previous data and research.
There is also a need for a small army of helpers that would verify genius' ideas, apply them in different contexts, make them known to wider society, and so on.
C. 'Native' abilities
The selection process for the 1% is described as follows:
'They are selected in various ways from the general population of plebs based on their native abilities.'
This is potentially highly problematic for two reasons:
ability != result
Talent plays a minor role when it comes to achievements. It is much more effective to provide more opportunities to more people.
high chance of missing experimental innovators
There are two types of creativity: Conceptual and experimental. Conceptual innovators tend to reach their peak early in life (the 20-30s), experimental innovators tend to produce results much later (the 50s). It is also worth mentioning that conceptual and experimental innovations are often qualitatively different. Experimental innovations tend to solve problems on a more general, abstract level.
As mentioned in the beginning, these are just a few problems with the proposed society. There are more other problems but discussing or even pointing them out would make this answer unbearably long.
1 There were differences between countries, regions, and time periods. For example, England had fewer nobles (members of the aristocracy) than many other European countries, but it had higher urbanisation levels. Eastern European countries had lower urbanisation levels but a higher percentage of the population were considered nobility (notably Poland and Hungary).
3%
. – Franz Gleichmann Dec 19 '21 at 16:45