I am trying to calculate the largest world that will meet the following criteria:
Exists within the Goldilocks zone of a G2V star similar to our sun.
Is survivable long-term by anatomically modern humans with a minimum of technology.
Has an atmosphere that is roughly 21% oxygen, with no significant quantities of toxic gases. The atmospheric composition of the inert elements is irrelevant, however no significant quantities of free hydrogen may exist.
There must be sufficient water for a somewhat earthlike water cycle.
There need not be any solid surface. I am aware that a planet with these characteristics will likely be similar to a gas giant.
Humans will exist upon artificial platforms suspended at an appropriate level by handwavium.
The Oxygen/Carbon dioxide cycle will be driven by plants growing upon the artificial platforms, as well as self-buoyant photosynthetic organisms in the atmosphere as necessary.
Elements other than those strictly necessary to support the existence of humans will be present in a reasonable, justifiable abundance.
Any radiation must be survivable by humans long-term without protective gear.
Assuming a hypothetical surface at an altitude with an atmospheric pressure of 1 ATM and gravity of 1g, with air temperatures in the range of those that occur naturally on Earth, what would the largest practical diameter of this world be?
How thick would the human-survivable and human-habitable atmosphere be, i.e. how high above and how far below the hypothetical 1-ATM, 1g 'surface' could humans survive short-term and indefinitely?
Would there necessarily be a discernable solid, rocky surface or would the atmosphere transition to some solid state at a sufficient depth at some distance above the rocky core?
Since there are currently no answers that calculate the size of the world in question, there are some additional criteria:
With a pure air world, the radius may be in the millions of kilometres, but the stars would not be visible, and indeed sunlight itself may not be visible. The maximum distance that may be seen through clear air is on the order of 240km, so I'd like the air thickness above the 1 ATM level to be around 200km so that the inhabitants can see stars.
The minimum molecular weight retained must be such that no more than about 5% of the atmospheric composition is Helium.
Unprotected humans can survive in normal air from about 0.5 ATM (due to hypoxia at lower pressures) to about 10 ATM (due to Nitrogen narcosis starting at about 2.5 ATM). As I don't want my human inhabitants to be able to reach any surface unprotected, I would like the maximum pressure to be at least 15 ATM.
There needs to be enough water and carbon for their respective cycles, and enough iron and other elements to support life and human industry.