I have this idea of putting dozens of terrestrial planets in the habitable zone of a Sun-like star. We know from the TRAPPIST-system that it's possible for two terrestrial, Earth-sized planets to come as close as 0.01 AU to each other, but I want to know if such close distances are plausible and/or realistically stable in the habitable zone of a G-type star like our Sun.
The answer is, that we don't know any strict maximum number, as man factors can effect how many can fit into the habitable zone, such as:
- Mass and Luminosity of the Star
- Atmospheric Composition of the planets
- Albedo of the Planets
- Mass and Radius of the Planets
- Orbital Characteristics (eccentricity and resonance)
- et cetera
For instance, part of why the Trappist system is so condensed is due to a complex series of resonances that allows them to orbit far more densely. Specifically a set of Laplace Resonances.
Mass and Radius
On mass and radius, that is due to the fact that the mass and radius of a planet influences how close another body can get to it without one destroying the other (as defined by the Roche Limit), or them substantially disrupting each other's orbits. This is a big limiting factor in it.
Planets with less mass and radius could theoretically be more densely packed.
Eccentricity is also important to look at, more densely packed systems have lower eccentricities, and lower eccentricities tend to stay at approximately the same distance from their star, and thus if in the habitable zone, they tend to stay there. This also means that low eccentricity planets can be packed tighter as they can get closer together without orbits crossing (which risks planetary collision, amongst other things) and without getting close enough to disrupt the orbits.
It is also observed that the more planets a system has, typically, the lesser the average eccentricity.
Trappist, for instance, has an average of 0.00629.
Atmospheric conditions influence it as the habitable zone is technically a myth, there is not one individual habitable zone, as it depends on the atmosphere of a body, as it comes down to the greenhouse effect. For instance, Earth would be -18 C if it lacked an atmosphere. And Venus is 464 C despite being much further from the sun than Mercury, which is 430 C, this is due to the fact that it has a very intense greenhouse effect.
Thus, planets with a more greenhouse effect heavy atmosphere would be able to hold on to more heat, and thus have higher temperatures at further distances from the sun. Which expands the theoretical habitable zone, but you have to be careful with changing this as it could easily make an atmosphere unbreathable to humans. But I thought I would mention the atmospheric greenhouse effect's importance in a planet being habitable.
Albedo is how much light and energy is reflected by a planet, and it is an important part of how much heat a planet retains from solar light. Higher albedo would make it reflect more and become colder, while lower would make it retain more and be hotter, this is why, for instance, black cars get hotter than white cars when left out in the sun. It is also one, of many, reasons why places with snow and ice tend to stay cold.
So, albedo can also work to expand and contract the habitable zone for a given planet.
So you can try to expand the amount by specifically tailoring the albedo and atmosphere to retain the proper amount of heat for liquid water to exist.
But yeah, the short answer is, we simply don't know, but Trappist has more than any we have observed. But they are likely uninhabitable due to tidal heating and their known lack of sufficent atmospheres for life or solar heat retention. But they are indeed in the habitable zone, for what it is worth.
I apologize if this doesn't help, there simply isn't an answer to your question. It would also essentially require a supercomputer and esoteric science programs to do countless calculations in order to get to a good estimation.