I understand that we have some estimate of its size, mass, orbital period, and distance from its star. But what else could we learn, with existing technology (you can either consider cost or not)

• What sort of telescope would be required in order to resolve some visible details of a planet that size, over such an immense distance? (And what other interesting things could we do with such a telescope?)
• Is there any information we can glean based on possible transits of the planet across Proxima Centauri? (ie composition, atmosphere, etc)
• Is there something else we could do that I have not thought of yet?
• Similar question with answer that largely answers this question: space.stackexchange.com/questions/15215/… – Lord Bubbacub Aug 25 '16 at 11:39
• Some rudimentary math tells me that at 1.1 times the diameter of earth, Proxima b would be approximately .000072 arcseconds in diameter. I see a formula online for converting angular diameter to aperature size, but I don't really know how to convert that to a mirror size. But suffice it to say, we have a long way to go before we have a telescope that good. Maybe in time, somebody will build such a telescope on the far side of the moon. – orulz Aug 25 '16 at 22:19