What did Jesus know?

The Internet Monk wonders, what are the implications of Jesus being both fully God and fully man?

5. Did Jesus, in his incarnation, know things about biology, astronomy and cosmology that were completely ahead of his time? For instance, did Jesus know that the sun did not orbit the earth?

6. Did Jesus understand diseases and conditions from within the understanding of a first century man or did he know the actual medical/​biological nature of diseases and conditions that were commonly blamed on demons or God’s punishment?

7. Did Jesus know about viruses and contagious disease? Did he know the nature of mental illnesses like schizophrenia? Did he understand brain tumors, etc? If so, did he explain these things or did he respond to them within a first century understanding?

Not surprisingly, the discussion in the comments is quite interesting. Speaking personally, I know that I tend to say that Jesus was fully God and fully man and leave it at that, without really wrestling with or thinking about the real implications of such a concept. I fear it shows a real degree of arrogance on my part — after all, it took the early Church decades, if not centuries, to work through it all, and here I am, saying it with ​‘nary a second thought.