World War II invasion of America:

Many people go on about the RAF being on its knees but forget that the Luftwaffe was spent. It had lost a huge amount of trained and experienced aircrew, planes were suffering from reliability problems along with lack of spares, crew morale was low.

The RAF had four air groups defending the UK only one of which was fully engaged, the other three rotated Squadrons with 11 Group (which defended the South East). RAF fighter strength was greater at the end of the BoB than when it started as was bomber and coastal command (luftwaffe strength was roughly what it was at the start but a higher percentage was unservicable). The Empire Air training Schools were providing increasing numbers of pilots so aircrew strength was also starting to increase.

At the very worst case scenario 11 group could have been pulled back to beyond German fighter range and still be able to hit the bombers.

Never mind the simple fact that the Kreigsmarine could not do its required job and they had no real way of transporting the troops across the Channel.

It was easier for the other services to blame the Luftwaffe than to admit none of them could actually fullfill their obligations for Sealion.

Even prior to the battle, the Luftwaffe had been engaged near continuously for the better part of a year. The Luftwaffe had also suffered real, serious losses in both Poland and France despite the near shocking speed and totality of the German victories, which sort of masked their losses. The aircrews were exhausted. The Luftwaffe was never equipped nor designed to sustain a major strategic campaign based on limitations in German industry…

The Junkers 52 fleet was very heavily hit by losses in the Netherlands (never mind the losses in other areas) which took over a year to make up the losses from. Hard to do an opposed para landing across the Channel when your transport aircraft fleet has had large losses and proved how vulnerable they are to AA fire (the Dutch had few aircraft to oppose them).

The bigger question remains why Japan attacked the US in the first place. It was an act of national suicide, which, considering the culture of death in Japan at the time, seems consistent with its culture. As to invasions of Australia and America, both were palpably un-realizable. It raises questions about the Japanese leaderships grasp on reality.
That is the bigger question.

  My feeling is that they believed that America was eventually destined to attack them, particularly given the FDR administration's behavior, which included such things as freezing all Japanese assets under US control, successfully cutting them from at least one of their oil suppliers, constructing a naval juggernaut whose only possible purpose was ostensibly to fight the Japanese in the pacific, actively supporting both Chiang and the Reds in China against Japan, along with American mercinaries already dogfighting them in that theater, they (quite reasonably) believed that 1) war with the US was inevitable  2) With each passing day, they knew that they grew weaker and America grew stronger

Oh dear Vonss. Please get a grip.