Operation Downfall was the codename for the Allied (mostly American) invasion designed to force the Empire of Japan into capitulation. The usage of atomic weapons against the cities of Hiroshima and Nagasaki prevented the invasion from ever having to take place.
A lengthy discussion about the moral and ethical implications of dropping the A-bombs can be found at Why the United States of America used the bomb against the Empire of Japan.
Operation Downfall was to be a two-pronged amphibious assault. The first stage, Operation Olympic, was set to begin on November 1, 1945. After four days of what would have been the heaviest naval and aerial bombardment in the history of warfare, 14 combat divisions would come ashore the beaches of Kyushu.
Kyushu, Japan's southernmost island, was extremely heavily fortified. American commanders were anticipating casualties over a quarter million, and that was assuming victory. Olympic was meant to be an occupation and conquest mission, and was expected to take four months to complete. On Kyushu, Japanese defenders would outnumber American invaders by a margin of 3 to 2, sometimes more. Throughout the Pacific War, the Americans had almost always outnumbered the Japanese during battles. Downfall was to be very different. A reserve force was planned to land on November 4 at Kagoshima Bay had the initial assault not been slaughtered on the beaches.
The second stage of Downfall, Operation Coronet, was set to begin on March 1, 1946. Twice the size of Olympic, Coronet would involve 28 American divisions landing on the beaches of Honshu, just east of Tokyo. Millions of American soldiers and Marines were to come ashore facing the most horrific defense the Rising Sun had to offer. Casualties for Coronet were estimated to be well over 1 million for each side. The American objective would be the eventual conquest of Tokyo, thus forcing the Japanese hierarchy to agree to unconditional surrender.
American casualties for all of Downfall were conservatively estimated to be about 1.5 million (and again, that is assuming victory). Japanese casualties, even had they fended off the invasion, were expected to be even more, as American planes were to be firebombing Japanese population centers night and day. None of these numbers even bring into consideration the very probable Soviet invasion of Hokkaido, Japan's northernmost island. Over 4 million American troops were to be part of Downfall. The Japanese government had been stockpiling the best planes, the best troops, and had even been mobilizing the civilian population in preparation for an invasion.
The Japanese plan for homeland defense was called Ketsu-Go. The main objective of Ketsu-Go was to annihilate the American forces while they were still at sea. The principle aspect of this plan was to be the deployment of thousands of Kamikaze fighters, including up to 3,000 Kamikaze planes. The planes were to hit American transports in coordinated waves, while hundreds of suicide motorboats, suicide manned-torpedoes, and suicide submarines were to further disrupt (or destroy) the invading American fleets. The Japanese mindset was one that would simply not permit them to have their homeland be taken. "The sooner the Americans come, the better. One hundred million die proudly" was the slogan of Ketsu-Go.
All of the preceding information (along with a whole heck of a lot of specific numbers regarding troop numbers, ships, planes, casualty predictions, etc.) can be found at the National Archives (or their website). This information used to be Top Secret, but has since been declassified, and is open to everyone to learn about. Check `em out.
This node was not designed to convince you that dropping the atomic bombs was a good idea. (Because "good" is nothing more than a subjective concept. An ambitious Russian commander would have preferred the invasion. To him, Downfall was a "good idea"). It is, however, designed to let you know that an insanely bloody invasion of Japan is not some fairytale that proponents of the A-bomb have conjured up. Downfall would have been the bloodiest campaign in the history of human warfare, no matter which side won. There is no question that millions of lives would have been lost on each side, along with the total devastation of the Japanese infrastructure and culture due to constant American firebombing. There is also speculation that Hokkaido could have quickly become Soviet territory, furthering complicating the situation for the remainder of the century.
Personally, I do not think that this issue is as clear cut as "invasion? or atomic bombs?". In my opinion, with hundreds of thousands of American men being wiped out every week, and Communists pouring in from the north and claiming territory, my guess is that Truman would have eventually decided to pull back and use atomic bombs anyway. I believe this, because I am far from convinced that the invasion would have been successful. We're talking about Japanese beaches much more fanatically defended (use of Kamikazes) than Normandy. Something to think about.
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