> it was uncertain if detonating the bomb would ignite the whole atmosphere and kill off all life on earth.
This was known before it was dropped on a city. The Trinity test happened about three weeks prior to dropping the first bomb on Japan. The second bomb was dropped with full knowledge of the potential casualties after the devastation of the first.
We Americans always justify these bombs, but really, there is no justification.
You presume that a beach landing was necessary. By this point in the war, the US had air superiority (the fire bombing of Tokyo...), and all sea lanes under control. The US had other options.
The best explanation for why the US wanted to have a swift end to the war with Japan was to deny the USSR the option of dividing Japan like was Germany.
There is no good way to justify killing civilians during the war, and it's impossible to say what would have happened if these bombs were not dropped and some other path was taken.
From a purely strategic perspective, the potential to avoid a costly land invasion must have seemed much more tangible than the at the time hypothetical and uncertain PR fallout (no pun intended) that would result from use of the new weapon.
Arguably keeping the USSR out of the islands may well have caused less misery over time for the Japanese people, from the purely utilitarian perspective of looking at how populations under Soviet rule fared.
This was known before it was dropped on a city. The Trinity test happened about three weeks prior to dropping the first bomb on Japan. The second bomb was dropped with full knowledge of the potential casualties after the devastation of the first.
We Americans always justify these bombs, but really, there is no justification.