Final answer:
The main concern leading to President Truman's authorization of the atomic bomb against Japan was to avoid the high casualties associated with an invasion of mainland Japan. Truman also considered several other factors such as the economic costs of the war and geopolitical concerns, before making his decision after the successful bomb test.
Step-by-step explanation:
One of the primary concerns that contributed to President Truman's decision to use atomic weapons against Japan was the number of casualties likely from an invasion of mainland Japan. The decision-making process was complex, influenced by various factors, including the desire to save American lives, the economic costs of continuing the war, and the geopolitical implications of Soviet influence post-war.
The Pacific War differed significantly from the war in Europe, as Japan controlled hundreds of islands that would need to be secured on the way to the Japanese mainland, entailing a protracted campaign with potentially high casualties. Ultimately, after a successful test of the bomb, Truman, considering all these factors and with the understanding that Japan might not surrender without a substantial show of force, authorized the use of the atomic bomb.