Do you really think that if Japan had surrendered after Hiroshima that the USA would have dropped a second bomb? Nope.
As I said, MacArthur was the main reason were able to keep Russia out of Japan. He refused to allow it, unlike FDR and Churchill did in Europe.
“...unlike FDR and Churchill did in Europe”
Absolutely true. Whether you like MacArthur or no, he was significant in the shaping of post war Japan and much of the Far East.
On the other hand, FDR and Churchill were suckers for a Russian Commie Stalin screw the West. Truman may have tempered it a bit, but the damage was already done. Had they not killed General Patton, his solution was to rearm the Germans and march them east to annihilate the Russians.
To this day the world would have been different, maybe better.
Who writes the history? Open your mind, and realize there are numerous conflicting writings of history. And Truman did not order a second strike. There was an authorization to use the first bomb, and that also covered using additional bombs as they became available. The plutonium bomb became available three days after Hiroshima and was automatically deployed by the military without any additional authorization beyond Hiroshima by Truman.
Many historical texts also say if Nagasaki wasn't bombed, then a half a million U.S. soldiers would die invading Japan. Others say millions. The truth? U.S. military worst-case scenario is that less than 50,000 soldiers could die. So what is believed comes down to who writes (and embellishes) the historical narrative.
Here is a good read, discussing the controversy.
http://www.japanfocus.org/-Tsuyoshi-Hasegawa/2501
It looks at different viewpoints, whether Nagasaki or the Soviets or other factors got the Japanese to surrender. As I said, history is unclear on what determined the surrender, no matter what the historical texts say. That it is controversial is the one thing to be agreed on.
The Soviets waited precisely three months after Germany surrendered, per a Yalta agreement with Roosevelt, before declaring war on Japan and invading Manchuria and other Japanese holdings. This happened August 8-9, 1945, after Hiroshima but before Nagasaki. Japan had their worst military defeats, ever in their history, by the Soviets. Emperor Hirohito feared the Soviets more than the nuke bombings, as he feared the Soviets would turn the Japanese populace to communism and dethrone him. He cared more about his throne than the people.
One of the strange things about the relationship between the Soviets and the Japanese, is that the Soviets actually helped the Japanese and hindered American forces, in order to prolong the war until they could enter the war with Japan. (They had to wait three months after Germany’s surrender before attacking.) The Americans were rushing to drop the nukes, to forestall the Soviets from invading the Japanese homeland. The Soviets got as far as the 38th parallel in Korea when Japan surrendered, ending up with the Soviets and Americans dividing Korea.
Western narratives taught in our schools tend to neglect discussing the Soviet factor in ending the war with Japan.