When did Christopher Columbus realize he was in a New World rather than the Far East?

[md2000]

This from the NASA website - https://www-spof.gsfc.nasa.gov/stargaze/Scolumb.htm

The idea of sailing westward to India dates back to the early Romans. According to Dr. Irene Fischer, who studied this subject, the Roman writer Strabo, not long after Erathosthenes and Posidonius, reported their results and noted:

"if of the more recent measurements of the Earth, the one which makes the Earth smallest in circumference be introduced–I mean that of Posidonius who estimates its circumference at about 180,000 stadia, then. . . "

and he continues:

"Posidonius suspects that the length of the inhabited world, about 70,000 stadia, is half the entire circle on which it had been taken, so that if you sail from the west in a straight course, you will reach India within 70,000 stadia. "

Notice that Strabo--for unclear reasons--reduced the 250,000 Stadia of Eratosthenes to 180,000, and then stated that half of that distance came to just 70,000 stadia. Handling his numbers in that loose fashion, he could argue that India was not far to the west. 

All these results were known to the panel of experts which King Ferdinand appointed to examine the proposal made by Columbus. They turned Columbus down, because using the original value by Eratosthenes, they calculated how far India was to the west of Spain, and concluded that the distance was far too great. 

  Columbus had an estimate of his own. Some historians have proposed that he used an argument like Strabo's, but Dr. Fischer found his claim to be based on incorrect units of distance. Columbus used an erroneous estimate by Ptolemy (whom we meet again), who based it on a later definition of the stadium, and in estimating the size of the settled world he confused the Arab mile, used by El Ma'mun, with the Roman mile on which our own mile is based. All the same, his final estimate of the distance to India was close to Strabo's.  

[Andy_L]

@md2000

This from the NASA website - https://www-spof.gsfc.nasa.gov/stargaze/Scolumb.htm

And from post 11!