While reading a book, I saw a phrase which distraced me. ("***upon/on entering the door***") And I searched the internet for more information on this usage "upon/on doing". Then I found a very competent comment here

As far as I understand, "upon/on doing" make a connection to the main clause but the temporal relationship is not obvious. It could refer to a time before the main clause or after the main clause or even simultaneous with the main clause . What I want to ask you is that:

***What is the different between "on doing"" and "in doing" if both "on doing" and "in doing" refers to some point in the process of doing something?*** ***Can I rewrite the sentence as I have done in the sentence below?***


> 1- ***Upon/on entering*** the castle, he is led to a banquet hall
> where he meets the Fisher King and sits down with him for a feast.
> 
> 1a- ***In entering*** the castle, he is led to a banquet hall where he
> meets the Fisher King and sits down with him for a feast.
> 
> 2- ***Upon/on purchasing*** the phone, I was assured that this was the
> latest and the best model available there.
> 
> 2a- ***In purchasing*** the phone, I was assured that this was the
> latest and the best model available there.
> 
> or vice versa:
> 
> 3- ***In running*** out the door, I slipped on the ice outside.
> 
> 3a- ***Upon/on running*** out the door, I slipped on the ice outside.
> 
> 4- ***In studying*** with her, I realized she was deeply interested in
> programming.
> 
> 4a- ***Upon/on studying*** with her, I realized she was deeply
> interested in programming.