The carrying capacity of the 747 was known, the weight of the Shuttle was known. The aerodynamic drag of each was also already known, as was the lift of each. Thus, it’s pretty easy to calculate whether it could potentially carry it. After that it’s just engineering to make it work.
As it is, they had to be modified. You have the butt cone on the Shuttle to decrease drag and the extra vertical stabilizers on the 747 because obviously that big thing sitting on top is going to interfere with the airflow over the main vertical stabilizer.
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