That's not true. US Code, title 8, sec. 1401(g):
a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than five years, at least two of which were after attaining the age of fourteen years....
The minimum age to satisfy this requirement would have been for his mother to be only 16 years old.
gekaap,
That's not quite correct. The law you site is the current status under 8 USC 1401. However that is not the law as it was in 1961, the law at that time was based on the Immigration and Naturalization Act of 1952. The corresponding section that was applicable at the time reads
(INA of 1952, Section 301, Page 236):
"(7) a person born outside the geographical limits of the United States and its outlying possessions of parents one of whom is an alien, and the other a citizen of the United States who, prior to the birth of such person, was physically present in the United States or its outlying possessions for a period or periods totaling not less than ten years, at least five of which were after attaining the age of fourteen years.... "
Using the law of the time, a married woman would have had to be at a minimum 19.
I say "married" for a reason.
The law at the time contained another interesting provision a few pages later in Section 309, which push-come-to-shove would have to be evaluated in a court. That section says that if a child is born to a woman out of wedlock, then the child acquires the nationality status of the mother. If the mother was a national (i.e. Legal Resident Alien) and not a citizen then the child is automatically a National. If the mother is a citizen, then the child has that same status and is therefore a citizen at birth.
Why might this be interesting, because Barack Obama Sr. had married Kezia Aoko prior to his departure for the United States. If he was marred prior to coming to the US, then his marriage to Stanley Dunham could be held void, in which case no matter where in the world Obama Jr. had been born he would have received citizenship status from his mother no matter what age she was.
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