I get it that a baby will be a us citizen if born anywhere to a us citizen mother, but cannot be eligible to be president unless born in a us state or territory under us control such as was the panama canal zone.

Let's take it a step further-what if the baby was born to us citizens while on a US AFB such as Ramstein in germany or Incirlik in turkey? Can that baby be president?

Yes.

From usconstitution.net --

Currently, Title 8 of the U.S. Code fills in those gaps. Section 1401 defines the following as people who are "citizens of the United States at birth:"

* Anyone born inside the United States *
* Any Indian or Eskimo born in the United States, provided being a citizen of the U.S. does not impair the person's status as a citizen of the tribe
* Any one born outside the United States, both of whose parents are citizens of the U.S., as long as one parent has lived in the U.S.
* Any one born outside the United States, if one parent is a citizen and lived in the U.S. for at least one year and the other parent is a U.S. national
* Any one born in a U.S. possession, if one parent is a citizen and lived in the U.S. for at least one year
* Any one found in the U.S. under the age of five, whose parentage cannot be determined, as long as proof of non-citizenship is not provided by age 21
* Any one born outside the United States, if one parent is an alien and as long as the other parent is a citizen of the U.S. who lived in the U.S. for at least five years (with military and diplomatic service included in this time)
* A final, historical condition: a person born before 5/24/1934 of an alien father and a U.S. citizen mother who has lived in the U.S.

* There is an exception in the law — the person must be "subject to the jurisdiction" of the United States. This would exempt the child of a diplomat, for example, from this provision.

Anyone falling into these categories is considered natural-born, and is eligible to run for President or Vice President. These provisions allow the children of military families to be considered natural-born, for example.