Exactly What IS a Natural Born Citizen?

Here are just a couple things on Obama's birth certificate:
On his birth certificate his name was Barrack Obama yet in his book he said that he changed his name to Barrack. So why do you think it would be on the birth certificate if he changed it. Either he was lying in his book or his birth certificate is a fake. 
 When people asked members of his family where he was born they all said Hawaii but they said different hospitals. Wouldn’t you think your family would know what hospital you were born at, even his parents said different hospitals.
Obama also spent 2.8 million dollars hiding the birth certificate from the public or in that fact anyone. If it was real why was he hiding it?
Also after a year of being president he only released a certification of live birth not a birth certificate  
 Before that he would just say Hawaii and nothing else.
And the document that the White House released is called a “Certification of Live Birth.” It does not bear a signature of authentication.

FACT: Obama's father never actually became a US citizen. He just came to the US as a student and then returned to Kenya. Thus meaning according to Article II Obama is not a "natural born" citizen.

FACT: Obama has NOT provided a certified copy of an original, typed, vault copy, long-form, birth certificate, signed by his mother and delivering doctor with the name of the hospital thereon, to be used to conclusively prove one of the two key elements used in determining his "natural born" citizenship status per the U.S. Constitution, i.e., where he was born. All he has provided to the public to see is a digital image on the internet of a purported copy of a short, summary, computer printed form called a Certification of Live Birth, aka COLB, which is not a Birth Certificate.

FACT: To serve as a U.S. Senator the person must be a U.S. Citizen.

For more facts check out this website:
http://www.obamacitizenshipfacts.org/
for a chart check this website: http://www.scribd.com/doc/11737124/Citizenship-Terms-Used-in-the-US-Constitution-The-5-Terms-Defined-Some-Legal-Reference-to-Same