Does the Captain of an airplane have the authority to marry people, while in flight?

Several years ago, i asked this question on Answerbag. no one really knew the answer. you are flying 35,000 feet above the United States in a commercial aircraft. you and your s/o want to be married, while onboard. does the airplane captain have authority to conduct a marriage, while the plane is in flight? if so, which state would be responsible for the marriage certificate?