The company already manages a Boeing 757, a Boeing 767, and two Gulfstream V's. These four aircraft, plus the new fighter jet, all have landing rights at Moffett Field, which is a located near Google's main offices.
According to a Google spokesperson, the Alpha Jet is being outfitted with scientific instruments for NASA missions, including instruments that the other planes could not carry.
The Times says that Google CEO Eric Schmidt is "an avid pilot."
The Dornier Alpha Fighter Jet is made by Dornier in Germany and Dassault-Breguet of France.