Gulfstream Private Jet with Mounted Weapons and Missile Pylons

It's a flying test aircraft for MIT. Those aren't "missiles" they're some sort of test equipment. They also have a 707, Falcon 20, and a Twin Otter. Great fodder for conspiracy theorists, but nothing terribly interesting.

http://registry.faa.gov/aircraftinquiry/NNum_Results.aspx?NNumbertxt=105tb

It belongs to the USAF Material Command.

It says what the purpose of the pylons in the description of the video u linked too.

While also a test bed, it is not uncommon for A/C of this type to be used for Navy target and tracking runs. I've "locked up" a few in my time.