In the second loop involving Special Operations Command, the next few sorties are to commit the search for the Orion-class MTD Auriga, which is the current head ship controlling the Morgan Technologies assets that have wreaked havoc and started pirate attacks across GTVA space.
Since GTVI has no leads on where to find the Auriga, some clue about their existence has to be in someone's hands...
This mission is only just Alpha 1 (the player) and two fighters from Beta, flying Perseus fighters by default (you also have the Myrmidon and Hercules Mark Two available).
Your job is to find a ship that holds personnel from Morgan Technologies, and disable it.
After a few minutes of searching, you see an Argo in an asteroid belt. Disable it. Wayfarer Station will be infuriated, but don't let that bother you. Beta 1 will transmit you're GTVI and will hold off.
A friendly ship will help tow the Argo, and you will be assaulted by some Hercules fighters, Ulysses, Perseus, and the like. Wayfarer Station's SecFor Wing (consisting of Ulysses fighters) will assist you in taking out the fighters...
... and some enemy Vasudan fighters come in. What the hell? Kill them anyway, and make sure the disabled Argo is towed out into subspace. Primary objective accomplished.
You will get clearance to return to base, but help SecFor wing destroy all other enemy fighters and your secondary objective will be done.