A Goa'uldSystem Lord named Ba'al traveled back in time from the future to 1939 to stop the Achilles from ever reaching the United States. Ba'al and his Jaffa used the Stargate to get to Earth while the gate was being transported on the Achilles, so Ba'al and his Jaffa arrived on the ship. The Jaffa killed the crew and planted a bomb. Then Ba'al and his Jaffa used the Stargate to escape the pending explosion; however the Captain, with his dying breath, pushes the bomb overboard. The bomb explodes under water, but Ba'al does succeed in preventing the Stargate from reaching the United States because is drifts to the North Pole. This event is what created an Alternate Timeline.
The formation of the Stargate Program in the year 1997 AD never happens. In this timeline, since Michell's ancestor was killed, he was never born, this is an example of the Grand Father Paradox. Samantha Carter was a mission commander for NASA; during a mission on the the Intrepid she was killed saving the rest of the crew in 1994 AD. DoctorDaniel Jackson in this timeline is a disgrace, no one believes his theories about the Pyramids that were built in Egypt; Jackson always believed that the pyramids were built by Aliens, in the original timeline, Jackson is proven to be right because the Goa'uld once enslaved Earth and used the population to build the pyramids, which were used as landing platforms for their Pyramid Ships.
In 2008 AD. SG-1 witnesses changes in the timeline, so Mitchell, Carter, and Jackson flee to the Stargate to get back to Earth. Teal'c and Vala Mal Doran have gone missing. During transport though the gate, the timeline shifts, protecting the remainder of SG-1 from any changes in the timeline. SG-1 arrives on the Achilles, witch is now in the North Pole. Michell uses C-4 to blow a hole in the surrounding ice. SG-1 is able to escape, but the Achilles is dislodged from the ice and then sinks; The United States never recovered the Stargate, but Russia was able to retrieve it. SG-1 is rescued by Colonel Jack O'Neill; however, Jackson got frostbite, so he loses a leg. SG-1 are able to convince the United States Government that they are apart of an alternate timeline, but they will not allow them to correct it.
During on an attack on Earth from Ba'al and other System Lords, the President allows the remaining members of SG-1 to go use the Stargate for a mission; this Stargate was the other Stargate, witch was found in the original timeline in Antarctica. The mission was to retrieve a ZPM to get the Ancient Weapon in Antarctica working. SG-1 orders were not to change the timeline, so they were accompanied by an alternate SG-2, who were eventfully killed. At this point the only way to save Earth is to correct the timeline. Mitchell travels back in time to 1929 AD and then 10 years later, he is apart of the Achilles crew. Knowing that Ba'al could come though the gate at any time, he was able to succeed in correcting the timeline. The Achilles arrived in the United States safely. A photograph is taken with Mitchell and the Captain, which is later displayed in Michell's locker at Stargate Command in 2008.