"PHILADELPHIA, Oct 17-Arrived-Brigs...Marietta, Shackford, Eastport." (New-York daily tribune., October 18, 1850, Page 8, Image 8)
"PHILADELPHIA. Cleared-...Brig Marietta, Shackford, Neponset." (New-York daily tribune., December 16, 1850, Page 8, Image 8)
"BOSTON, Mar 19-Arr...;brigs Marietta, Shackford, Wilmington, NC" (New-York daily tribune. (New-York [N.Y.]) 1842-1866, March 12, 1851, Page 8, Image 8)
"EASTPORT. Nov...-Arr. 30th Brig Marietta, Shackford, Boston" (New-York daily tribune., December 08, 1851, Page 3, Image 3)
I did find more information about a Brig Marietta. While I'm not certain this is the same ship, a 150-ton Brig Marietta was built in 1802 in Marietta, Ohio (Marietta Register July 17, 1873), a brig Marietta had the telegraph register 16 46 in Boston harbor (Parker, John R, The new semaphoric signal book, Light and Stearns, 1836, p. 6). Also, a March 31, 1853 New York Times titled "Loss of the Brig Marietta" states that the Brig Marietta ship bilged while loaded with flour at Minot's Ledge, southeast of Boston on March 31, 1853. The captain is not mentioned. There is a Brig Marietta mentioned after this date but it appears to be a new brig built in Europe.
If you know if these comments reference the same Brig, which Shackford was the captain of this ship, or where else it went, or what it carried during these and other trips, I'd love to hear from you!
Also if you want to learn a bit more about life a sea in the 1800s I'd recomment the National Park Service document called "What is it like at sea?". While it's a lesson plan for school teachers, it includes a great description that describes life of a family sailing from Boston around Cape Horn, to San Francisco.