To a large pot, add 1 quart water (4 cups) and apple cider.
Squeeze juice from orange sections into pot. Cut each spent orange section in half and add to pot. Add remaining brine ingredients and stir. Heat brine to a simmer, stirring to dissolve salt and brown sugar.
Remove pot of brine from heat and cool to room temperature.
If using a plastic bag for brining, place bag in bucket with edges of bag folded over the outside of the bucket. Set aside.
To clean turkey: Remove neck and giblets from turkey cavities; reserve for use in the dressing or for making gravy, if desired. Remove any remaining pin feathers from turkey and rinse turkey well under cool, running water, being sure to thoroughly rinse the large cavity.
Place turkey in plastic bag or directly in bucket if not using plastic bag. Pour brine over turkey. Add remaining water (28 cups). Seal bag, expressing as much air as possible before sealing. If the turkey is not submerged, weight it with a plate and a heavy object of choice (clean brick or rock, plastic bag filled with ice, etc.)
Refrigerate for 8-24 hours, turning turkey once halfway through brining process. Alternately: If there isn’t enough room in the refrigerator, place the bagged turkey in an ice chest. Cover with ice, replacing ice as necessary to keep turkey at 40° F or below. If you are not using a brining bag, the turkey can be kept cold by placing well-secured plastic bags of ice on the turkey or in the brine. Change ice as needed to keep turkey at 40° F or below.