Combine the water, cider, brown sugar, salt, peppercorns, bay leaves, garlic, orange strips, and rosemary leaves in a large pot. Stir until the salt and sugar dissolve. Bring to a boil, and then turn off the heat and cover. Allow to cool completely, and then place into the fridge to chill.
Place an uncooked, fresh turke in the chilled brine solution, and then refrigerate for 16 to 24 hours. (You may add more cold water if you need more liquid for the size of turkey you have.).
When you're ready to roast the turkey, remove the turkey from the brine. Submerge the turkey in a pot or sink of fresh, cold water. Allow to sit in the clean water for 15 to 20 minutes to remove excess salt from the outside. Discard the brine.
Remove the turkey from the water, and then rinse again, pat dry and cook according to your normal roasting method.
COOK'S NOTES: Only brine fresh turkeys. Brining a frozen turkey is never a good idea, because frozen turkeys are most typicaly injected with a sodium solution. There are some organic fresh turkeys that have a much lower concentration of the sodium solution. Generally speaking, though, you'll want to brine fresh, not frozen, turkeys.
Making gravy from the drippings of a brined turkey can result in a really salty gravy if you're not careful. Don't add salt to your gravy without tasting first; it may not need it.