I'm not sure you realize it but some of your figures/formulae are
unnecessary.

More simply Battery 110 AH (/2) Load = .5 A 55/.5 = 110 hrs

Typically batteries are charged at .10 of their 1 hr rate (when fully
discharged) but the type of battery (Gel-Cell, NiCad, NiMH, etc.), must
be considered. Also, while .1C might be good for a discharged battery,
the charge should diminish as the battery becomes fully charged (or some
other mechanism, temperature rise, e.g.), must shut down the charger.)

See the battery mfr. for recommended charge rate and charger technology.
Also, consider how fast a recharge you want. A 4 ampere charger will
recharge the battery (but slowly) as will a 100 Amp charger

Bryan Martin wrote:
The unit I will be using is 12V 0.5A

12V X 0.5A = 6 Watts
6W x 24hours = 144 Watts per day
144W / 12V = 12 amp hours

Now given a battery with 110 amp hours
(http://www.defender.com/product.jsp?path=-1|328|51495|306219&id=51496)

We should only draw the battery down 50% so we will actually only get

110 / 2 = 55 amp hours

12 amp hours needed / 55 amp hours available = 4.58 days
so with this battery we have enough juice to potentially run our unit for
4.58 days w/out charging.

Now if the above is not correct then please explain. And the next question
is how would I now figure out approx how large of a panel I would need to
keep the battery charged. I am really looking for the formula and a
understanding of how you got from A to B as oppose to "this panel should
work".