moon's motion?

Question

I need help I am doing something wrong here

question:
the moon orbits the earth at a distance of 3.85 X10^8m. assume that this distance is between the centers of the earth and the moon and that the mass of the earth is 5.98 X 10^24 kg.
find the period (in days) for the moon's motion around the earth?
I have:::::
time period of satelite T = 2n squared {(R+h) squared + Gm)
mass of earth m = 5.98 *10^ 24 kg
distance of the moon's orbit = h=3.85 * 10 ^ 8 m
radius of the earth = R = 6.37 * 10 ^ 6 m
gravitational constant = G = 6.67 * 10 ^ -11 N.m ^ 2 / kg squared
by subtracting all the values
T = 2 n squared {(6.67 * 10 ^ 6m + 3.35 * 10 ^ 8 m) ^ 2 / 6.67 * 10 ^ -11 N.m ^ 21 kg ^ 2)(5.98 * 10 ^ 24 kg)} =
12306.5s = (12306.5 / 86400) day = 0.142 days
but....
this is not one of the answers
the answers are:::::
a. 26.9 days
b. 28.1 days
c. 29.2 days
d. 27.5 days
e. 28.7 days
so!!!!!!! what am I doing wrong!!!!!!!
please help I don't understand

Answer 1

I would check your formula to make sure it is correct. I am not certain offhand what the formula is for period of a satellite. I would also check all your constants to ensure that you have the right units and orders of magnitude.

Answer 2

your formula for the time period of the satellite seems to be wrong. confirm it first. and then check your answer again.